Fragility of evidence for anti-fracture efficacy: A systematic review

Data management

Libraries needed:

library(tidyverse)

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library(dplyr)
library(fragility)

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library(expss)

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library(ggplot2)
library(gridExtra)

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library(grid)
library(table1)

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library(compareGroups)

Set-up data:

fi = read.csv("C:\\Thach\\Research projects\\Nick's projects\\FI for fracture efficacy\\Analysis\\fi_analysis.csv")
head(fi)

##    id study_ext            author year journal       country blinding
## 1 a_1        5b Leder_ACTIVExtend 2020    JCEM International   Double
## 2 a_2         1           Kendler 2018  Lancet International   Double
## 3 a_3         1           Kendler 2018  Lancet International   Double
## 4 a_4         1           Kendler 2018  Lancet International   Double
## 5 a_5         1           Kendler 2018  Lancet International   Double
## 6 a_6         1           Kendler 2018  Lancet International   Double
##    intervention     control women_per timing fi        fq      pval
## 1 Abaloparatide Alendronate         1      4  4 0.0035971 0.0092162
## 2  Teriparatide Risedronate         1      4 15 0.0142993 0.0002691
## 3  Teriparatide Risedronate         1      4 17 0.0162059 0.0002114
## 4  Teriparatide Risedronate         1      4 12 0.0088235 0.0010345
## 5  Teriparatide Risedronate         1      4  2 0.0019066 0.0208278
## 6  Teriparatide Risedronate         1      2  3 0.0025884 0.0229448
##           fx_site outcome e_con n_rand_con e_intv n_rand_intv      x95_ci
## 1        Vert_24m       1    16        581      3         558  0.10, 0.87
## 2        Vert_24m       1    64        680     28         680 [0.29,0.68]
## 3 NworsenVert_24m       1    69        680     31         680 [0.31,0.68]
## 4      ClinFx_24m       2    61        680     30         680 [0.32,0.74]
## 5       MVert_24m       1    12        680      2         680  0.04, 0.74
## 6        Vert_12m       1    18        680     35         680  [0.3,0.91]
##   p_value pri_endpoint sen_analysis extended                           notes
## 1  0.0270            0            1        1      post-hoc analysis/extended
## 2  0.0001            1            0        0 6 pt excluded from the analyses
## 3  0.0001            0            0        0                                
## 4  0.0009            0            0        0                                
## 5  0.0070            0            0        0                                
## 6  0.0190            0            0        0                                
##                                             st_cohort rep_loss rep_withdr
## 1                   postm osteoporotic women aged 49+        9         62
## 2 postm women aged 45+: <=-1.5, 2+ mod/1+ sev vert fx       12        185
## 3 postm women aged 45+: <=-1.5, 2+ mod/1+ sev vert fx       12        185
## 4 postm women aged 45+: <=-1.5, 2+ mod/1+ sev vert fx       12        185
## 5 postm women aged 45+: <=-1.5, 2+ mod/1+ sev vert fx       12        185
## 6 postm women aged 45+: <=-1.5, 2+ mod/1+ sev vert fx       12        185
##   rep_death rep_compt n_control n_interven
## 1        68      1861       568        544
## 2        20      1013       533        516
## 3        20      1013       533        516
## 4        20      1013       563        538
## 5        20      1013       533        516
## 6        20      1013       574        585

fi$no_rand = fi$n_rand_con + fi$n_rand_intv
fi$active_sample = fi$n_control + fi$n_interven
fi$n_event = fi$e_con + fi$e_intv

Data management:

Fracture sites:

table(fi$fx_site)

## 
##                      ClinFx_12m                      ClinFx_18m 
##                               2                               1 
##                      ClinFx_24m                      ClinFx_36m 
##                               3                               2 
##                      ClinFx_72m                      ClinFx_72w 
##                               1                               2 
##                    ClinVert_12m                    ClinVert_24m 
##                               1                               1 
##                    ClinVert_36m                    ClinVert_48m 
##                               6                               1 
##                    ClinVert_72m                    ClinVert_72w 
##                               1                               2 
##                     Forearm_60m                ForearmWrist_72m 
##                               1                               1 
##                          Fx_36m                          Fx_70m 
##                               2                               1 
##                         Hip_18m                         Hip_24m 
##                               3                               1 
##                         Hip_36m                         Hip_60m 
##                               5                               1 
##           Hip_Wrist_Forearm_70m Hip_Wrist_Forearm_Vertebrae_70m 
##                               1                               1 
##                MajorNonVert_12m                MajorNonVert_24m 
##                               1                               2 
##                MajorNonVert_36m                MajorNonVert_60m 
##                               1                               1 
##                     MajVert_24m                MNworsenVert_12m 
##                               2                               1 
##                MNworsenVert_24m                         MOF_12m 
##                               1                               1 
##                         MOF_18m                         MOF_24m 
##                               1                               2 
##                     MultiFx_36m                   MultiVert_24m 
##                               1                               2 
##                   MultiVert_36m                       MVert_24m 
##                               1                               1 
##                       MVert_36m                    NmodVert_12m 
##                               2                               1 
##                    NmodVert_24m                     Nonvert_18m 
##                               1                               3 
##                     NonVert_18m                     NonVert_24m 
##                               1                               4 
##                     NonVert_36m                     NonVert_60m 
##                               6                               1 
##                     NonVert_72m                  NonVertOFx_24m 
##                               1                               2 
##                 NworsenVert_12m                 NworsenVert_24m 
##                               2                               4 
##                         OFx_12m                         OFx_24m 
##                               1                               1 
##                         Ofx_48m                         OFx_72m 
##                               1                               1 
##                 OtherClinFx_48m                        Vert_12m 
##                               1                              10 
##                        Vert_18m                        Vert_24m 
##                               3                              13 
##                        Vert_36m                        Vert_48m 
##                              10                               3 
##                        Vert_48w                        Vert_60m 
##                               1                               2 
##                         Vert_6m                        Vert_72m 
##                               1                               1 
##                        Vert_72w 
##                               2

fi_final = fi %>% 
  mutate(fx_code1 = case_when(fx_site == "Fx_36m" | fx_site == "Fx_70m" | fx_site == "Fx_72m" | fx_site == "MultiFx_36m" ~ 1,
                             fx_site == "ClinFx_12m" | fx_site == "ClinFx_18m" | fx_site == "ClinFx_24m" | 
                               fx_site == "ClinFx_36m" | fx_site == "ClinFx_72m" | fx_site == "ClinFx_72w" | 
                               fx_site == "OtherClinFx_48m" ~ 2,
                             fx_site == "OFx_12m" | fx_site == "OFx_24m" | fx_site == "Ofx_48m" | fx_site == "OFx_72m" ~ 3,
                             fx_site == "MOF_12m" | fx_site == "MOF_18m" | fx_site == "MOF_24m"  ~ 4,
                             fx_site == "Hip_Wrist_Forearm_70m" | fx_site == "Hip_Wrist_Forearm_Vertebrae_70m" ~ 5,
                             fx_site == "MajorNonVert_12m" | fx_site == "MajorNonVert_24m" | fx_site == "MajorNonVert_36m" | 
                               fx_site == "MajorNonVert_60m"   | fx_site == "Nonvert_18m"  | fx_site == "NonVert_18m"  | 
                               fx_site == "NonVert_24m" | fx_site == "NonVert_36m" | fx_site == "NonVert_60m" | 
                               fx_site == "NonVert_72m" | fx_site == "NonVertOFx_24m" ~ 6,
                             fx_site == "MajVert_24m" | fx_site == "MNworsenVert_12m" | fx_site == "MNworsenVert_24m" | 
                               fx_site == "MultiVert_24m" | fx_site == "MultiVert_36m" | fx_site == "MVert_24m" | 
                               fx_site == "MVert_36m" | fx_site == "NmodVert_12m" | fx_site == "NmodVert_24m" | 
                               fx_site == "NworsenVert_12m" | fx_site == "NworsenVert_24m"  | fx_site == "Vert_12m" | 
                               fx_site == "Vert_18m"  | fx_site == "Vert_24m" | fx_site == "Vert_36m" | 
                               fx_site == "Vert_48m" | fx_site == "Vert_48w" | fx_site == "Vert_60m" | fx_site == "Vert_6m" | 
                               fx_site == "Vert_72m" | fx_site == "Vert_72w" ~ 7, 
                            fx_site == "ClinVert_12m" | fx_site == "ClinVert_24m" | fx_site == "ClinVert_36m" | 
                              fx_site == "ClinVert_48m" | fx_site == "ClinVert_72m" | fx_site == "ClinVert_72w"   ~ 8,
                            fx_site == "Hip_18m" | fx_site == "Hip_24m" | fx_site == "Hip_36m" | fx_site == "Hip_60m" ~ 9,
                            fx_site == "Forearm_60m" | fx_site == "ForearmWrist_72m" ~ 10))
var_lab(fi_final$fx_code1) = "Fracture sites"
val_lab(fi_final$fx_code1) = num_lab("
                                    1 Any_fx
                                    2 Clin_fx
                                    3 OFx
                                    4 MOF
                                    5 Dif_comb
                                    6 NonVert_fx
                                    7 Vert_fx
                                    8 ClinVert_fx
                                    9 Hip
                                    10 Forearm")
table(fi_final$fx_code1)

## 
##      Any_fx     Clin_fx         OFx         MOF    Dif_comb  NonVert_fx 
##           4          12           4           4           2          23 
##     Vert_fx ClinVert_fx         Hip     Forearm 
##          64          12          10           2

fi_final = fi_final %>% 
  mutate(fx_code2 = case_when(fx_code1 == "1" | fx_code1 == "2" ~ 1,
                              fx_code1 == "3" | fx_code1 == "4" | fx_code1 == "5" ~ 2,
                              fx_code1 == "6" ~ 3,
                              fx_code1 == "7" ~ 4,
                              fx_code1 == "8" ~ 5,
                              fx_code1 == "9" ~ 6,
                              fx_code1 == "10" ~ 7))
var_lab(fi_final$fx_code2) = "Fracture sites"
val_lab(fi_final$fx_code2) = num_lab("
                                    1 Any
                                    2 Osteoporotic 
                                    3 Non-Vertebrae
                                    4 Vertebrae
                                    5 Clinical Vertebrae
                                    6 Hip
                                    7 Forearm")
table(fi_final$fx_code2)

## 
##                Any       Osteoporotic      Non-Vertebrae          Vertebrae 
##                 16                 10                 23                 64 
## Clinical Vertebrae                Hip            Forearm 
##                 12                 10                  2

Interventions:

table(fi$intervention)

## 
##            Abaloparatide              Alendronate                  Calcium 
##                        5                        2                        3 
##          Calcium + vit D                Denosumab        Ibandronate daily 
##                       11                        9                        4 
## Ibandronate intermittent              Minodronate             Risendronate 
##                        2                        4                        5 
##              Romosozumab       Strontium Ranelate             Teriparatide 
##                       28                       17                       13 
##          Teriparatide_20          Teriparatide_40                    Vit D 
##                        5                        5                        3 
##              Zoledronate 
##                       21

fi_final = fi_final %>%
  mutate(interv_code1 = case_when(intervention == "Alendronate"  ~ 1.1,
                                 intervention == "Ibandronate daily" | intervention == "Ibandronate intermittent" ~ 1.2, 
                                 intervention == "Risendronate" ~ 1.3, 
                                 intervention == "Minodronate" ~ 1.4, 
                                 intervention == "Zoledronate" ~ 1.5, 
                                 intervention == "Teriparatide" | intervention == "Teriparatide_20" | 
                                   intervention == "Teriparatide_40" ~ 2.1, 
                                 intervention == "Abaloparatide" ~ 2.2, 
                                 intervention == "Romosozumab" ~ 3, 
                                 intervention == "Denosumab" ~ 4, 
                                 intervention == "Strontium Ranelate" ~ 5,
                                 intervention == "Calcium" | intervention == "Calcium + vit D" | intervention == "Vit D" ~ 6))
var_lab(fi_final$interv_code1) = "Interventions"
val_lab(fi_final$interv_code1) = num_lab("
                                    1.1 Alendronate
                                    1.2 Ibandronate
                                    1.3 Risedronate
                                    1.4 Minodronate
                                    1.5 Zoledronate
                                    2.1 Teriparatide
                                    2.2 Abaloparatide
                                    3 Romosozumab
                                    4 Denosumab
                                    5 Strontium_ranelate
                                    6 Calcium_VitD")
table(fi_final$interv_code1)

## 
##        Alendronate        Ibandronate        Risedronate        Minodronate 
##                  2                  6                  5                  4 
##        Zoledronate       Teriparatide      Abaloparatide        Romosozumab 
##                 21                 23                  5                 28 
##          Denosumab Strontium_ranelate       Calcium_VitD 
##                  9                 17                 17

fi_final = fi_final %>%
  mutate(interv_code2 = case_when(intervention == "Alendronate" | intervention == "Ibandronate daily" | 
                                    intervention == "Ibandronate intermittent" | intervention == "Risendronate" | 
                                    intervention == "Minodronate" | intervention == "Zoledronate" ~ 1, 
                                 intervention == "Teriparatide" | intervention == "Teriparatide_20" | 
                                   intervention == "Teriparatide_40" | intervention == "Abaloparatide" ~ 2, 
                                 intervention == "Romosozumab" ~ 3, 
                                 intervention == "Denosumab" ~ 4, 
                                 intervention == "Strontium Ranelate" ~ 5,
                                 intervention == "Calcium" | intervention == "Calcium + vit D" | intervention == "Vit D" ~ 6))
var_lab(fi_final$interv_code2) = "Interventions"
val_lab(fi_final$interv_code2) = num_lab("
                                    1 Bisphosphonates
                                    2 PTH analog
                                    3 Romosozumab
                                    4 Denosumab
                                    5 Strontium_ranelate
                                    6 Calcium_VitD")
table(fi_final$interv_code2)

## 
##    Bisphosphonates         PTH analog        Romosozumab          Denosumab 
##                 38                 28                 28                  9 
## Strontium_ranelate       Calcium_VitD 
##                 17                 17

Journals:

table(fi$journal)

## 
## Am J Clin Nutr      Arth Rheu            BMJ           JAMA           JBMR 
##              1              4              7             11              6 
##           JCEM           JECM         Lancet           NEJM             OI 
##              8              5              5             81              9

fi_final = fi_final %>%
  mutate(journal_code1 = case_when(journal == "NEJM" ~ 1,
                                   journal == "Lancet" ~ 2,
                                   journal == "BMJ" ~ 3,
                                   journal == "JAMA" ~ 4, 
                                   journal == "JBMR" ~ 5, 
                                   journal == "JCEM" | journal == "JECM" ~ 6, 
                                   journal == "OI" ~ 7,
                                   journal == "Am J Clin Nutr" | journal == "Arth Rheu" ~ 8))
var_lab(fi_final$journal_code1) = "Journal"
val_lab(fi_final$journal_code1) = num_lab("
                                    1 NEJM
                                    2 Lancet
                                    3 BMJ
                                    4 JAMA
                                    5 JBMR
                                    6 JCEM
                                    7 OI
                                    8 Other")
table(fi_final$journal_code1)

## 
##   NEJM Lancet    BMJ   JAMA   JBMR   JCEM     OI  Other 
##     81      5      7     11      6     13      9      5

fi_final = fi_final %>%
  mutate(journal_code2 = case_when(journal == "NEJM" ~ 1,
                                   journal == "Lancet" ~ 2,
                                   journal == "BMJ" ~ 3,
                                   journal == "JAMA" ~ 4, 
                                   journal == "JBMR" ~ 5, 
                                   journal == "JCEM" | journal == "JECM" ~ 6, 
                                   journal == "OI" | journal == "Am J Clin Nutr" | journal == "Arth Rheu" ~ 7))
var_lab(fi_final$journal_code2) = "Journal"
val_lab(fi_final$journal_code2) = num_lab("
                                    1 NEJM
                                    2 Lancet
                                    3 BMJ
                                    4 JAMA
                                    5 JBMR
                                    6 JCEM
                                    7 Other")
table(fi_final$journal_code2)

## 
##   NEJM Lancet    BMJ   JAMA   JBMR   JCEM  Other 
##     81      5      7     11      6     13     14

Others:

var_lab(fi_final$outcome) = "Types of fracture outcome"
val_lab(fi_final$outcome) = num_lab("
                                    1 Binary
                                    2 Time-to-event")

var_lab(fi_final$timing) = "Timing of outcome assessed"
val_lab(fi_final$outcome) = num_lab("
                                    1 0-6m
                                    2 >6-12m
                                    3 >12-18m
                                    4 >18-24m
                                    5 >24-36m
                                    6 >36-48m
                                    7 >48-60m
                                    8 >60-72m
                                    9 >72m")

fi_final = fi_final %>%
  mutate(sex = case_when(women_per == 0 ~ "Men",
                         women_per == 1 ~ "Women",
                         women_per > 0 & women_per < 1 ~ "Both"))
var_lab(fi_final$sex) = "Sex"
table(fi_final$sex)

## 
##  Both   Men Women 
##    15    10   112

fi_final = fi_final %>%
  mutate(placebo = case_when(control == "Placebo" ~ "Placebo",
                             control == "Alendronate" | control == "Risedronate" ~ "Active"))
var_lab(fi_final$placebo) = "Placebo"
table(fi_final$placebo)

## 
##  Active Placebo 
##      27     110

Calculate Fragility index (FI)

All documented analyses (some with significant results from Cox PH might turn out to be statistically non-significant using logistic regression) n= 8 analyses with P>0.05 from logistic regression will be excluded (NO studies are excluded)

fi_screen = frag.studies(e_con, n_control, e_intv, n_interven, data = fi_final, methods = "RR")
fi_screen

## The input dataset contains 137 studies
## Significance level = 0.05
## Null hypothesis: RR = 1
## p-value (two-sided) is based on:
##   relative risk  
## 
## Fragility index (FI) and fragility quotient (FQ):
## Based on relative risk,
##   129 studies yield significance with
##     median FI = 9, range 1-171, IQR 4-22 and
##     median FQ = 0.5%, range 0.0%-9.7%, IQR 0.2%-0.9%;
##   8 studies yield non-significance with
##     median FI = 1, range 1-16, IQR 1-4 and
##     median FQ = 0.1%, range 0.0%-1.4%, IQR 0.0%-0.9%;
##   overall, among all studies,
##     median FI = 8, range 1-171, IQR 4-20 and
##     median FQ = 0.5%, range 0.0%-9.7%, IQR 0.2%-0.9%

fi_final$Pval_screen = fi_screen$pval

Only analyses with statistical significant results from logistic regression (binary outcome) will be analysed

fi_sig = subset(fi_final, Pval_screen<= 0.05)
fi_only_sig = frag.studies(e_con, n_control, e_intv, n_interven, data = fi_sig, methods = "RR")
fi_only_sig

## The input dataset contains 129 studies
## Significance level = 0.05
## Null hypothesis: RR = 1
## p-value (two-sided) is based on:
##   relative risk  
## 
## Fragility index (FI) and fragility quotient (FQ):
## Based on relative risk,
##   129 studies yield significance with
##     median FI = 9, range 1-171, IQR 4-22 and
##     median FQ = 0.5%, range 0.0%-9.7%, IQR 0.2%-0.9%;
##   0 study yields non-significance
##   overall, among all studies,
##     median FI = 9, range 1-171, IQR 4-22 and
##     median FQ = 0.5%, range 0.0%-9.7%, IQR 0.2%-0.9%

plot(fi_only_sig, bar = FALSE, freq = FALSE)

fi_sig$FI_final = fi_only_sig$FI
fi_sig$FQ_final = fi_only_sig$FQ
fi_sig$Pval_final = fi_only_sig$pval

(1) All analyses with statistically significant results from logistic regression

n= 129 analyses from all 23 studies (+ 6 extended studies)

(1.1) Overall

(1.1.1) Overall

fi_sig$missing_fi[fi_sig$rep_loss > fi_sig$FI_final] = 1
fi_sig$missing_fi[fi_sig$rep_loss <= fi_sig$FI_final] = 0
is.na(fi_sig$rep_loss)

##   [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [49] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
##  [61]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE
##  [73] FALSE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85] FALSE  TRUE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
##  [97]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
## [109]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
## [121]  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE

fi_sig$missing_fi[fi_sig$rep_loss == NA] = NA

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Overall (N=129)
no_rand
Mean (SD)	3090 (2360)
Median [Q1, Q3]	1960 [1360, 4090]
Median [min, max]	1960 [450, 7870]
active_sample
Mean (SD)	2700 (2140)
Median [Q1, Q3]	1860 [1130, 3700]
Median [min, max]	1860 [339, 7810]
n_event
Mean (SD)	174 (176)
Median [Q1, Q3]	101 [51.0, 246]
Median [min, max]	101 [10.0, 764]
FI_final
Mean (SD)	17.5 (24.8)
Median [Q1, Q3]	9.00 [4.00, 22.0]
Median [min, max]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00815 (0.0111)
Median [Q1, Q3]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	10 (7.8%)
1	73 (56.6%)
Missing	46 (35.7%)

Relationship between sample size/active sample/no. events and FI

p = ggplot(data = fi_sig, aes(x = no_rand, y = FI_final))
p1 = p + geom_point() + geom_smooth() + labs(x = "Number of participants at randomisation", y = "Fragility index") + theme_bw()

p0 = ggplot(data = fi_sig, aes(x = active_sample, y = FI_final))
p2 = p0 + geom_point() + geom_smooth() + labs(x = "Number of participants included in the analyses", y = "Fragility index") + theme_bw()

p.0 = ggplot(data = fi_sig, aes(x = n_event, y = FI_final))
p3 = p.0 + geom_point() + geom_smooth() + labs(x = "Number of participants with fracture events", y = "Fragility index") + theme_bw()

#grid.arrange(p1, p2, p3, nrow = 1)
grid.arrange(p1, p3, nrow = 1, top = textGrob("Relationship between Number of participants and Fragility index", gp = gpar(fontsize = 20, font = 3)))

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

(1.1.2) By fracture sites

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code1), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any_fx (N=3)	Clin_fx (N=12)	OFx (N=4)	MOF (N=4)	Dif_comb (N=1)	NonVert_fx (N=19)	Vert_fx (N=63)	ClinVert_fx (N=12)	Hip (N=9)	Forearm (N=2)	Overall (N=129)
no_rand
Mean (SD)	1850 (423)	3580 (2630)	2780 (1580)	5020 (2680)	NA	3930 (2380)	2690 (2320)	2820 (2490)	3950 (2300)	1740 (374)	3090 (2360)
Median [Q1, Q3]	1770 [1620, 2030]	3110 [1570, 5120]	3050 [1730, 4090]	5640 [3480, 7180]	2690 [2690, 2690]	4090 [1810, 5090]	1630 [1200, 4090]	1960 [1650, 2620]	3270 [2300, 4090]	1740 [1600, 1870]	1960 [1360, 4090]
Median [min, max]	1770 [1470, 2300]	3110 [549, 7740]	3050 [930, 4090]	5640 [1650, 7180]	2690 [2690, 2690]	4090 [450, 7870]	1630 [549, 7870]	1960 [549, 7870]	3270 [1770, 7870]	1740 [1470, 2000]	1960 [450, 7870]
active_sample
Mean (SD)	1830 (439)	3100 (2480)	2670 (1490)	4320 (2410)	NA	3450 (2200)	2370 (2100)	2370 (2380)	3260 (1920)	1160 (810)	2700 (2140)
Median [Q1, Q3]	1770 [1600, 2030]	2820 [946, 4930]	2890 [1690, 3870]	4820 [2970, 6170]	2690 [2690, 2690]	3560 [1700, 4940]	1350 [1050, 3520]	1650 [975, 2270]	2380 [1980, 3320]	1160 [876, 1450]	1860 [1130, 3700]
Median [min, max]	1770 [1430, 2300]	2820 [426, 6690]	2890 [930, 3980]	4820 [1270, 6380]	2690 [2690, 2690]	3560 [389, 6670]	1350 [426, 7390]	1650 [339, 7810]	2380 [1770, 6600]	1160 [590, 1740]	1860 [339, 7810]
n_event
Mean (SD)	354 (290)	255 (217)	334 (251)	170 (135)	NA	295 (211)	125 (145)	86.4 (62.5)	158 (86.9)	111 (16.3)	174 (176)
Median [Q1, Q3]	475 [249, 519]	210 [87.3, 385]	318 [245, 407]	140 [86.8, 222]	147 [147, 147]	249 [116, 433]	73.0 [36.5, 125]	63.0 [57.0, 108]	140 [106, 190]	111 [105, 116]	101 [51.0, 246]
Median [min, max]	475 [23.0, 563]	210 [31.0, 764]	318 [44.0, 658]	140 [44.0, 355]	147 [147, 147]	249 [37.0, 680]	73.0 [10.0, 696]	63.0 [19.0, 207]	140 [58.0, 315]	111 [99.0, 122]	101 [10.0, 764]
FI_final
Mean (SD)	16.7 (11.9)	18.0 (24.4)	32.3 (26.2)	13.8 (9.14)	NA	10.9 (11.5)	21.8 (31.2)	12.3 (14.1)	6.67 (5.34)	5.50 (4.95)	17.5 (24.8)
Median [Q1, Q3]	22.0 [12.5, 23.5]	7.50 [5.00, 17.8]	31.5 [22.8, 41.0]	12.0 [8.00, 17.8]	4.00 [4.00, 4.00]	5.00 [2.00, 17.5]	11.0 [4.00, 23.5]	6.50 [3.50, 13.5]	5.00 [2.00, 11.0]	5.50 [3.75, 7.25]	9.00 [4.00, 22.0]
Median [min, max]	22.0 [3.00, 25.0]	7.50 [4.00, 89.0]	31.5 [1.00, 65.0]	12.0 [5.00, 26.0]	4.00 [4.00, 4.00]	5.00 [1.00, 43.0]	11.0 [1.00, 171]	6.50 [1.00, 42.0]	5.00 [1.00, 16.0]	5.50 [2.00, 9.00]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00847 (0.00558)	0.00710 (0.00471)	0.0106 (0.00776)	0.00443 (0.00331)	NA	0.00340 (0.00299)	0.0115 (0.0146)	0.00517 (0.00325)	0.00254 (0.00247)	0.00429 (0.00127)	0.00815 (0.0111)
Median [Q1, Q3]	0.0109 [0.00647, 0.0117]	0.00731 [0.00275, 0.00975]	0.0122 [0.00592, 0.0169]	0.00478 [0.00204, 0.00717]	0.00149 [0.00149, 0.00149]	0.00255 [0.00108, 0.00454]	0.00666 [0.00302, 0.0153]	0.00456 [0.00305, 0.00542]	0.00150 [0.00101, 0.00337]	0.00429 [0.00384, 0.00474]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.0109 [0.00209, 0.0125]	0.00731 [0.00124, 0.0146]	0.0122 [0.00108, 0.0169]	0.00478 [0.000783, 0.00736]	0.00149 [0.00149, 0.00149]	0.00255 [0.000203, 0.0105]	0.00666 [0.000151, 0.0966]	0.00456 [0.00205, 0.0125]	0.00150 [0.000303, 0.00695]	0.00429 [0.00339, 0.00519]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	0 (0%)	1 (8.3%)	2 (50.0%)	0 (0%)	0 (0%)	1 (5.3%)	5 (7.9%)	0 (0%)	0 (0%)	1 (50.0%)	10 (7.8%)
1	1 (33.3%)	8 (66.7%)	2 (50.0%)	4 (100%)	1 (100%)	11 (57.9%)	35 (55.6%)	4 (33.3%)	6 (66.7%)	1 (50.0%)	73 (56.6%)
Missing	2 (66.7%)	3 (25.0%)	0 (0%)	0 (0%)	0 (0%)	7 (36.8%)	23 (36.5%)	8 (66.7%)	3 (33.3%)	0 (0%)	46 (35.7%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code2), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any (N=15)	Osteoporotic (N=9)	Non-Vertebrae (N=19)	Vertebrae (N=63)	Clinical Vertebrae (N=12)	Hip (N=9)	Forearm (N=2)	Overall (N=129)
no_rand
Mean (SD)	3230 (2440)	3770 (2250)	3930 (2380)	2690 (2320)	2820 (2490)	3950 (2300)	1740 (374)	3090 (2360)
Median [Q1, Q3]	2130 [1560, 4260]	4090 [2000, 4090]	4090 [1810, 5090]	1630 [1200, 4090]	1960 [1650, 2620]	3270 [2300, 4090]	1740 [1600, 1870]	1960 [1360, 4090]
Median [min, max]	2130 [549, 7740]	4090 [930, 7180]	4090 [450, 7870]	1630 [549, 7870]	1960 [549, 7870]	3270 [1770, 7870]	1740 [1470, 2000]	1960 [450, 7870]
active_sample
Mean (SD)	2850 (2270)	3410 (1940)	3450 (2200)	2370 (2100)	2370 (2380)	3260 (1920)	1160 (810)	2700 (2140)
Median [Q1, Q3]	2010 [1190, 4070]	3530 [1950, 3980]	3560 [1700, 4940]	1350 [1050, 3520]	1650 [975, 2270]	2380 [1980, 3320]	1160 [876, 1450]	1860 [1130, 3700]
Median [min, max]	2010 [426, 6690]	3530 [930, 6380]	3560 [389, 6670]	1350 [426, 7390]	1650 [339, 7810]	2380 [1770, 6600]	1160 [590, 1740]	1860 [339, 7810]
n_event
Mean (SD)	275 (225)	240 (196)	295 (211)	125 (145)	86.4 (62.5)	158 (86.9)	111 (16.3)	174 (176)
Median [Q1, Q3]	231 [83.5, 437]	178 [101, 323]	249 [116, 433]	73.0 [36.5, 125]	63.0 [57.0, 108]	140 [106, 190]	111 [105, 116]	101 [51.0, 246]
Median [min, max]	231 [23.0, 764]	178 [44.0, 658]	249 [37.0, 680]	73.0 [10.0, 696]	63.0 [19.0, 207]	140 [58.0, 315]	111 [99.0, 122]	101 [10.0, 764]
FI_final
Mean (SD)	17.7 (22.1)	20.9 (20.3)	10.9 (11.5)	21.8 (31.2)	12.3 (14.1)	6.67 (5.34)	5.50 (4.95)	17.5 (24.8)
Median [Q1, Q3]	8.00 [5.00, 23.5]	15.0 [5.00, 30.0]	5.00 [2.00, 17.5]	11.0 [4.00, 23.5]	6.50 [3.50, 13.5]	5.00 [2.00, 11.0]	5.50 [3.75, 7.25]	9.00 [4.00, 22.0]
Median [min, max]	8.00 [3.00, 89.0]	15.0 [1.00, 65.0]	5.00 [1.00, 43.0]	11.0 [1.00, 171]	6.50 [1.00, 42.0]	5.00 [1.00, 16.0]	5.50 [2.00, 9.00]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00737 (0.00471)	0.00685 (0.00635)	0.00340 (0.00299)	0.0115 (0.0146)	0.00517 (0.00325)	0.00254 (0.00247)	0.00429 (0.00127)	0.00815 (0.0111)
Median [Q1, Q3]	0.00748 [0.00261, 0.0113]	0.00711 [0.00149, 0.00754]	0.00255 [0.00108, 0.00454]	0.00666 [0.00302, 0.0153]	0.00456 [0.00305, 0.00542]	0.00150 [0.00101, 0.00337]	0.00429 [0.00384, 0.00474]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00748 [0.00124, 0.0146]	0.00711 [0.000783, 0.0169]	0.00255 [0.000203, 0.0105]	0.00666 [0.000151, 0.0966]	0.00456 [0.00205, 0.0125]	0.00150 [0.000303, 0.00695]	0.00429 [0.00339, 0.00519]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	1 (6.7%)	2 (22.2%)	1 (5.3%)	5 (7.9%)	0 (0%)	0 (0%)	1 (50.0%)	10 (7.8%)
1	9 (60.0%)	7 (77.8%)	11 (57.9%)	35 (55.6%)	4 (33.3%)	6 (66.7%)	1 (50.0%)	73 (56.6%)
Missing	5 (33.3%)	0 (0%)	7 (36.8%)	23 (36.5%)	8 (66.7%)	3 (33.3%)	0 (0%)	46 (35.7%)

kruskal.test(FI_final ~ fx_code2, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by fx_code2
## Kruskal-Wallis chi-squared = 8.475, df = 6, p-value = 0.2053

kruskal.test(FQ_final ~ fx_code2, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by fx_code2
## Kruskal-Wallis chi-squared = 19.86, df = 6, p-value = 0.002932

Box plots

p1 = ggplot(data = fi_sig, aes(y = FI_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Fracture sites", y = "Fragility index")
p2 = ggplot(data = fi_sig, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Fracture sites", y = "Fragility quotient")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by fracture sites", gp = gpar(fontsize = 20, font = 1)))

(1.1.3) By pharmacological interventions

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code1), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Alendronate (N=2)	Ibandronate (N=6)	Risedronate (N=5)	Minodronate (N=3)	Zoledronate (N=20)	Teriparatide (N=22)	Abaloparatide (N=4)	Romosozumab (N=28)	Denosumab (N=9)	Strontium_ranelate (N=15)	Calcium_VitD (N=15)	Overall (N=129)
no_rand
Mean (SD)	4430 (0)	1960 (0)	1490 (308)	704 (0)	3490 (2870)	1010 (342)	1520 (253)	5420 (1560)	5020 (3370)	2610 (1570)	2320 (965)	3090 (2360)
Median [Q1, Q3]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	2000 [1200, 7740]	1090 [578, 1290]	1650 [1520, 1650]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1650, 3750]	2300 [1620, 3270]	1960 [1360, 4090]
Median [min, max]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [939, 1630]	704 [704, 704]	2000 [1200, 7740]	1090 [549, 1640]	1650 [1140, 1650]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1220, 5090]	2300 [450, 3270]	1960 [450, 7870]
active_sample
Mean (SD)	4280 (211)	1950 (0)	1270 (317)	575 (27.7)	2810 (2350)	810 (288)	1260 (118)	4910 (1500)	4600 (3080)	2330 (1490)	1810 (830)	2700 (2140)
Median [Q1, Q3]	4280 [4210, 4360]	1950 [1950, 1950]	1330 [1280, 1370]	582 [563, 590]	1860 [1130, 5680]	882 [457, 1010]	1270 [1230, 1310]	4040 [3640, 6640]	6600 [1350, 7390]	1440 [1390, 3030]	1770 [1350, 2380]	1860 [1130, 3700]
Median [min, max]	4280 [4130, 4430]	1950 [1950, 1950]	1330 [759, 1630]	582 [544, 598]	1860 [339, 6550]	882 [426, 1430]	1270 [1110, 1400]	4040 [3240, 6910]	6600 [1350, 7810]	1440 [1150, 4940]	1770 [389, 2790]	1860 [339, 7810]
n_event
Mean (SD)	265 (204)	81.5 (23.1)	86.0 (39.3)	79.3 (20.5)	189 (219)	50.3 (26.7)	43.3 (24.1)	209 (146)	140 (180)	347 (221)	223 (163)	174 (176)
Median [Q1, Q3]	265 [193, 337]	70.5 [64.5, 101]	68.0 [65.0, 85.0]	79.0 [69.0, 89.5]	86.0 [38.5, 265]	44.0 [31.8, 75.5]	39.0 [30.3, 52.0]	173 [106, 272]	69.0 [29.0, 121]	330 [166, 504]	176 [96.0, 335]	101 [51.0, 246]
Median [min, max]	265 [121, 409]	70.5 [63.0, 112]	68.0 [58.0, 154]	79.0 [59.0, 100]	86.0 [13.0, 764]	44.0 [14.0, 100]	39.0 [19.0, 76.0]	173 [10.0, 658]	69.0 [15.0, 531]	330 [66.0, 696]	176 [37.0, 563]	101 [10.0, 764]
FI_final
Mean (SD)	10.0 (4.24)	8.50 (4.68)	5.80 (4.87)	10.0 (9.17)	25.5 (40.6)	9.32 (7.65)	7.50 (4.36)	22.7 (19.2)	25.1 (43.7)	25.1 (29.2)	9.67 (9.01)	17.5 (24.8)
Median [Q1, Q3]	10.0 [8.50, 11.5]	7.50 [4.50, 12.0]	4.00 [2.00, 11.0]	8.00 [5.00, 14.0]	9.50 [3.50, 34.3]	7.00 [2.25, 14.5]	6.50 [4.00, 10.0]	19.5 [7.00, 31.5]	4.00 [3.00, 17.0]	18.0 [4.50, 37.0]	6.00 [2.00, 16.5]	9.00 [4.00, 22.0]
Median [min, max]	10.0 [7.00, 13.0]	7.50 [4.00, 15.0]	4.00 [1.00, 11.0]	8.00 [2.00, 20.0]	9.50 [1.00, 171]	7.00 [1.00, 25.0]	6.50 [4.00, 13.0]	19.5 [1.00, 77.0]	4.00 [2.00, 137]	18.0 [1.00, 111]	6.00 [1.00, 25.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00236 (0.00111)	0.00435 (0.00240)	0.00475 (0.00356)	0.0180 (0.0171)	0.00720 (0.00710)	0.0120 (0.00941)	0.00578 (0.00293)	0.00501 (0.00481)	0.00432 (0.00546)	0.0171 (0.0246)	0.00508 (0.00378)	0.00815 (0.0111)
Median [Q1, Q3]	0.00236 [0.00197, 0.00275]	0.00384 [0.00231, 0.00615]	0.00527 [0.00156, 0.00801]	0.0137 [0.00855, 0.0253]	0.00535 [0.00268, 0.00800]	0.00897 [0.00450, 0.0185]	0.00535 [0.00348, 0.00765]	0.00354 [0.00147, 0.00629]	0.00255 [0.00222, 0.00296]	0.0104 [0.00189, 0.0187]	0.00353 [0.00243, 0.00659]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00236 [0.00158, 0.00314]	0.00384 [0.00205, 0.00768]	0.00527 [0.000615, 0.00828]	0.0137 [0.00334, 0.0368]	0.00535 [0.000887, 0.0301]	0.00897 [0.00114, 0.0288]	0.00535 [0.00314, 0.00928]	0.00354 [0.000151, 0.0188]	0.00255 [0.000303, 0.0185]	0.0104 [0.000203, 0.0966]	0.00353 [0.000567, 0.0125]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	0 (0%)	0 (0%)	5 (25.0%)	2 (9.1%)	0 (0%)	2 (7.1%)	0 (0%)	1 (6.7%)	0 (0%)	10 (7.8%)
1	0 (0%)	0 (0%)	4 (80.0%)	3 (100%)	15 (75.0%)	4 (18.2%)	4 (100%)	26 (92.9%)	4 (44.4%)	3 (20.0%)	10 (66.7%)	73 (56.6%)
Missing	2 (100%)	6 (100%)	1 (20.0%)	0 (0%)	0 (0%)	16 (72.7%)	0 (0%)	0 (0%)	5 (55.6%)	11 (73.3%)	5 (33.3%)	46 (35.7%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code2), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Bisphosphonates (N=36)	PTH analog (N=26)	Romosozumab (N=28)	Denosumab (N=9)	Strontium_ranelate (N=15)	Calcium_VitD (N=15)	Overall (N=129)
no_rand
Mean (SD)	2780 (2380)	1090 (375)	5420 (1560)	5020 (3370)	2610 (1570)	2320 (965)	3090 (2360)
Median [Q1, Q3]	1960 [1200, 2130]	1100 [705, 1360]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1650, 3750]	2300 [1620, 3270]	1960 [1360, 4090]
Median [min, max]	1960 [704, 7740]	1100 [549, 1650]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1220, 5090]	2300 [450, 3270]	1960 [450, 7870]
active_sample
Mean (SD)	2350 (1950)	880 (315)	4910 (1500)	4600 (3080)	2330 (1490)	1810 (830)	2700 (2140)
Median [Q1, Q3]	1860 [1130, 1970]	887 [567, 1090]	4040 [3640, 6640]	6600 [1350, 7390]	1440 [1390, 3030]	1770 [1350, 2380]	1860 [1130, 3700]
Median [min, max]	1860 [339, 6550]	887 [426, 1430]	4040 [3240, 6910]	6600 [1350, 7810]	1440 [1150, 4940]	1770 [389, 2790]	1860 [339, 7810]
n_event
Mean (SD)	152 (176)	49.2 (26.0)	209 (146)	140 (180)	347 (221)	223 (163)	174 (176)
Median [Q1, Q3]	76.0 [59.8, 144]	44.0 [31.8, 70.3]	173 [106, 272]	69.0 [29.0, 121]	330 [166, 504]	176 [96.0, 335]	101 [51.0, 246]
Median [min, max]	76.0 [13.0, 764]	44.0 [14.0, 100]	173 [10.0, 658]	69.0 [15.0, 531]	330 [66.0, 696]	176 [37.0, 563]	101 [10.0, 764]
FI_final
Mean (SD)	17.8 (31.4)	9.04 (7.20)	22.7 (19.2)	25.1 (43.7)	25.1 (29.2)	9.67 (9.01)	17.5 (24.8)
Median [Q1, Q3]	8.50 [4.00, 15.0]	7.00 [3.25, 13.0]	19.5 [7.00, 31.5]	4.00 [3.00, 17.0]	18.0 [4.50, 37.0]	6.00 [2.00, 16.5]	9.00 [4.00, 22.0]
Median [min, max]	8.50 [1.00, 171]	7.00 [1.00, 25.0]	19.5 [1.00, 77.0]	4.00 [2.00, 137]	18.0 [1.00, 111]	6.00 [1.00, 25.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00701 (0.00774)	0.0111 (0.00898)	0.00501 (0.00481)	0.00432 (0.00546)	0.0171 (0.0246)	0.00508 (0.00378)	0.00815 (0.0111)
Median [Q1, Q3]	0.00523 [0.00205, 0.00776]	0.00864 [0.00381, 0.0157]	0.00354 [0.00147, 0.00629]	0.00255 [0.00222, 0.00296]	0.0104 [0.00189, 0.0187]	0.00353 [0.00243, 0.00659]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00523 [0.000615, 0.0368]	0.00864 [0.00114, 0.0288]	0.00354 [0.000151, 0.0188]	0.00255 [0.000303, 0.0185]	0.0104 [0.000203, 0.0966]	0.00353 [0.000567, 0.0125]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	5 (13.9%)	2 (7.7%)	2 (7.1%)	0 (0%)	1 (6.7%)	0 (0%)	10 (7.8%)
1	22 (61.1%)	8 (30.8%)	26 (92.9%)	4 (44.4%)	3 (20.0%)	10 (66.7%)	73 (56.6%)
Missing	9 (25.0%)	16 (61.5%)	0 (0%)	5 (55.6%)	11 (73.3%)	5 (33.3%)	46 (35.7%)

kruskal.test(FI_final ~ interv_code2, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by interv_code2
## Kruskal-Wallis chi-squared = 12.27, df = 5, p-value = 0.03126

kruskal.test(FQ_final ~ interv_code2, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by interv_code2
## Kruskal-Wallis chi-squared = 13.403, df = 5, p-value = 0.01988

Box plots

p1 = ggplot(data = fi_sig, aes(y = FI_final, x = as.factor(interv_code2), fill = as.factor(interv_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Pharmacological interventions", y = "Fragility index")
p2 = ggplot(data = fi_sig, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Pharmacological interventions", y = "Fragility quotine")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by intervention sites", gp = gpar(fontsize = 20, font = 1)))

(1.1.4) Timing of fracture assessment

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(timing), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	2 (N=21)	3 (N=17)	4 (N=39)	5 (N=34)	6 (N=6)	7 (N=5)	8 (N=7)	Overall (N=129)
no_rand
Mean (SD)	3500 (2440)	1780 (1210)	3040 (2320)	3820 (2870)	2340 (1650)	3640 (1980)	2100 (259)	3090 (2360)
Median [Q1, Q3]	4090 [1470, 4090]	1650 [578, 3270]	1470 [1120, 4090]	2050 [1650, 7740]	1650 [1120, 3740]	5090 [1470, 5090]	2000 [2000, 2000]	1960 [1360, 4090]
Median [min, max]	4090 [578, 7180]	1650 [549, 3270]	1470 [704, 7180]	2050 [450, 7870]	1650 [930, 4430]	5090 [1470, 5090]	2000 [2000, 2690]	1960 [450, 7870]
active_sample
Mean (SD)	3170 (2280)	1320 (872)	2710 (2150)	3310 (2490)	2090 (1710)	2930 (2210)	2000 (315)	2700 (2140)
Median [Q1, Q3]	3400 [1280, 4090]	1280 [451, 1770]	1350 [971, 3660]	1950 [1440, 6240]	1150 [985, 3390]	3650 [590, 4940]	1890 [1860, 1980]	1860 [1130, 3700]
Median [min, max]	3400 [476, 6910]	1280 [426, 2790]	1350 [544, 6690]	1950 [339, 7810]	1150 [759, 4430]	3650 [567, 4940]	1890 [1740, 2690]	1860 [339, 7810]
n_event
Mean (SD)	100 (78.7)	105 (112)	141 (147)	239 (198)	257 (252)	418 (301)	186 (127)	174 (176)
Median [Q1, Q3]	75.0 [53.0, 147]	48.0 [34.0, 163]	86.0 [41.5, 200]	147 [82.8, 346]	163 [81.3, 358]	537 [122, 671]	147 [85.5, 281]	101 [51.0, 246]
Median [min, max]	75.0 [10.0, 323]	48.0 [19.0, 375]	86.0 [14.0, 658]	147 [23.0, 764]	163 [44.0, 696]	537 [70.0, 691]	147 [48.0, 377]	101 [10.0, 764]
FI_final
Mean (SD)	9.19 (8.95)	8.35 (6.26)	18.0 (17.9)	27.5 (37.8)	24.7 (42.5)	8.20 (11.7)	13.6 (9.85)	17.5 (24.8)
Median [Q1, Q3]	5.00 [3.00, 11.0]	8.00 [4.00, 11.0]	14.0 [4.50, 24.0]	15.5 [4.00, 38.8]	9.50 [4.75, 12.8]	3.00 [2.00, 5.00]	10.0 [7.50, 16.5]	9.00 [4.00, 22.0]
Median [min, max]	5.00 [1.00, 30.0]	8.00 [1.00, 25.0]	14.0 [1.00, 77.0]	15.5 [1.00, 171]	9.50 [1.00, 111]	3.00 [2.00, 29.0]	10.0 [4.00, 33.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00366 (0.00333)	0.00885 (0.00788)	0.00857 (0.00878)	0.00902 (0.00918)	0.0197 (0.0378)	0.00330 (0.00292)	0.00703 (0.00510)	0.00815 (0.0111)
Median [Q1, Q3]	0.00259 [0.00136, 0.00440]	0.00711 [0.00340, 0.0105]	0.00532 [0.00271, 0.0123]	0.00656 [0.00236, 0.0125]	0.00421 [0.00197, 0.00915]	0.00339 [0.00101, 0.00353]	0.00537 [0.00421, 0.00851]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00259 [0.000151, 0.0137]	0.00711 [0.000567, 0.0288]	0.00532 [0.000554, 0.0368]	0.00656 [0.000203, 0.0361]	0.00421 [0.00108, 0.0966]	0.00339 [0.000608, 0.00795]	0.00537 [0.00149, 0.0169]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	1 (4.8%)	0 (0%)	3 (7.7%)	1 (2.9%)	0 (0%)	0 (0%)	5 (71.4%)	10 (7.8%)
1	17 (81.0%)	11 (64.7%)	25 (64.1%)	15 (44.1%)	1 (16.7%)	2 (40.0%)	2 (28.6%)	73 (56.6%)
Missing	3 (14.3%)	6 (35.3%)	11 (28.2%)	18 (52.9%)	5 (83.3%)	3 (60.0%)	0 (0%)	46 (35.7%)

kruskal.test(FI_final ~ timing, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by timing
## Kruskal-Wallis chi-squared = 9.2682, df = 6, p-value = 0.159

kruskal.test(FQ_final ~ timing, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by timing
## Kruskal-Wallis chi-squared = 10.638, df = 6, p-value = 0.1002

Box plots

p1 = ggplot(data = fi_sig, aes(y = FI_final, x = as.factor(timing), fill = as.factor(timing))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index")
p1

(1.1.5) By journal

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(journal_code2), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	NEJM (N=79)	Lancet (N=5)	BMJ (N=5)	JAMA (N=10)	JBMR (N=6)	JCEM (N=12)	Other (N=12)	Overall (N=129)
no_rand
Mean (SD)	3880 (2550)	1360 (0)	2160 (397)	2190 (1180)	1960 (0)	1320 (1340)	2120 (1820)	3090 (2360)
Median [Q1, Q3]	3270 [1560, 7180]	1360 [1360, 1360]	2300 [1770, 2300]	1640 [1630, 1650]	1960 [1960, 1960]	578 [571, 1410]	1470 [874, 2510]	1960 [1360, 4090]
Median [min, max]	3270 [450, 7870]	1360 [1360, 1360]	2300 [1770, 2690]	1640 [1630, 4430]	1960 [1960, 1960]	578 [549, 5090]	1470 [704, 5090]	1960 [450, 7870]
active_sample
Mean (SD)	3360 (2330)	1080 (48.9)	2160 (397)	1950 (1230)	1950 (0)	1230 (1350)	1700 (1740)	2700 (2140)
Median [Q1, Q3]	2790 [1350, 6240]	1050 [1050, 1100]	2300 [1770, 2300]	1390 [1290, 1580]	1950 [1950, 1950]	464 [445, 1410]	845 [588, 1770]	1860 [1130, 3700]
Median [min, max]	2790 [339, 7810]	1050 [1050, 1160]	2300 [1770, 2690]	1390 [1270, 4430]	1950 [1950, 1950]	464 [426, 4930]	845 [544, 4940]	1860 [339, 7810]
n_event
Mean (SD)	177 (165)	70.0 (36.2)	352 (167)	108 (112)	81.5 (23.1)	118 (151)	278 (279)	174 (176)
Median [Q1, Q3]	117 [54.5, 248]	91.0 [53.0, 92.0]	315 [262, 475]	70.5 [47.5, 112]	70.5 [64.5, 101]	38.0 [28.5, 145]	111 [69.5, 571]	101 [51.0, 246]
Median [min, max]	117 [10.0, 764]	91.0 [14.0, 100]	315 [147, 563]	70.5 [34.0, 409]	70.5 [63.0, 112]	38.0 [19.0, 471]	111 [44.0, 696]	101 [10.0, 764]
FI_final
Mean (SD)	21.3 (28.3)	9.40 (6.80)	15.6 (8.44)	8.20 (4.47)	8.50 (4.68)	9.67 (12.8)	16.6 (30.9)	17.5 (24.8)
Median [Q1, Q3]	12.0 [4.50, 26.0]	10.0 [3.00, 15.0]	16.0 [11.0, 22.0]	10.0 [4.75, 11.0]	7.50 [4.50, 12.0]	4.00 [2.00, 11.5]	4.50 [2.00, 14.0]	9.00 [4.00, 22.0]
Median [min, max]	12.0 [1.00, 171]	10.0 [2.00, 17.0]	16.0 [4.00, 25.0]	10.0 [1.00, 13.0]	7.50 [4.00, 15.0]	4.00 [1.00, 45.0]	4.50 [1.00, 111]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00727 (0.00800)	0.00882 (0.00654)	0.00760 (0.00430)	0.00504 (0.00332)	0.00435 (0.00240)	0.0113 (0.00964)	0.0153 (0.0275)	0.00815 (0.0111)
Median [Q1, Q3]	0.00393 [0.00226, 0.00831]	0.00908 [0.00259, 0.0143]	0.00695 [0.00623, 0.0109]	0.00513 [0.00197, 0.00793]	0.00384 [0.00231, 0.00615]	0.00864 [0.00423, 0.0187]	0.00440 [0.00278, 0.0113]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00393 [0.000151, 0.0361]	0.00908 [0.00191, 0.0162]	0.00695 [0.00149, 0.0125]	0.00513 [0.000615, 0.00928]	0.00384 [0.00205, 0.00768]	0.00864 [0.000203, 0.0288]	0.00440 [0.000608, 0.0966]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	7 (8.9%)	2 (40.0%)	0 (0%)	0 (0%)	0 (0%)	1 (8.3%)	0 (0%)	10 (7.8%)
1	51 (64.6%)	3 (60.0%)	1 (20.0%)	8 (80.0%)	0 (0%)	4 (33.3%)	6 (50.0%)	73 (56.6%)
Missing	21 (26.6%)	0 (0%)	4 (80.0%)	2 (20.0%)	6 (100%)	7 (58.3%)	6 (50.0%)	46 (35.7%)

kruskal.test(FI_final ~ journal_code2, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by journal_code2
## Kruskal-Wallis chi-squared = 7.8264, df = 6, p-value = 0.2511

kruskal.test(FQ_final ~ journal_code2, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by journal_code2
## Kruskal-Wallis chi-squared = 4.192, df = 6, p-value = 0.6507

Box plots

p1 = ggplot(data = fi_sig, aes(y = FI_final, x = as.factor(timing), fill = as.factor(journal_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index") 
p1

(1.1.6) By sex

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | sex, data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Both (N=12)	Men (N=10)	Women (N=107)	Overall (N=129)
no_rand
Mean (SD)	1020 (798)	1310 (139)	3490 (2380)	3090 (2360)
Median [Q1, Q3]	578 [549, 1230]	1200 [1200, 1470]	2300 [1640, 4760]	1960 [1360, 4090]
Median [min, max]	578 [450, 2690]	1200 [1200, 1470]	2300 [704, 7870]	1960 [450, 7870]
active_sample
Mean (SD)	661 (655)	1220 (137)	3070 (2160)	2700 (2140)
Median [Q1, Q3]	451 [426, 477]	1130 [1130, 1350]	1980 [1300, 4280]	1860 [1130, 3700]
Median [min, max]	451 [339, 2690]	1130 [1060, 1430]	1980 [544, 7810]	1860 [339, 7810]
n_event
Mean (SD)	62.3 (62.8)	26.5 (9.06)	200 (181)	174 (176)
Median [Q1, Q3]	39.0 [33.3, 51.0]	26.0 [21.5, 34.3]	121 [71.0, 314]	101 [51.0, 246]
Median [min, max]	39.0 [19.0, 231]	26.0 [13.0, 39.0]	121 [10.0, 764]	101 [10.0, 764]
FI_final
Mean (SD)	4.67 (3.87)	2.90 (1.66)	20.3 (26.4)	17.5 (24.8)
Median [Q1, Q3]	4.00 [2.00, 5.50]	3.00 [1.25, 4.00]	12.0 [5.00, 24.5]	9.00 [4.00, 22.0]
Median [min, max]	4.00 [1.00, 13.0]	3.00 [1.00, 6.00]	12.0 [1.00, 171]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00984 (0.00913)	0.00236 (0.00140)	0.00851 (0.0116)	0.00815 (0.0111)
Median [Q1, Q3]	0.00677 [0.00406, 0.0125]	0.00216 [0.00115, 0.00296]	0.00527 [0.00242, 0.0100]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00677 [0.00108, 0.0288]	0.00216 [0.000887, 0.00532]	0.00527 [0.000151, 0.0966]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	10 (9.3%)	10 (7.8%)
1	4 (33.3%)	10 (100%)	59 (55.1%)	73 (56.6%)
Missing	8 (66.7%)	0 (0%)	38 (35.5%)	46 (35.7%)

kruskal.test(FI_final ~ sex, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by sex
## Kruskal-Wallis chi-squared = 23.592, df = 2, p-value = 7.534e-06

kruskal.test(FQ_final ~ sex, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by sex
## Kruskal-Wallis chi-squared = 8.7259, df = 2, p-value = 0.01274

Box plots

p1 = ggplot(data = fi_sig, aes(y = FI_final, x = as.factor(sex), fill = as.factor(sex))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by sex", x = "Sex", y = "Fragility index") 
p1

(1.1.7) By placebo

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | placebo, data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Active (N=26)	Placebo (N=103)	Overall (N=129)
no_rand
Mean (SD)	3080 (1320)	3100 (2560)	3090 (2360)
Median [Q1, Q3]	4090 [1640, 4090]	1960 [1200, 5090]	1960 [1360, 4090]
Median [min, max]	4090 [1140, 4090]	1960 [450, 7870]	1960 [450, 7870]
active_sample
Mean (SD)	2700 (1240)	2700 (2320)	2700 (2140)
Median [Q1, Q3]	3400 [1270, 3660]	1770 [994, 4680]	1860 [1130, 3700]
Median [min, max]	3400 [1050, 4090]	1770 [339, 7810]	1860 [339, 7810]
n_event
Mean (SD)	191 (162)	169 (179)	174 (176)
Median [Q1, Q3]	144 [65.5, 306]	99.0 [48.0, 228]	101 [51.0, 246]
Median [min, max]	144 [14.0, 658]	99.0 [10.0, 764]	101 [10.0, 764]
FI_final
Mean (SD)	18.3 (19.6)	17.3 (26.1)	17.5 (24.8)
Median [Q1, Q3]	10.5 [5.00, 24.0]	8.00 [3.50, 21.5]	9.00 [4.00, 22.0]
Median [min, max]	10.5 [2.00, 77.0]	8.00 [1.00, 171]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00685 (0.00539)	0.00848 (0.0121)	0.00815 (0.0111)
Median [Q1, Q3]	0.00575 [0.00260, 0.00923]	0.00499 [0.00226, 0.00931]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00575 [0.000554, 0.0188]	0.00499 [0.000151, 0.0966]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	4 (15.4%)	6 (5.8%)	10 (7.8%)
1	22 (84.6%)	51 (49.5%)	73 (56.6%)
Missing	0 (0%)	46 (44.7%)	46 (35.7%)

kruskal.test(FI_final ~ placebo, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by placebo
## Kruskal-Wallis chi-squared = 1.3147, df = 1, p-value = 0.2515

kruskal.test(FQ_final ~ placebo, data = fi_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by placebo
## Kruskal-Wallis chi-squared = 0.12409, df = 1, p-value = 0.7246

Box plots

p1 = ggplot(data = fi_sig, aes(y = FI_final, x = as.factor(control), fill = as.factor(control))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by types of control", x = "Types of control", y = "Fragility index") 
p1

(1.2) Fracture as the predefined primary endpoint

(1.2.1) Overall

fx_prim = subset(fi_sig, pri_endpoint == 1)
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi), data = fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Overall (N=30)
no_rand
Mean (SD)	3110 (2350)
Median [Q1, Q3]	1980 [1430, 4090]
Median [min, max]	1980 [549, 7870]
active_sample
Mean (SD)	2670 (2130)
Median [Q1, Q3]	1860 [1070, 3980]
Median [min, max]	1860 [426, 7390]
n_event
Mean (SD)	186 (158)
Median [Q1, Q3]	117 [77.0, 292]
Median [min, max]	117 [29.0, 671]
FI_final
Mean (SD)	29.0 (38.3)
Median [Q1, Q3]	14.0 [11.0, 31.3]
Median [min, max]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0137 (0.0116)
Median [Q1, Q3]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	3 (10.0%)
1	16 (53.3%)
Missing	11 (36.7%)

# By fracture as the predefined primary endpoint
fi_sig$fx_primary[fi_sig$pri_endpoint == 1] = "Primary endpoint"
fi_sig$fx_primary[fi_sig$pri_endpoint == 0] = "Secondary endpoint"

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | fx_primary , data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Primary endpoint (N=30)	Secondary endpoint (N=99)	Overall (N=129)
no_rand
Mean (SD)	3110 (2350)	3090 (2370)	3090 (2360)
Median [Q1, Q3]	1980 [1430, 4090]	1960 [1360, 4090]	1960 [1360, 4090]
Median [min, max]	1980 [549, 7870]	1960 [450, 7870]	1960 [450, 7870]
active_sample
Mean (SD)	2670 (2130)	2710 (2150)	2700 (2140)
Median [Q1, Q3]	1860 [1070, 3980]	1860 [1130, 3690]	1860 [1130, 3700]
Median [min, max]	1860 [426, 7390]	1860 [339, 7810]	1860 [339, 7810]
n_event
Mean (SD)	186 (158)	170 (181)	174 (176)
Median [Q1, Q3]	117 [77.0, 292]	91.0 [47.0, 236]	101 [51.0, 246]
Median [min, max]	117 [29.0, 671]	91.0 [10.0, 764]	101 [10.0, 764]
FI_final
Mean (SD)	29.0 (38.3)	14.0 (17.9)	17.5 (24.8)
Median [Q1, Q3]	14.0 [11.0, 31.3]	7.00 [3.50, 18.0]	9.00 [4.00, 22.0]
Median [min, max]	14.0 [1.00, 171]	7.00 [1.00, 111]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.0137 (0.0116)	0.00648 (0.0104)	0.00815 (0.0111)
Median [Q1, Q3]	0.00864 [0.00404, 0.0240]	0.00360 [0.00208, 0.00751]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00864 [0.000567, 0.0368]	0.00360 [0.000151, 0.0966]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	3 (10.0%)	7 (7.1%)	10 (7.8%)
1	16 (53.3%)	57 (57.6%)	73 (56.6%)
Missing	11 (36.7%)	35 (35.4%)	46 (35.7%)

fi_sig$missing_fi = factor(fi_sig$missing_fi)
createTable(compareGroups(fx_primary ~ no_rand + active_sample + n_event + FI_final + FQ_final + missing_fi, data = fi_sig, method = c(no_rand = 2, active_sample = 2, n_event = 2, FI_final = 2, FQ_final = 2)))

## Warning in chisq.test(xx, correct = FALSE): Chi-squared approximation may be
## incorrect

## 
## --------Summary descriptives table by 'fx_primary'---------
## 
## ___________________________________________________________ 
##               Primary endpoint Secondary endpoint p.overall 
##                     N=30              N=99                  
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 
## no_rand       1982 [1427;4093]  1964 [1360;4093]    0.880   
## active_sample 1856 [1074;3984]  1861 [1127;3690]    0.980   
## n_event        116 [77.0;292]   91.0 [47.0;236]     0.219   
## FI_final      14.0 [11.0;31.2]  7.00 [3.50;18.0]    0.004   
## FQ_final      0.01 [0.00;0.02]  0.00 [0.00;0.01]    0.001   
## missing_fi:                                         0.689   
##     0            3 (15.8%)         7 (10.9%)                
##     1            16 (84.2%)        57 (89.1%)               
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Relationship between sample size/active sample/no. events and FI

p = ggplot(data = fx_prim, aes(x = no_rand, y = FI_final))
p1 = p + geom_point() + geom_smooth() + labs(x = "Number of participants at randomisation", y = "Fragility index") + theme_bw()

p0 = ggplot(data = fx_prim, aes(x = active_sample, y = FI_final))
p2 = p0 + geom_point() + geom_smooth() + labs(x = "Number of participants included in the analyses", y = "Fragility index") + theme_bw()

p.0 = ggplot(data =  fx_prim, aes(x = n_event, y = FI_final))
p3 = p.0 + geom_point() + geom_smooth() + labs(x = "Number of participants with fracture events", y = "Fragility index") + theme_bw()

#grid.arrange(p1, p2, p3, nrow = 1)
grid.arrange(p1, p3, nrow = 1, top = textGrob("Relationship between Number of participants and Fragility index", gp = gpar(fontsize = 20, font = 3)))

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

(1.2.2) By fracture sites

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code1), data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Clin_fx (N=2)	OFx (N=1)	NonVert_fx (N=1)	Vert_fx (N=22)	Hip (N=4)	Overall (N=30)
no_rand
Mean (SD)	3110 (1390)	NA	NA	2840 (2490)	4390 (2230)	3110 (2350)
Median [Q1, Q3]	3110 [2620, 3600]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [1200, 4090]	3270 [3270, 4390]	1980 [1430, 4090]
Median [min, max]	3110 [2130, 4090]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [549, 7870]	3270 [3270, 7740]	1980 [549, 7870]
active_sample
Mean (SD)	2060 (2240)	NA	NA	2530 (2240)	3340 (2110)	2670 (2130)
Median [Q1, Q3]	2060 [1270, 2850]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [1050, 3980]	2580 [2220, 3700]	1860 [1070, 3980]
Median [min, max]	2060 [479, 3640]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [426, 7390]	2580 [1770, 6450]	1860 [426, 7390]
n_event
Mean (SD)	348 (165)	NA	NA	151 (129)	141 (59.2)	186 (158)
Median [Q1, Q3]	348 [289, 406]	312 [312, 312]	671 [671, 671]	103 [54.8, 204]	158 [120, 180]	117 [77.0, 292]
Median [min, max]	348 [231, 464]	312 [312, 312]	671 [671, 671]	103 [29.0, 402]	158 [58.0, 190]	117 [29.0, 671]
FI_final
Mean (SD)	16.5 (13.4)	NA	NA	35.4 (42.6)	6.00 (4.97)	29.0 (38.3)
Median [Q1, Q3]	16.5 [11.8, 21.3]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [13.0, 41.5]	5.50 [2.50, 9.00]	14.0 [11.0, 31.3]
Median [min, max]	16.5 [7.00, 26.0]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [1.00, 171]	5.50 [1.00, 12.0]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0109 (0.00529)	NA	NA	0.0166 (0.0117)	0.00172 (0.00122)	0.0137 (0.0116)
Median [Q1, Q3]	0.0109 [0.00901, 0.0127]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0129 [0.00692, 0.0277]	0.00147 [0.000948, 0.00224]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.0109 [0.00714, 0.0146]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0129 [0.000946, 0.0368]	0.00147 [0.000567, 0.00337]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	1 (100%)	0 (0%)	2 (9.1%)	0 (0%)	3 (10.0%)
1	2 (100%)	0 (0%)	0 (0%)	10 (45.5%)	4 (100%)	16 (53.3%)
Missing	0 (0%)	0 (0%)	1 (100%)	10 (45.5%)	0 (0%)	11 (36.7%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code2), data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any (N=2)	Osteoporotic (N=1)	Non-Vertebrae (N=1)	Vertebrae (N=22)	Hip (N=4)	Overall (N=30)
no_rand
Mean (SD)	3110 (1390)	NA	NA	2840 (2490)	4390 (2230)	3110 (2350)
Median [Q1, Q3]	3110 [2620, 3600]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [1200, 4090]	3270 [3270, 4390]	1980 [1430, 4090]
Median [min, max]	3110 [2130, 4090]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [549, 7870]	3270 [3270, 7740]	1980 [549, 7870]
active_sample
Mean (SD)	2060 (2240)	NA	NA	2530 (2240)	3340 (2110)	2670 (2130)
Median [Q1, Q3]	2060 [1270, 2850]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [1050, 3980]	2580 [2220, 3700]	1860 [1070, 3980]
Median [min, max]	2060 [479, 3640]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [426, 7390]	2580 [1770, 6450]	1860 [426, 7390]
n_event
Mean (SD)	348 (165)	NA	NA	151 (129)	141 (59.2)	186 (158)
Median [Q1, Q3]	348 [289, 406]	312 [312, 312]	671 [671, 671]	103 [54.8, 204]	158 [120, 180]	117 [77.0, 292]
Median [min, max]	348 [231, 464]	312 [312, 312]	671 [671, 671]	103 [29.0, 402]	158 [58.0, 190]	117 [29.0, 671]
FI_final
Mean (SD)	16.5 (13.4)	NA	NA	35.4 (42.6)	6.00 (4.97)	29.0 (38.3)
Median [Q1, Q3]	16.5 [11.8, 21.3]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [13.0, 41.5]	5.50 [2.50, 9.00]	14.0 [11.0, 31.3]
Median [min, max]	16.5 [7.00, 26.0]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [1.00, 171]	5.50 [1.00, 12.0]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0109 (0.00529)	NA	NA	0.0166 (0.0117)	0.00172 (0.00122)	0.0137 (0.0116)
Median [Q1, Q3]	0.0109 [0.00901, 0.0127]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0129 [0.00692, 0.0277]	0.00147 [0.000948, 0.00224]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.0109 [0.00714, 0.0146]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0129 [0.000946, 0.0368]	0.00147 [0.000567, 0.00337]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	1 (100%)	0 (0%)	2 (9.1%)	0 (0%)	3 (10.0%)
1	2 (100%)	0 (0%)	0 (0%)	10 (45.5%)	4 (100%)	16 (53.3%)
Missing	0 (0%)	0 (0%)	1 (100%)	10 (45.5%)	0 (0%)	11 (36.7%)

kruskal.test(FI_final ~ fx_code2, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by fx_code2
## Kruskal-Wallis chi-squared = 8.85, df = 4, p-value = 0.06496

kruskal.test(FQ_final ~ fx_code2, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by fx_code2
## Kruskal-Wallis chi-squared = 10.855, df = 4, p-value = 0.02824

Box plots

p1 = ggplot(data = fx_prim, aes(y = FI_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Fracture sites", y = "Fragility index")
p2 = ggplot(data =  fx_prim, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Fracture sites", y = "Fragility quotient")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by fracture sites", gp = gpar(fontsize = 20, font = 1)))

(1.2.3) By pharmacological interventions

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code1), data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Alendronate (N=1)	Ibandronate (N=2)	Risedronate (N=1)	Minodronate (N=1)	Zoledronate (N=6)	Teriparatide (N=6)	Abaloparatide (N=1)	Romosozumab (N=5)	Denosumab (N=1)	Strontium_ranelate (N=3)	Calcium_VitD (N=3)	Overall (N=30)
no_rand
Mean (SD)	NA	1960 (0)	NA	NA	3670 (3180)	1050 (429)	NA	5330 (1690)	NA	2800 (1990)	3270 (0)	3110 (2350)
Median [Q1, Q3]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	2060 [1400, 6330]	1090 [705, 1290]	1650 [1650, 1650]	4090 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 3370]	3270 [3270, 3270]	1980 [1430, 4090]
Median [min, max]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	2060 [1200, 7740]	1090 [549, 1640]	1650 [1650, 1650]	4090 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 5090]	3270 [3270, 3270]	1980 [549, 7870]
active_sample
Mean (SD)	NA	1950 (0)	NA	NA	2790 (2590)	855 (378)	NA	4940 (1570)	NA	2610 (2020)	2310 (516)	2670 (2130)
Median [Q1, Q3]	4130 [4130, 4130]	1950 [1950, 1950]	1370 [1370, 1370]	544 [544, 544]	1540 [1070, 4740]	887 [559, 1010]	1400 [1400, 1400]	4090 [3660, 6640]	7390 [7390, 7390]	1440 [1440, 3190]	2380 [2070, 2580]	1860 [1070, 3980]
Median [min, max]	4130 [4130, 4130]	1950 [1950, 1950]	1370 [1370, 1370]	544 [544, 544]	1540 [479, 6450]	887 [426, 1430]	1400 [1400, 1400]	4090 [3640, 6650]	7390 [7390, 7390]	1440 [1440, 4940]	2380 [1770, 2790]	1860 [426, 7390]
n_event
Mean (SD)	NA	111 (1.41)	NA	NA	192 (151)	64.3 (25.3)	NA	247 (168)	NA	463 (182)	141 (72.5)	186 (158)
Median [Q1, Q3]	121 [121, 121]	111 [111, 112]	154 [154, 154]	100 [100, 100]	186 [62.8, 292]	65.5 [42.8, 85.3]	34.0 [34.0, 34.0]	221 [105, 370]	350 [350, 350]	387 [360, 529]	176 [117, 183]	117 [77.0, 292]
Median [min, max]	121 [121, 121]	111 [110, 112]	154 [154, 154]	100 [100, 100]	186 [29.0, 402]	65.5 [36.0, 92.0]	34.0 [34.0, 34.0]	221 [75.0, 464]	350 [350, 350]	387 [332, 671]	176 [58.0, 190]	117 [29.0, 671]
FI_final
Mean (SD)	NA	14.0 (1.41)	NA	NA	38.3 (65.9)	16.3 (6.15)	NA	41.8 (21.3)	NA	33.3 (26.5)	4.00 (3.61)	29.0 (38.3)
Median [Q1, Q3]	13.0 [13.0, 13.0]	14.0 [13.5, 14.5]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	9.50 [6.25, 27.8]	14.0 [11.5, 21.0]	13.0 [13.0, 13.0]	40.0 [26.0, 42.0]	137 [137, 137]	45.0 [24.0, 48.5]	3.00 [2.00, 5.50]	14.0 [11.0, 31.3]
Median [min, max]	13.0 [13.0, 13.0]	14.0 [13.0, 15.0]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	9.50 [1.00, 171]	14.0 [11.0, 25.0]	13.0 [13.0, 13.0]	40.0 [24.0, 77.0]	137 [137, 137]	45.0 [3.00, 52.0]	3.00 [1.00, 8.00]	14.0 [1.00, 171]
FQ_final
Mean (SD)	NA	0.00717 (0.000724)	NA	NA	0.0116 (0.0112)	0.0218 (0.00871)	NA	0.00941 (0.00598)	NA	0.0226 (0.0192)	0.00167 (0.00149)	0.0137 (0.0116)
Median [Q1, Q3]	0.00314 [0.00314, 0.00314]	0.00717 [0.00692, 0.00743]	0.00801 [0.00801, 0.00801]	0.0368 [0.0368, 0.0368]	0.00997 [0.00273, 0.0164]	0.0258 [0.0172, 0.0277]	0.00928 [0.00928, 0.00928]	0.00714 [0.00601, 0.0115]	0.0185 [0.0185, 0.0185]	0.0312 [0.0159, 0.0336]	0.00108 [0.000821, 0.00222]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.00314 [0.00314, 0.00314]	0.00717 [0.00666, 0.00768]	0.00801 [0.00801, 0.00801]	0.0368 [0.0368, 0.0368]	0.00997 [0.000946, 0.0301]	0.0258 [0.00770, 0.0288]	0.00928 [0.00928, 0.00928]	0.00714 [0.00361, 0.0188]	0.0185 [0.0185, 0.0185]	0.0312 [0.000608, 0.0361]	0.00108 [0.000567, 0.00337]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	0 (0%)	0 (0%)	1 (16.7%)	1 (16.7%)	0 (0%)	1 (20.0%)	0 (0%)	0 (0%)	0 (0%)	3 (10.0%)
1	0 (0%)	0 (0%)	1 (100%)	1 (100%)	5 (83.3%)	1 (16.7%)	1 (100%)	4 (80.0%)	0 (0%)	0 (0%)	3 (100%)	16 (53.3%)
Missing	1 (100%)	2 (100%)	0 (0%)	0 (0%)	0 (0%)	4 (66.7%)	0 (0%)	0 (0%)	1 (100%)	3 (100%)	0 (0%)	11 (36.7%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code2), data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Bisphosphonates (N=11)	PTH analog (N=7)	Romosozumab (N=5)	Denosumab (N=1)	Strontium_ranelate (N=3)	Calcium_VitD (N=3)	Overall (N=30)
no_rand
Mean (SD)	2970 (2540)	1140 (451)	5330 (1690)	NA	2800 (1990)	3270 (0)	3110 (2350)
Median [Q1, Q3]	1960 [1410, 3280]	1100 [832, 1500]	4090 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 3370]	3270 [3270, 3270]	1980 [1430, 4090]
Median [min, max]	1960 [704, 7740]	1100 [549, 1650]	4090 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 5090]	3270 [3270, 3270]	1980 [549, 7870]
active_sample
Mean (SD)	2430 (2060)	933 (402)	4940 (1570)	NA	2610 (2020)	2310 (516)	2670 (2130)
Median [Q1, Q3]	1950 [1090, 3040]	892 [667, 1230]	4090 [3660, 6640]	7390 [7390, 7390]	1440 [1440, 3190]	2380 [2070, 2580]	1860 [1070, 3980]
Median [min, max]	1950 [479, 6450]	892 [426, 1430]	4090 [3640, 6650]	7390 [7390, 7390]	1440 [1440, 4940]	2380 [1770, 2790]	1860 [426, 7390]
n_event
Mean (SD)	159 (114)	60.0 (25.8)	247 (168)	NA	463 (182)	141 (72.5)	186 (158)
Median [Q1, Q3]	121 [105, 193]	48.0 [38.5, 84.5]	221 [105, 370]	350 [350, 350]	387 [360, 529]	176 [117, 183]	117 [77.0, 292]
Median [min, max]	121 [29.0, 402]	48.0 [34.0, 92.0]	221 [75.0, 464]	350 [350, 350]	387 [332, 671]	176 [58.0, 190]	117 [29.0, 671]
FI_final
Mean (SD)	27.5 (48.3)	15.9 (5.76)	41.8 (21.3)	NA	33.3 (26.5)	4.00 (3.61)	29.0 (38.3)
Median [Q1, Q3]	13.0 [9.00, 17.5]	13.0 [12.0, 19.0]	40.0 [26.0, 42.0]	137 [137, 137]	45.0 [24.0, 48.5]	3.00 [2.00, 5.50]	14.0 [11.0, 31.3]
Median [min, max]	13.0 [1.00, 171]	13.0 [11.0, 25.0]	40.0 [24.0, 77.0]	137 [137, 137]	45.0 [3.00, 52.0]	3.00 [1.00, 8.00]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0120 (0.0118)	0.0200 (0.00925)	0.00941 (0.00598)	NA	0.0226 (0.0192)	0.00167 (0.00149)	0.0137 (0.0116)
Median [Q1, Q3]	0.00768 [0.00423, 0.0158]	0.0258 [0.0118, 0.0271]	0.00714 [0.00601, 0.0115]	0.0185 [0.0185, 0.0185]	0.0312 [0.0159, 0.0336]	0.00108 [0.000821, 0.00222]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.00768 [0.000946, 0.0368]	0.0258 [0.00770, 0.0288]	0.00714 [0.00361, 0.0188]	0.0185 [0.0185, 0.0185]	0.0312 [0.000608, 0.0361]	0.00108 [0.000567, 0.00337]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	1 (9.1%)	1 (14.3%)	1 (20.0%)	0 (0%)	0 (0%)	0 (0%)	3 (10.0%)
1	7 (63.6%)	2 (28.6%)	4 (80.0%)	0 (0%)	0 (0%)	3 (100%)	16 (53.3%)
Missing	3 (27.3%)	4 (57.1%)	0 (0%)	1 (100%)	3 (100%)	0 (0%)	11 (36.7%)

kruskal.test(FI_final ~ interv_code2, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by interv_code2
## Kruskal-Wallis chi-squared = 13.133, df = 5, p-value = 0.02216

kruskal.test(FQ_final ~ interv_code2, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by interv_code2
## Kruskal-Wallis chi-squared = 9.1436, df = 5, p-value = 0.1035

Box plots

p1 = ggplot(data =  fx_prim, aes(y = FI_final, x = as.factor(interv_code2), fill = as.factor(interv_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Pharmacological interventions", y = "Fragility index")
p2 = ggplot(data =  fx_prim, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Pharmacological interventions", y = "Fragility quotine")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by intervention sites", gp = gpar(fontsize = 20, font = 1)))

(1.2.4) Timing of fracture assessment

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(timing), data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	2 (N=1)	3 (N=7)	4 (N=10)	5 (N=9)	6 (N=1)	7 (N=1)	8 (N=1)	Overall (N=30)
no_rand
Mean (SD)	NA	2030 (1240)	2610 (2140)	3810 (2980)	NA	NA	NA	3110 (2350)
Median [Q1, Q3]	7180 [7180, 7180]	1650 [1110, 3270]	1280 [1120, 4090]	1960 [1650, 7740]	4430 [4430, 4430]	5090 [5090, 5090]	2000 [2000, 2000]	1980 [1430, 4090]
Median [min, max]	7180 [7180, 7180]	1650 [549, 3270]	1280 [704, 7180]	1960 [1630, 7870]	4430 [4430, 4430]	5090 [5090, 5090]	2000 [2000, 2000]	1980 [549, 7870]
active_sample
Mean (SD)	NA	1520 (891)	2360 (2040)	3130 (2600)	NA	NA	NA	2670 (2130)
Median [Q1, Q3]	6640 [6640, 6640]	1430 [926, 2070]	1090 [931, 3660]	1950 [1440, 5680]	4130 [4130, 4130]	4940 [4940, 4940]	1950 [1950, 1950]	1860 [1070, 3980]
Median [min, max]	6640 [6640, 6640]	1430 [426, 2790]	1090 [544, 6650]	1950 [479, 7390]	4130 [4130, 4130]	4940 [4940, 4940]	1950 [1950, 1950]	1860 [426, 7390]
n_event
Mean (SD)	NA	83.3 (68.7)	159 (147)	246 (122)	NA	NA	NA	186 (158)
Median [Q1, Q3]	75.0 [75.0, 75.0]	48.0 [38.5, 117]	96.0 [83.8, 192]	231 [140, 350]	121 [121, 121]	671 [671, 671]	312 [312, 312]	117 [77.0, 292]
Median [min, max]	75.0 [75.0, 75.0]	48.0 [34.0, 190]	96.0 [29.0, 464]	231 [110, 402]	121 [121, 121]	671 [671, 671]	312 [312, 312]	117 [29.0, 671]
FI_final
Mean (SD)	NA	8.57 (4.83)	27.5 (21.7)	51.4 (60.9)	NA	NA	NA	29.0 (38.3)
Median [Q1, Q3]	24.0 [24.0, 24.0]	11.0 [5.50, 12.0]	24.0 [16.3, 36.5]	15.0 [12.0, 52.0]	13.0 [13.0, 13.0]	3.00 [3.00, 3.00]	33.0 [33.0, 33.0]	14.0 [11.0, 31.3]
Median [min, max]	24.0 [24.0, 24.0]	11.0 [1.00, 13.0]	24.0 [1.00, 77.0]	15.0 [7.00, 171]	13.0 [13.0, 13.0]	3.00 [3.00, 3.00]	33.0 [33.0, 33.0]	14.0 [1.00, 171]
FQ_final
Mean (SD)	NA	0.0109 (0.0117)	0.0155 (0.0117)	0.0172 (0.0125)	NA	NA	NA	0.0137 (0.0116)
Median [Q1, Q3]	0.00361 [0.00361, 0.00361]	0.00770 [0.00222, 0.0176]	0.0129 [0.00629, 0.0240]	0.0146 [0.00768, 0.0301]	0.00314 [0.00314, 0.00314]	0.000608 [0.000608, 0.000608]	0.0169 [0.0169, 0.0169]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.00361 [0.00361, 0.00361]	0.00770 [0.000567, 0.0288]	0.0129 [0.000946, 0.0368]	0.0146 [0.00186, 0.0361]	0.00314 [0.00314, 0.00314]	0.000608 [0.000608, 0.000608]	0.0169 [0.0169, 0.0169]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	2 (20.0%)	0 (0%)	0 (0%)	0 (0%)	1 (100%)	3 (10.0%)
1	1 (100%)	5 (71.4%)	6 (60.0%)	4 (44.4%)	0 (0%)	0 (0%)	0 (0%)	16 (53.3%)
Missing	0 (0%)	2 (28.6%)	2 (20.0%)	5 (55.6%)	1 (100%)	1 (100%)	0 (0%)	11 (36.7%)

kruskal.test(FI_final ~ timing, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by timing
## Kruskal-Wallis chi-squared = 9.7937, df = 6, p-value = 0.1336

kruskal.test(FQ_final ~ timing, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by timing
## Kruskal-Wallis chi-squared = 6.4225, df = 6, p-value = 0.3776

Box plots

p1 = ggplot(data =  fx_prim, aes(y = FI_final, x = as.factor(timing), fill = as.factor(timing))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index")
p1

(1.2.5) By journal

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(journal_code2), data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	NEJM (N=19)	Lancet (N=1)	JAMA (N=4)	JBMR (N=2)	JCEM (N=2)	Other (N=2)	Overall (N=30)
no_rand
Mean (SD)	3780 (2530)	NA	2340 (1400)	1960 (0)	564 (20.5)	2900 (3100)	3110 (2350)
Median [Q1, Q3]	3270 [1650, 5640]	1360 [1360, 1360]	1640 [1640, 2340]	1960 [1960, 1960]	564 [556, 571]	2900 [1800, 3990]	1980 [1430, 4090]
Median [min, max]	3270 [1090, 7870]	1360 [1360, 1360]	1640 [1630, 4430]	1960 [1960, 1960]	564 [549, 578]	2900 [704, 5090]	1980 [549, 7870]
active_sample
Mean (SD)	3180 (2320)	NA	2080 (1370)	1950 (0)	439 (17.7)	2740 (3100)	2670 (2130)
Median [Q1, Q3]	2380 [1280, 4880]	1050 [1050, 1050]	1410 [1390, 2100]	1950 [1950, 1950]	439 [432, 445]	2740 [1640, 3840]	1860 [1070, 3980]
Median [min, max]	2380 [479, 7390]	1050 [1050, 1050]	1410 [1370, 4130]	1950 [1950, 1950]	439 [426, 451]	2740 [544, 4940]	1860 [426, 7390]
n_event
Mean (SD)	213 (141)	NA	86.3 (60.7)	111 (1.41)	44.5 (4.95)	386 (404)	186 (158)
Median [Q1, Q3]	190 [84.5, 341]	92.0 [92.0, 92.0]	78.5 [35.5, 129]	111 [111, 112]	44.5 [42.8, 46.3]	386 [243, 528]	117 [77.0, 292]
Median [min, max]	190 [29.0, 464]	92.0 [92.0, 92.0]	78.5 [34.0, 154]	111 [110, 112]	44.5 [41.0, 48.0]	386 [100, 671]	117 [29.0, 671]
FI_final
Mean (SD)	38.6 (45.7)	NA	12.0 (1.15)	14.0 (1.41)	12.0 (1.41)	11.5 (12.0)	29.0 (38.3)
Median [Q1, Q3]	25.0 [7.50, 43.5]	15.0 [15.0, 15.0]	12.0 [11.0, 13.0]	14.0 [13.5, 14.5]	12.0 [11.5, 12.5]	11.5 [7.25, 15.8]	14.0 [11.0, 31.3]
Median [min, max]	25.0 [1.00, 171]	15.0 [15.0, 15.0]	12.0 [11.0, 13.0]	14.0 [13.0, 15.0]	12.0 [11.0, 13.0]	11.5 [3.00, 20.0]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0138 (0.0118)	NA	0.00703 (0.00268)	0.00717 (0.000724)	0.0273 (0.00212)	0.0187 (0.0256)	0.0137 (0.0116)
Median [Q1, Q3]	0.0115 [0.00349, 0.0223]	0.0143 [0.0143, 0.0143]	0.00785 [0.00656, 0.00832]	0.00717 [0.00692, 0.00743]	0.0273 [0.0266, 0.0281]	0.0187 [0.00965, 0.0277]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.0115 [0.000567, 0.0361]	0.0143 [0.0143, 0.0143]	0.00785 [0.00314, 0.00928]	0.00717 [0.00666, 0.00768]	0.0273 [0.0258, 0.0288]	0.0187 [0.000608, 0.0368]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	2 (10.5%)	1 (100%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	3 (10.0%)
1	12 (63.2%)	0 (0%)	3 (75.0%)	0 (0%)	0 (0%)	1 (50.0%)	16 (53.3%)
Missing	5 (26.3%)	0 (0%)	1 (25.0%)	2 (100%)	2 (100%)	1 (50.0%)	11 (36.7%)

kruskal.test(FI_final ~ journal_code2, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by journal_code2
## Kruskal-Wallis chi-squared = 2.8427, df = 5, p-value = 0.7242

kruskal.test(FQ_final ~ journal_code2, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by journal_code2
## Kruskal-Wallis chi-squared = 3.1363, df = 5, p-value = 0.679

Box plots

p1 = ggplot(data =  fx_prim, aes(y = FI_final, x = as.factor(timing), fill = as.factor(journal_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index") 
p1

(1.2.6) By sex

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | sex, data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Both (N=3)	Men (N=2)	Women (N=25)	Overall (N=30)
no_rand
Mean (SD)	1080 (903)	1200 (0)	3510 (2370)	3110 (2350)
Median [Q1, Q3]	578 [564, 1350]	1200 [1200, 1200]	3270 [1650, 4430]	1980 [1430, 4090]
Median [min, max]	578 [549, 2130]	1200 [1200, 1200]	3270 [704, 7870]	1980 [549, 7870]
active_sample
Mean (SD)	452 (26.5)	1090 (49.5)	3060 (2130)	2670 (2130)
Median [Q1, Q3]	451 [439, 465]	1090 [1070, 1110]	1950 [1430, 4130]	1860 [1070, 3980]
Median [min, max]	451 [426, 479]	1090 [1060, 1130]	1950 [544, 7390]	1860 [426, 7390]
n_event
Mean (SD)	107 (108)	33.0 (5.66)	207 (161)	186 (158)
Median [Q1, Q3]	48.0 [44.5, 140]	33.0 [31.0, 35.0]	140 [92.0, 332]	117 [77.0, 292]
Median [min, max]	48.0 [41.0, 231]	33.0 [29.0, 37.0]	140 [34.0, 671]	117 [29.0, 671]
FI_final
Mean (SD)	10.3 (3.06)	3.50 (3.54)	33.3 (40.6)	29.0 (38.3)
Median [Q1, Q3]	11.0 [9.00, 12.0]	3.50 [2.25, 4.75]	20.0 [12.0, 40.0]	14.0 [11.0, 31.3]
Median [min, max]	11.0 [7.00, 13.0]	3.50 [1.00, 6.00]	20.0 [1.00, 171]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0231 (0.00749)	0.00313 (0.00310)	0.0134 (0.0117)	0.0137 (0.0116)
Median [Q1, Q3]	0.0258 [0.0202, 0.0273]	0.00313 [0.00204, 0.00423]	0.00801 [0.00361, 0.0188]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.0258 [0.0146, 0.0288]	0.00313 [0.000946, 0.00532]	0.00801 [0.000567, 0.0368]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	3 (12.0%)	3 (10.0%)
1	1 (33.3%)	2 (100%)	13 (52.0%)	16 (53.3%)
Missing	2 (66.7%)	0 (0%)	9 (36.0%)	11 (36.7%)

kruskal.test(FI_final ~ sex, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by sex
## Kruskal-Wallis chi-squared = 6.2219, df = 2, p-value = 0.04456

kruskal.test(FQ_final ~ sex, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by sex
## Kruskal-Wallis chi-squared = 4.5128, df = 2, p-value = 0.1047

Box plots

p1 = ggplot(data =  fx_prim, aes(y = FI_final, x = as.factor(sex), fill = as.factor(sex))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by sex", x = "Sex", y = "Fragility index") 
p1

(1.2.7) By placebo

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | placebo, data =  fx_prim, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Active (N=6)	Placebo (N=24)	Overall (N=30)
no_rand
Mean (SD)	2820 (1400)	3180 (2550)	3110 (2350)
Median [Q1, Q3]	2870 [1640, 4090]	1980 [1200, 4600]	1980 [1430, 4090]
Median [min, max]	2870 [1360, 4090]	1980 [549, 7870]	1980 [549, 7870]
active_sample
Mean (SD)	2550 (1390)	2700 (2310)	2670 (2130)
Median [Q1, Q3]	2540 [1410, 3660]	1860 [1020, 4330]	1860 [1070, 3980]
Median [min, max]	2540 [1050, 4090]	1860 [426, 7390]	1860 [426, 7390]
n_event
Mean (SD)	203 (182)	181 (156)	186 (158)
Median [Q1, Q3]	157 [50.0, 333]	117 [81.0, 251]	117 [77.0, 292]
Median [min, max]	157 [34.0, 464]	117 [29.0, 671]	117 [29.0, 671]
FI_final
Mean (SD)	30.7 (25.5)	28.6 (41.3)	29.0 (38.3)
Median [Q1, Q3]	20.5 [13.5, 38.0]	13.0 [7.75, 27.0]	14.0 [11.0, 31.3]
Median [min, max]	20.5 [11.0, 77.0]	13.0 [1.00, 171]	14.0 [1.00, 171]
FQ_final
Mean (SD)	0.0115 (0.00447)	0.0142 (0.0128)	0.0137 (0.0116)
Median [Q1, Q3]	0.0104 [0.00810, 0.0136]	0.00785 [0.00331, 0.0265]	0.00864 [0.00404, 0.0240]
Median [min, max]	0.0104 [0.00714, 0.0188]	0.00785 [0.000567, 0.0368]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	2 (33.3%)	1 (4.2%)	3 (10.0%)
1	4 (66.7%)	12 (50.0%)	16 (53.3%)
Missing	0 (0%)	11 (45.8%)	11 (36.7%)

kruskal.test(FI_final ~ placebo, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by placebo
## Kruskal-Wallis chi-squared = 1.19, df = 1, p-value = 0.2753

kruskal.test(FQ_final ~ placebo, data = fx_prim)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by placebo
## Kruskal-Wallis chi-squared = 0.096774, df = 1, p-value = 0.7557

Box plots

p1 = ggplot(data =  fx_prim, aes(y = FI_final, x = as.factor(control), fill = as.factor(control))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by types of control", x = "Types of control", y = "Fragility index") 
p1

(1.3) Analyses with P< 0.001

Data set:

p_sig = subset(fi_sig, Pval_screen<=0.001)

(1.3.1) Overall

# Comparison of different P values:
fi_sig$p_sig1[fi_sig$p_value<=0.001] = "Highly significant"
  fi_sig$p_sig1[fi_sig$p_value>0.001] = "Significant"
fi_sig$p_sig2[fi_sig$Pval_screen<=0.001] = "Highly significant"
  fi_sig$p_sig2[fi_sig$Pval_screen>0.001] = "Significant"

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | p_sig2 , data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Highly significant (N=44)	Significant (N=85)	Overall (N=129)
no_rand
Mean (SD)	3900 (2800)	2680 (1980)	3090 (2360)
Median [Q1, Q3]	2840 [1640, 7180]	1960 [1200, 4090]	1960 [1360, 4090]
Median [min, max]	2840 [549, 7870]	1960 [450, 7870]	1960 [450, 7870]
active_sample
Mean (SD)	3460 (2540)	2300 (1790)	2700 (2140)
Median [Q1, Q3]	2400 [1260, 6530]	1770 [1100, 3400]	1860 [1130, 3700]
Median [min, max]	2400 [426, 7810]	1770 [339, 6670]	1860 [339, 7810]
n_event
Mean (SD)	220 (193)	150 (162)	174 (176)
Median [Q1, Q3]	125 [80.5, 331]	79.0 [39.0, 178]	101 [51.0, 246]
Median [min, max]	125 [34.0, 764]	79.0 [10.0, 691]	101 [10.0, 764]
FI_final
Mean (SD)	37.9 (33.4)	6.93 (6.19)	17.5 (24.8)
Median [Q1, Q3]	25.5 [17.8, 42.3]	5.00 [2.00, 9.00]	9.00 [4.00, 22.0]
Median [min, max]	25.5 [9.00, 171]	5.00 [1.00, 29.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.0162 (0.0156)	0.00401 (0.00333)	0.00815 (0.0111)
Median [Q1, Q3]	0.0128 [0.00667, 0.0189]	0.00307 [0.00150, 0.00532]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.0128 [0.00230, 0.0966]	0.00307 [0.000151, 0.0146]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	6 (13.6%)	4 (4.7%)	10 (7.8%)
1	23 (52.3%)	50 (58.8%)	73 (56.6%)
Missing	15 (34.1%)	31 (36.5%)	46 (35.7%)

createTable(compareGroups(p_sig2 ~ no_rand + active_sample + n_event + FI_final + FQ_final + missing_fi, data = fi_sig, method = c(no_rand = 2, active_sample = 2, n_event = 2, FI_final = 2, FQ_final = 2)))

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning in chisq.test(xx, correct = FALSE): Chi-squared approximation may be
## incorrect

## 
## --------Summary descriptives table by 'p_sig2'---------
## 
## ___________________________________________________________ 
##               Highly significant   Significant    p.overall 
##                      N=44              N=85                 
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 
## no_rand        2843 [1636;7180]  1964 [1199;4093]   0.046   
## active_sample  2396 [1256;6533]  1765 [1101;3399]   0.020   
## n_event         124 [80.5;330]   79.0 [39.0;178]    0.006   
## FI_final       25.5 [17.8;42.2]  5.00 [2.00;9.00]  <0.001   
## FQ_final       0.01 [0.01;0.02]  0.00 [0.00;0.01]  <0.001   
## missing_fi:                                         0.090   
##     0             6 (20.7%)         4 (7.41%)               
##     1             23 (79.3%)        50 (92.6%)              
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

# Subset of analyses whose P-value<= 0.001
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Overall (N=44)
no_rand
Mean (SD)	3900 (2800)
Median [Q1, Q3]	2840 [1640, 7180]
Median [min, max]	2840 [549, 7870]
active_sample
Mean (SD)	3460 (2540)
Median [Q1, Q3]	2400 [1260, 6530]
Median [min, max]	2400 [426, 7810]
n_event
Mean (SD)	220 (193)
Median [Q1, Q3]	125 [80.5, 331]
Median [min, max]	125 [34.0, 764]
FI_final
Mean (SD)	37.9 (33.4)
Median [Q1, Q3]	25.5 [17.8, 42.3]
Median [min, max]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.0162 (0.0156)
Median [Q1, Q3]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	6 (13.6%)
1	23 (52.3%)
Missing	15 (34.1%)

Relationship between sample size/active sample/no. events and FI

p = ggplot(data = p_sig, aes(x = no_rand, y = FI_final))
p1 = p + geom_point() + geom_smooth() + labs(x = "Number of participants at randomisation", y = "Fragility index") + theme_bw()

p0 = ggplot(data = p_sig, aes(x = active_sample, y = FI_final))
p2 = p0 + geom_point() + geom_smooth() + labs(x = "Number of participants included in the analyses", y = "Fragility index") + theme_bw()

p.0 = ggplot(data = p_sig, aes(x = n_event, y = FI_final))
p3 = p.0 + geom_point() + geom_smooth() + labs(x = "Number of participants with fracture events", y = "Fragility index") + theme_bw()

#grid.arrange(p1, p2, p3, nrow = 1)
grid.arrange(p1, p3, nrow = 1, top = textGrob("Relationship between Number of participants and Fragility index", gp = gpar(fontsize = 20, font = 3)))

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

(1.3.2) By fracture sites

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code1), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Clin_fx (N=2)	OFx (N=3)	MOF (N=2)	NonVert_fx (N=4)	Vert_fx (N=30)	ClinVert_fx (N=3)	Overall (N=44)
no_rand
Mean (SD)	7460 (393)	3400 (1210)	2870 (1730)	6340 (2060)	3270 (2740)	5750 (3550)	3900 (2800)
Median [Q1, Q3]	7460 [7320, 7600]	4090 [3050, 4090]	2870 [2260, 3480]	7180 [6200, 7320]	1650 [1260, 6410]	7740 [4690, 7800]	2840 [1640, 7180]
Median [min, max]	7460 [7180, 7740]	4090 [2000, 4090]	2870 [1650, 4090]	7180 [3270, 7740]	1650 [549, 7870]	7740 [1650, 7870]	2840 [549, 7870]
active_sample
Mean (SD)	6620 (100)	3250 (1130)	2400 (1600)	5560 (2120)	2890 (2480)	5230 (3350)	3460 (2540)
Median [Q1, Q3]	6620 [6580, 6660]	3840 [2890, 3910]	2400 [1830, 2970]	6590 [5490, 6650]	1440 [1050, 5280]	6430 [3940, 7120]	2400 [1260, 6530]
Median [min, max]	6620 [6550, 6690]	3840 [1950, 3980]	2400 [1270, 3530]	6590 [2380, 6670]	1440 [426, 7390]	6430 [1440, 7810]	2400 [426, 7810]
n_event
Mean (SD)	505 (366)	431 (197)	200 (220)	357 (229)	171 (156)	144 (55.6)	220 (193)
Median [Q1, Q3]	505 [376, 635]	323 [318, 491]	200 [122, 277]	290 [211, 436]	100 [73.5, 260]	121 [112, 164]	125 [80.5, 331]
Median [min, max]	505 [246, 764]	323 [312, 658]	200 [44.0, 355]	290 [168, 680]	100 [34.0, 696]	121 [103, 207]	125 [34.0, 764]
FI_final
Mean (SD)	62.5 (37.5)	42.7 (19.4)	17.5 (12.0)	28.0 (10.1)	38.9 (38.2)	33.0 (13.1)	37.9 (33.4)
Median [Q1, Q3]	62.5 [49.3, 75.8]	33.0 [31.5, 49.0]	17.5 [13.3, 21.8]	24.0 [22.5, 29.5]	23.5 [17.0, 44.3]	39.0 [28.5, 40.5]	25.5 [17.8, 42.3]
Median [min, max]	62.5 [36.0, 89.0]	33.0 [30.0, 65.0]	17.5 [9.00, 26.0]	24.0 [21.0, 43.0]	23.5 [11.0, 171]	39.0 [18.0, 42.0]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.00949 (0.00580)	0.0138 (0.00543)	0.00723 (0.000175)	0.00593 (0.00343)	0.0196 (0.0177)	0.00800 (0.00395)	0.0162 (0.0156)
Median [Q1, Q3]	0.00949 [0.00743, 0.0115]	0.0169 [0.0122, 0.0169]	0.00723 [0.00717, 0.00730]	0.00502 [0.00338, 0.00757]	0.0174 [0.00785, 0.0258]	0.00653 [0.00576, 0.00951]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.00949 [0.00538, 0.0136]	0.0169 [0.00754, 0.0169]	0.00723 [0.00711, 0.00736]	0.00502 [0.00315, 0.0105]	0.0174 [0.00230, 0.0966]	0.00653 [0.00499, 0.0125]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	2 (66.7%)	0 (0%)	0 (0%)	4 (13.3%)	0 (0%)	6 (13.6%)
1	2 (100%)	1 (33.3%)	2 (100%)	4 (100%)	13 (43.3%)	1 (33.3%)	23 (52.3%)
Missing	0 (0%)	0 (0%)	0 (0%)	0 (0%)	13 (43.3%)	2 (66.7%)	15 (34.1%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code2), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any (N=2)	Osteoporotic (N=5)	Non-Vertebrae (N=4)	Vertebrae (N=30)	Clinical Vertebrae (N=3)	Overall (N=44)
no_rand
Mean (SD)	7460 (393)	3180 (1250)	6340 (2060)	3270 (2740)	5750 (3550)	3900 (2800)
Median [Q1, Q3]	7460 [7320, 7600]	4090 [2000, 4090]	7180 [6200, 7320]	1650 [1260, 6410]	7740 [4690, 7800]	2840 [1640, 7180]
Median [min, max]	7460 [7180, 7740]	4090 [1650, 4090]	7180 [3270, 7740]	1650 [549, 7870]	7740 [1650, 7870]	2840 [549, 7870]
active_sample
Mean (SD)	6620 (100)	2910 (1230)	5560 (2120)	2890 (2480)	5230 (3350)	3460 (2540)
Median [Q1, Q3]	6620 [6580, 6660]	3530 [1950, 3840]	6590 [5490, 6650]	1440 [1050, 5280]	6430 [3940, 7120]	2400 [1260, 6530]
Median [min, max]	6620 [6550, 6690]	3530 [1270, 3980]	6590 [2380, 6670]	1440 [426, 7390]	6430 [1440, 7810]	2400 [426, 7810]
n_event
Mean (SD)	505 (366)	338 (218)	357 (229)	171 (156)	144 (55.6)	220 (193)
Median [Q1, Q3]	505 [376, 635]	323 [312, 355]	290 [211, 436]	100 [73.5, 260]	121 [112, 164]	125 [80.5, 331]
Median [min, max]	505 [246, 764]	323 [44.0, 658]	290 [168, 680]	100 [34.0, 696]	121 [103, 207]	125 [34.0, 764]
FI_final
Mean (SD)	62.5 (37.5)	32.6 (20.4)	28.0 (10.1)	38.9 (38.2)	33.0 (13.1)	37.9 (33.4)
Median [Q1, Q3]	62.5 [49.3, 75.8]	30.0 [26.0, 33.0]	24.0 [22.5, 29.5]	23.5 [17.0, 44.3]	39.0 [28.5, 40.5]	25.5 [17.8, 42.3]
Median [min, max]	62.5 [36.0, 89.0]	30.0 [9.00, 65.0]	24.0 [21.0, 43.0]	23.5 [11.0, 171]	39.0 [18.0, 42.0]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.00949 (0.00580)	0.0112 (0.00526)	0.00593 (0.00343)	0.0196 (0.0177)	0.00800 (0.00395)	0.0162 (0.0156)
Median [Q1, Q3]	0.00949 [0.00743, 0.0115]	0.00754 [0.00736, 0.0169]	0.00502 [0.00338, 0.00757]	0.0174 [0.00785, 0.0258]	0.00653 [0.00576, 0.00951]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.00949 [0.00538, 0.0136]	0.00754 [0.00711, 0.0169]	0.00502 [0.00315, 0.0105]	0.0174 [0.00230, 0.0966]	0.00653 [0.00499, 0.0125]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	2 (40.0%)	0 (0%)	4 (13.3%)	0 (0%)	6 (13.6%)
1	2 (100%)	3 (60.0%)	4 (100%)	13 (43.3%)	1 (33.3%)	23 (52.3%)
Missing	0 (0%)	0 (0%)	0 (0%)	13 (43.3%)	2 (66.7%)	15 (34.1%)

kruskal.test(FI_final ~ fx_code2, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by fx_code2
## Kruskal-Wallis chi-squared = 1.8727, df = 4, p-value = 0.7592

kruskal.test(FQ_final ~ fx_code2, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by fx_code2
## Kruskal-Wallis chi-squared = 9.4802, df = 4, p-value = 0.05016

Box plots

p1 = ggplot(data = p_sig, aes(y = FI_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Fracture sites", y = "Fragility index")
p2 = ggplot(data = p_sig, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Fracture sites", y = "Fragility quotient")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by fracture sites", gp = gpar(fontsize = 20, font = 1)))

(1.3.3) By pharmacological interventions

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code1), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Ibandronate (N=1)	Risedronate (N=1)	Minodronate (N=1)	Zoledronate (N=6)	Teriparatide (N=9)	Abaloparatide (N=2)	Romosozumab (N=13)	Denosumab (N=3)	Strontium_ranelate (N=7)	Calcium_VitD (N=1)	Overall (N=44)
no_rand
Mean (SD)	NA	NA	NA	6780 (2340)	1090 (354)	1650 (0)	5760 (1600)	7870 (0)	1700 (354)	NA	3900 (2800)
Median [Q1, Q3]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	7740 [7740, 7740]	1100 [1090, 1360]	1650 [1650, 1650]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 1650]	3270 [3270, 3270]	2840 [1640, 7180]
Median [min, max]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	7740 [2000, 7740]	1100 [549, 1640]	1650 [1650, 1650]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1220, 2420]	3270 [3270, 3270]	2840 [549, 7870]
active_sample
Mean (SD)	NA	NA	NA	5470 (1770)	883 (306)	1330 (95.5)	5360 (1510)	7530 (240)	1500 (421)	NA	3460 (2540)
Median [Q1, Q3]	1950 [1950, 1950]	1330 [1330, 1330]	544 [544, 544]	6050 [5680, 6500]	892 [882, 1050]	1330 [1300, 1370]	6640 [3840, 6650]	7390 [7390, 7600]	1440 [1300, 1440]	2380 [2380, 2380]	2400 [1260, 6530]
Median [min, max]	1950 [1950, 1950]	1330 [1330, 1330]	544 [544, 544]	6050 [1950, 6550]	892 [426, 1430]	1330 [1270, 1400]	6640 [3530, 6910]	7390 [7390, 7810]	1440 [1150, 2420]	2380 [2380, 2380]	2400 [426, 7810]
n_event
Mean (SD)	NA	NA	NA	389 (287)	64.8 (25.0)	39.0 (7.07)	245 (160)	184 (145)	334 (182)	NA	220 (193)
Median [Q1, Q3]	110 [110, 110]	58.0 [58.0, 58.0]	100 [100, 100]	357 [155, 611]	51.0 [46.0, 86.0]	39.0 [36.5, 41.5]	225 [106, 323]	121 [102, 236]	330 [234, 360]	355 [355, 355]	125 [80.5, 331]
Median [min, max]	110 [110, 110]	58.0 [58.0, 58.0]	100 [100, 100]	357 [73.0, 764]	51.0 [36.0, 100]	39.0 [34.0, 44.0]	225 [75.0, 658]	121 [82.0, 350]	330 [128, 696]	355 [355, 355]	125 [34.0, 764]
FI_final
Mean (SD)	NA	NA	NA	69.3 (53.8)	17.1 (5.21)	11.0 (2.83)	38.3 (16.9)	64.3 (63.9)	44.7 (32.4)	NA	37.9 (33.4)
Median [Q1, Q3]	15.0 [15.0, 15.0]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	42.5 [39.0, 77.5]	17.0 [13.0, 22.0]	11.0 [10.0, 12.0]	36.0 [26.0, 42.0]	39.0 [28.0, 88.0]	45.0 [21.0, 48.5]	25.0 [25.0, 25.0]	25.5 [17.8, 42.3]
Median [min, max]	15.0 [15.0, 15.0]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	42.5 [33.0, 171]	17.0 [11.0, 25.0]	11.0 [9.00, 13.0]	36.0 [21.0, 77.0]	39.0 [17.0, 137]	45.0 [18.0, 111]	25.0 [25.0, 25.0]	25.5 [9.00, 171]
FQ_final
Mean (SD)	NA	NA	NA	0.0134 (0.00928)	0.0212 (0.00726)	0.00819 (0.00153)	0.00820 (0.00525)	0.00861 (0.00870)	0.0325 (0.0296)	NA	0.0162 (0.0156)
Median [Q1, Q3]	0.00768 [0.00768, 0.00768]	0.00828 [0.00828, 0.00828]	0.0368 [0.0368, 0.0368]	0.0101 [0.00661, 0.0161]	0.0247 [0.0162, 0.0258]	0.00819 [0.00765, 0.00874]	0.00601 [0.00391, 0.0115]	0.00499 [0.00365, 0.0118]	0.0188 [0.0162, 0.0336]	0.0105 [0.0105, 0.0105]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.00768 [0.00768, 0.00768]	0.00828 [0.00828, 0.00828]	0.0368 [0.0368, 0.0368]	0.0101 [0.00653, 0.0301]	0.0247 [0.00770, 0.0288]	0.00819 [0.00711, 0.00928]	0.00601 [0.00315, 0.0188]	0.00499 [0.00230, 0.0185]	0.0188 [0.0125, 0.0966]	0.0105 [0.0105, 0.0105]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	0 (0%)	1 (16.7%)	2 (22.2%)	0 (0%)	2 (15.4%)	0 (0%)	1 (14.3%)	0 (0%)	6 (13.6%)
1	0 (0%)	1 (100%)	1 (100%)	5 (83.3%)	1 (11.1%)	2 (100%)	11 (84.6%)	0 (0%)	1 (14.3%)	1 (100%)	23 (52.3%)
Missing	1 (100%)	0 (0%)	0 (0%)	0 (0%)	6 (66.7%)	0 (0%)	0 (0%)	3 (100%)	5 (71.4%)	0 (0%)	15 (34.1%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code2), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Bisphosphonates (N=9)	PTH analog (N=11)	Romosozumab (N=13)	Denosumab (N=3)	Strontium_ranelate (N=7)	Calcium_VitD (N=1)	Overall (N=44)
no_rand
Mean (SD)	5000 (3270)	1190 (387)	5760 (1600)	7870 (0)	1700 (354)	NA	3900 (2800)
Median [Q1, Q3]	7740 [1960, 7740]	1100 [1090, 1500]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 1650]	3270 [3270, 3270]	2840 [1640, 7180]
Median [min, max]	7740 [704, 7740]	1100 [549, 1650]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1220, 2420]	3270 [3270, 3270]	2840 [549, 7870]
active_sample
Mean (SD)	4070 (2550)	965 (330)	5360 (1510)	7530 (240)	1500 (421)	NA	3460 (2540)
Median [Q1, Q3]	5680 [1950, 6430]	892 [882, 1160]	6640 [3840, 6650]	7390 [7390, 7600]	1440 [1300, 1440]	2380 [2380, 2380]	2400 [1260, 6530]
Median [min, max]	5680 [544, 6550]	892 [426, 1430]	6640 [3530, 6910]	7390 [7390, 7810]	1440 [1150, 2420]	2380 [2380, 2380]	2400 [426, 7810]
n_event
Mean (SD)	289 (273)	60.1 (24.7)	245 (160)	184 (145)	334 (182)	NA	220 (193)
Median [Q1, Q3]	110 [100, 402]	48.0 [42.5, 84.5]	225 [106, 323]	121 [102, 236]	330 [234, 360]	355 [355, 355]	125 [80.5, 331]
Median [min, max]	110 [58.0, 764]	48.0 [34.0, 100]	225 [75.0, 658]	121 [82.0, 350]	330 [128, 696]	355 [355, 355]	125 [34.0, 764]
FI_final
Mean (SD)	51.3 (50.4)	16.0 (5.35)	38.3 (16.9)	64.3 (63.9)	44.7 (32.4)	NA	37.9 (33.4)
Median [Q1, Q3]	38.0 [20.0, 43.0]	15.0 [12.0, 19.5]	36.0 [26.0, 42.0]	39.0 [28.0, 88.0]	45.0 [21.0, 48.5]	25.0 [25.0, 25.0]	25.5 [17.8, 42.3]
Median [min, max]	38.0 [11.0, 171]	15.0 [9.00, 25.0]	36.0 [21.0, 77.0]	39.0 [17.0, 137]	45.0 [18.0, 111]	25.0 [25.0, 25.0]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.0148 (0.0113)	0.0188 (0.00838)	0.00820 (0.00525)	0.00861 (0.00870)	0.0325 (0.0296)	NA	0.0162 (0.0156)
Median [Q1, Q3]	0.00828 [0.00670, 0.0169]	0.0193 [0.0118, 0.0258]	0.00601 [0.00391, 0.0115]	0.00499 [0.00365, 0.0118]	0.0188 [0.0162, 0.0336]	0.0105 [0.0105, 0.0105]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.00828 [0.00653, 0.0368]	0.0193 [0.00711, 0.0288]	0.00601 [0.00315, 0.0188]	0.00499 [0.00230, 0.0185]	0.0188 [0.0125, 0.0966]	0.0105 [0.0105, 0.0105]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	1 (11.1%)	2 (18.2%)	2 (15.4%)	0 (0%)	1 (14.3%)	0 (0%)	6 (13.6%)
1	7 (77.8%)	3 (27.3%)	11 (84.6%)	0 (0%)	1 (14.3%)	1 (100%)	23 (52.3%)
Missing	1 (11.1%)	6 (54.5%)	0 (0%)	3 (100%)	5 (71.4%)	0 (0%)	15 (34.1%)

kruskal.test(FI_final ~ interv_code2, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by interv_code2
## Kruskal-Wallis chi-squared = 16.156, df = 5, p-value = 0.006412

kruskal.test(FQ_final ~ interv_code2, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by interv_code2
## Kruskal-Wallis chi-squared = 17.135, df = 5, p-value = 0.00425

Box plots

p1 = ggplot(data = p_sig, aes(y = FI_final, x = as.factor(interv_code2), fill = as.factor(interv_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Pharmacological interventions", y = "Fragility index")
p2 = ggplot(data = p_sig, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Pharmacological interventions", y = "Fragility quotine")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by intervention sites", gp = gpar(fontsize = 20, font = 1)))

(1.3.4) Timing of fracture assessment

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(timing), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	2 (N=5)	3 (N=6)	4 (N=17)	5 (N=14)	6 (N=1)	8 (N=1)	Overall (N=44)
no_rand
Mean (SD)	4350 (2770)	1550 (993)	3770 (2600)	5200 (3110)	NA	NA	3900 (2800)
Median [Q1, Q3]	4090 [1650, 7180]	1640 [843, 1650]	4090 [1100, 7180]	7740 [1730, 7740]	1650 [1650, 1650]	2000 [2000, 2000]	2840 [1640, 7180]
Median [min, max]	4090 [1630, 7180]	1640 [549, 3270]	4090 [704, 7180]	7740 [1220, 7870]	1650 [1650, 1650]	2000 [2000, 2000]	2840 [549, 7870]
active_sample
Mean (SD)	4050 (2710)	1220 (726)	3430 (2480)	4530 (2660)	NA	NA	3460 (2540)
Median [Q1, Q3]	3980 [1390, 6640]	1330 [655, 1420]	3660 [892, 6650]	5680 [1570, 6540]	1150 [1150, 1150]	1950 [1950, 1950]	2400 [1260, 6530]
Median [min, max]	3980 [1330, 6910]	1330 [426, 2380]	3660 [544, 6690]	5680 [1220, 7810]	1150 [1150, 1150]	1950 [1950, 1950]	2400 [426, 7810]
n_event
Mean (SD)	132 (110)	93.0 (128)	192 (156)	300 (215)	NA	NA	220 (193)
Median [Q1, Q3]	76.0 [75.0, 128]	42.5 [37.3, 47.0]	106 [92.0, 246]	296 [113, 378]	696 [696, 696]	312 [312, 312]	125 [80.5, 331]
Median [min, max]	76.0 [58.0, 323]	42.5 [34.0, 355]	106 [46.0, 658]	296 [73.0, 764]	696 [696, 696]	312 [312, 312]	125 [34.0, 764]
FI_final
Mean (SD)	22.2 (7.46)	13.7 (5.75)	32.7 (17.6)	55.3 (46.3)	NA	NA	37.9 (33.4)
Median [Q1, Q3]	24.0 [19.0, 27.0]	12.0 [11.0, 13.0]	25.0 [21.0, 40.0]	42.5 [26.8, 50.3]	111 [111, 111]	33.0 [33.0, 33.0]	25.5 [17.8, 42.3]
Median [min, max]	24.0 [11.0, 30.0]	12.0 [9.00, 25.0]	25.0 [15.0, 77.0]	42.5 [15.0, 171]	111 [111, 111]	33.0 [33.0, 33.0]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.00741 (0.00410)	0.0149 (0.00976)	0.0151 (0.00970)	0.0153 (0.0108)	NA	NA	0.0162 (0.0156)
Median [Q1, Q3]	0.00754 [0.00391, 0.00828]	0.00990 [0.00810, 0.0220]	0.0143 [0.00601, 0.0193]	0.0130 [0.00661, 0.0187]	0.0966 [0.0966, 0.0966]	0.0169 [0.0169, 0.0169]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.00754 [0.00361, 0.0137]	0.00990 [0.00711, 0.0288]	0.0143 [0.00315, 0.0368]	0.0130 [0.00230, 0.0361]	0.0966 [0.0966, 0.0966]	0.0169 [0.0169, 0.0169]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	1 (20.0%)	0 (0%)	3 (17.6%)	1 (7.1%)	0 (0%)	1 (100%)	6 (13.6%)
1	3 (60.0%)	4 (66.7%)	10 (58.8%)	6 (42.9%)	0 (0%)	0 (0%)	23 (52.3%)
Missing	1 (20.0%)	2 (33.3%)	4 (23.5%)	7 (50.0%)	1 (100%)	0 (0%)	15 (34.1%)

kruskal.test(FI_final ~ timing, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by timing
## Kruskal-Wallis chi-squared = 16.328, df = 5, p-value = 0.005967

kruskal.test(FQ_final ~ timing, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by timing
## Kruskal-Wallis chi-squared = 5.6791, df = 5, p-value = 0.3387

Box plots

p1 = ggplot(data = p_sig, aes(y = FI_final, x = as.factor(timing), fill = as.factor(timing))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index")
p1

(1.3.5) By journal

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(journal_code2), data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	NEJM (N=31)	Lancet (N=2)	JAMA (N=4)	JBMR (N=1)	JCEM (N=4)	Other (N=2)	Overall (N=44)
no_rand
Mean (SD)	4950 (2700)	1360 (0)	1640 (8.02)	NA	1190 (874)	1180 (668)	3900 (2800)
Median [Q1, Q3]	4090 [1820, 7460]	1360 [1360, 1360]	1640 [1640, 1650]	1960 [1960, 1960]	901 [571, 1520]	1180 [940, 1410]	2840 [1640, 7180]
Median [min, max]	4090 [1090, 7870]	1360 [1360, 1360]	1640 [1630, 1650]	1960 [1960, 1960]	901 [549, 2420]	1180 [704, 1650]	2840 [549, 7870]
active_sample
Mean (SD)	4410 (2450)	1050 (0)	1360 (73.1)	NA	1130 (934)	847 (428)	3460 (2540)
Median [Q1, Q3]	4090 [1700, 6650]	1050 [1050, 1050]	1370 [1310, 1410]	1950 [1950, 1950]	838 [445, 1520]	847 [695, 998]	2400 [1260, 6530]
Median [min, max]	4090 [882, 7810]	1050 [1050, 1050]	1370 [1270, 1430]	1950 [1950, 1950]	838 [426, 2420]	847 [544, 1150]	2400 [426, 7810]
n_event
Mean (SD)	250 (190)	96.0 (5.66)	43.0 (10.9)	NA	170 (148)	398 (421)	220 (193)
Median [Q1, Q3]	221 [94.5, 353]	96.0 [94.0, 98.0]	40.0 [35.5, 47.5]	110 [110, 110]	155 [46.3, 278]	398 [249, 547]	125 [80.5, 331]
Median [min, max]	221 [46.0, 764]	96.0 [92.0, 100]	40.0 [34.0, 58.0]	110 [110, 110]	155 [41.0, 330]	398 [100, 696]	125 [34.0, 764]
FI_final
Mean (SD)	43.6 (34.3)	16.0 (1.41)	11.0 (1.63)	NA	23.0 (15.6)	65.5 (64.3)	37.9 (33.4)
Median [Q1, Q3]	36.0 [23.5, 44.0]	16.0 [15.5, 16.5]	11.0 [10.5, 11.5]	15.0 [15.0, 15.0]	18.0 [12.5, 28.5]	65.5 [42.8, 88.3]	25.5 [17.8, 42.3]
Median [min, max]	36.0 [17.0, 171]	16.0 [15.0, 17.0]	11.0 [9.00, 13.0]	15.0 [15.0, 15.0]	18.0 [11.0, 45.0]	65.5 [20.0, 111]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.0134 (0.00951)	0.0153 (0.00135)	0.00809 (0.000924)	NA	0.0230 (0.00512)	0.0667 (0.0423)	0.0162 (0.0156)
Median [Q1, Q3]	0.0115 [0.00594, 0.0187]	0.0153 [0.0148, 0.0157]	0.00799 [0.00755, 0.00853]	0.00768 [0.00768, 0.00768]	0.0223 [0.0187, 0.0266]	0.0667 [0.0517, 0.0816]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.0115 [0.00230, 0.0361]	0.0153 [0.0143, 0.0162]	0.00799 [0.00711, 0.00928]	0.00768 [0.00768, 0.00768]	0.0223 [0.0186, 0.0288]	0.0667 [0.0368, 0.0966]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	3 (9.7%)	2 (100%)	0 (0%)	0 (0%)	1 (25.0%)	0 (0%)	6 (13.6%)
1	17 (54.8%)	0 (0%)	4 (100%)	0 (0%)	1 (25.0%)	1 (50.0%)	23 (52.3%)
Missing	11 (35.5%)	0 (0%)	0 (0%)	1 (100%)	2 (50.0%)	1 (50.0%)	15 (34.1%)

kruskal.test(FI_final ~ journal_code2, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by journal_code2
## Kruskal-Wallis chi-squared = 18.002, df = 5, p-value = 0.002943

kruskal.test(FQ_final ~ journal_code2, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by journal_code2
## Kruskal-Wallis chi-squared = 11.179, df = 5, p-value = 0.04794

Box plots

p1 = ggplot(data = p_sig, aes(y = FI_final, x = as.factor(timing), fill = as.factor(journal_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index") 
p1

(1.3.6) By sex

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | sex, data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Both (N=2)	Women (N=42)	Overall (N=44)
no_rand
Mean (SD)	564 (20.5)	4060 (2760)	3900 (2800)
Median [Q1, Q3]	564 [556, 571]	3680 [1650, 7180]	2840 [1640, 7180]
Median [min, max]	564 [549, 578]	3680 [704, 7870]	2840 [549, 7870]
active_sample
Mean (SD)	439 (17.7)	3610 (2510)	3460 (2540)
Median [Q1, Q3]	439 [432, 445]	2980 [1340, 6540]	2400 [1260, 6530]
Median [min, max]	439 [426, 451]	2980 [544, 7810]	2400 [426, 7810]
n_event
Mean (SD)	44.5 (4.95)	229 (193)	220 (193)
Median [Q1, Q3]	44.5 [42.8, 46.3]	148 [83.8, 332]	125 [80.5, 331]
Median [min, max]	44.5 [41.0, 48.0]	148 [34.0, 764]	125 [34.0, 764]
FI_final
Mean (SD)	12.0 (1.41)	39.1 (33.7)	37.9 (33.4)
Median [Q1, Q3]	12.0 [11.5, 12.5]	26.5 [19.3, 42.8]	25.5 [17.8, 42.3]
Median [min, max]	12.0 [11.0, 13.0]	26.5 [9.00, 171]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.0273 (0.00212)	0.0156 (0.0158)	0.0162 (0.0156)
Median [Q1, Q3]	0.0273 [0.0266, 0.0281]	0.0120 [0.00661, 0.0187]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.0273 [0.0258, 0.0288]	0.0120 [0.00230, 0.0966]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	6 (14.3%)	6 (13.6%)
1	0 (0%)	23 (54.8%)	23 (52.3%)
Missing	2 (100%)	13 (31.0%)	15 (34.1%)

kruskal.test(FI_final ~ sex, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by sex
## Kruskal-Wallis chi-squared = 4.2347, df = 1, p-value = 0.0396

kruskal.test(FQ_final ~ sex, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by sex
## Kruskal-Wallis chi-squared = 3.0508, df = 1, p-value = 0.0807

Box plots

p1 = ggplot(data = p_sig, aes(y = FI_final, x = as.factor(sex), fill = as.factor(sex))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by sex", x = "Sex", y = "Fragility index") 
p1

(1.3.7) By placebo

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | placebo, data = p_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Active (N=11)	Placebo (N=33)	Overall (N=44)
no_rand
Mean (SD)	2930 (1340)	4230 (3080)	3900 (2800)
Median [Q1, Q3]	4090 [1640, 4090]	2420 [1630, 7180]	2840 [1640, 7180]
Median [min, max]	4090 [1360, 4090]	2420 [549, 7870]	2840 [549, 7870]
active_sample
Mean (SD)	2630 (1350)	3740 (2790)	3460 (2540)
Median [Q1, Q3]	3530 [1330, 3750]	2380 [1220, 6650]	2400 [1260, 6530]
Median [min, max]	3530 [1050, 4090]	2380 [426, 7810]	2400 [426, 7810]
n_event
Mean (SD)	226 (193)	218 (195)	220 (193)
Median [Q1, Q3]	221 [68.0, 339]	121 [82.0, 330]	125 [80.5, 331]
Median [min, max]	221 [34.0, 658]	121 [41.0, 764]	125 [34.0, 764]
FI_final
Mean (SD)	32.1 (23.1)	39.8 (36.3)	37.9 (33.4)
Median [Q1, Q3]	26.0 [14.0, 45.0]	25.0 [20.0, 42.0]	25.5 [17.8, 42.3]
Median [min, max]	26.0 [9.00, 77.0]	25.0 [11.0, 171]	25.5 [9.00, 171]
FQ_final
Mean (SD)	0.0118 (0.00431)	0.0176 (0.0177)	0.0162 (0.0156)
Median [Q1, Q3]	0.0115 [0.00762, 0.0153]	0.0136 [0.00601, 0.0258]	0.0128 [0.00667, 0.0189]
Median [min, max]	0.0115 [0.00711, 0.0188]	0.0136 [0.00230, 0.0966]	0.0128 [0.00230, 0.0966]
as.factor(missing_fi)
0	4 (36.4%)	2 (6.1%)	6 (13.6%)
1	7 (63.6%)	16 (48.5%)	23 (52.3%)
Missing	0 (0%)	15 (45.5%)	15 (34.1%)

kruskal.test(FI_final ~ placebo, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by placebo
## Kruskal-Wallis chi-squared = 0.42368, df = 1, p-value = 0.5151

kruskal.test(FQ_final ~ placebo, data = p_sig)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by placebo
## Kruskal-Wallis chi-squared = 0.097153, df = 1, p-value = 0.7553

Box plots

p1 = ggplot(data = p_sig, aes(y = FI_final, x = as.factor(control), fill = as.factor(control))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by types of control", x = "Types of control", y = "Fragility index") 
p1

(2) Only analyses from the primary analyses (i.e., those from the extended studies or sensitivity/subgroup analyses will be excluded)

Set-up data

ori_st = subset(fi_sig, sen_analysis == 0)

(2.1) Overall

(2.1.1) Overall

# Comparison
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(sen_analysis), data = fi_sig, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	0 (N=112)	1 (N=17)	Overall (N=129)
no_rand
Mean (SD)	3240 (2450)	2110 (1220)	3090 (2360)
Median [Q1, Q3]	1980 [1360, 4430]	1650 [1200, 3270]	1960 [1360, 4090]
Median [min, max]	1980 [450, 7870]	1650 [549, 4090]	1960 [450, 7870]
active_sample
Mean (SD)	2820 (2230)	1880 (1140)	2700 (2140)
Median [Q1, Q3]	1860 [1130, 4020]	1440 [1110, 2420]	1860 [1130, 3700]
Median [min, max]	1860 [339, 7810]	1440 [426, 4090]	1860 [339, 7810]
n_event
Mean (SD)	172 (181)	186 (133)	174 (176)
Median [Q1, Q3]	95.5 [52.5, 227]	190 [41.0, 330]	101 [51.0, 246]
Median [min, max]	95.5 [10.0, 764]	190 [19.0, 375]	101 [10.0, 764]
FI_final
Mean (SD)	17.4 (25.5)	18.1 (20.5)	17.5 (24.8)
Median [Q1, Q3]	9.00 [4.00, 21.3]	11.0 [4.00, 23.0]	9.00 [4.00, 22.0]
Median [min, max]	9.00 [1.00, 171]	11.0 [1.00, 77.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00782 (0.0113)	0.0104 (0.00932)	0.00815 (0.0111)
Median [Q1, Q3]	0.00480 [0.00219, 0.00852]	0.00609 [0.00337, 0.0186]	0.00499 [0.00230, 0.00928]
Median [min, max]	0.00480 [0.000151, 0.0966]	0.00609 [0.000946, 0.0312]	0.00499 [0.000151, 0.0966]
as.factor(missing_fi)
0	8 (7.1%)	2 (11.8%)	10 (7.8%)
1	64 (57.1%)	9 (52.9%)	73 (56.6%)
Missing	40 (35.7%)	6 (35.3%)	46 (35.7%)

fi_sig$sensitive[fi_sig$sen_analysis == 1] = "Sensitivity/Posthoc"
  fi_sig$sensitive[fi_sig$sen_analysis == 0] = "Original"
createTable(compareGroups(sensitive ~ no_rand + active_sample + n_event + FI_final + FQ_final + missing_fi, data = fi_sig, method = c(no_rand = 2, active_sample = 2, n_event = 2, FI_final = 2, FQ_final = 2)))

## Warning in chisq.test(xx, correct = FALSE): Chi-squared approximation may be
## incorrect

## 
## --------Summary descriptives table by 'sensitive'---------
## 
## ____________________________________________________________ 
##                   Original     Sensitivity/Posthoc p.overall 
##                    N=112              N=17                   
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 
## no_rand       1982 [1360;4432]  1649 [1199;3270]     0.159   
## active_sample 1861 [1127;4017]  1442 [1112;2416]     0.338   
## n_event       95.5 [52.5;226]    190 [41.0;330]      0.442   
## FI_final      9.00 [4.00;21.2]  11.0 [4.00;23.0]     0.725   
## FQ_final      0.00 [0.00;0.01]  0.01 [0.00;0.02]     0.189   
## missing_fi:                                          0.615   
##     0            8 (11.1%)          2 (18.2%)                
##     1            64 (88.9%)         9 (81.8%)                
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

# Description

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Overall (N=112)
no_rand
Mean (SD)	3240 (2450)
Median [Q1, Q3]	1980 [1360, 4430]
Median [min, max]	1980 [450, 7870]
active_sample
Mean (SD)	2820 (2230)
Median [Q1, Q3]	1860 [1130, 4020]
Median [min, max]	1860 [339, 7810]
n_event
Mean (SD)	172 (181)
Median [Q1, Q3]	95.5 [52.5, 227]
Median [min, max]	95.5 [10.0, 764]
FI_final
Mean (SD)	17.4 (25.5)
Median [Q1, Q3]	9.00 [4.00, 21.3]
Median [min, max]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00782 (0.0113)
Median [Q1, Q3]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	8 (7.1%)
1	64 (57.1%)
Missing	40 (35.7%)

Relationship between sample size/active sample/no. events and FI

p = ggplot(data = ori_st, aes(x = no_rand, y = FI_final))
p1 = p + geom_point() + geom_smooth() + labs(x = "Number of participants at randomisation", y = "Fragility index") + theme_bw()

p0 = ggplot(data = ori_st, aes(x = active_sample, y = FI_final))
p2 = p0 + geom_point() + geom_smooth() + labs(x = "Number of participants included in the analyses", y = "Fragility index") + theme_bw()

p.0 = ggplot(data = ori_st, aes(x = n_event, y = FI_final))
p3 = p.0 + geom_point() + geom_smooth() + labs(x = "Number of participants with fracture events", y = "Fragility index") + theme_bw()

#grid.arrange(p1, p2, p3, nrow = 1)
grid.arrange(p1, p3, nrow = 1, top = textGrob("Relationship between Number of participants and Fragility index", gp = gpar(fontsize = 20, font = 3)))

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

(2.1.2) By fracture sites

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code1), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any_fx (N=3)	Clin_fx (N=11)	OFx (N=4)	MOF (N=4)	Dif_comb (N=1)	NonVert_fx (N=17)	Vert_fx (N=54)	ClinVert_fx (N=10)	Hip (N=6)	Forearm (N=2)	Overall (N=112)
no_rand
Mean (SD)	1850 (423)	3860 (2570)	2780 (1580)	5020 (2680)	NA	4010 (2510)	2800 (2440)	3160 (2590)	4510 (2680)	1740 (374)	3240 (2450)
Median [Q1, Q3]	1770 [1620, 2030]	4090 [1820, 5810]	3050 [1730, 4090]	5640 [3480, 7180]	2690 [2690, 2690]	4090 [1630, 5090]	1630 [1200, 4090]	1980 [1730, 3600]	3680 [2540, 6830]	1740 [1600, 1870]	1980 [1360, 4430]
Median [min, max]	1770 [1470, 2300]	4090 [578, 7740]	3050 [930, 4090]	5640 [1650, 7180]	2690 [2690, 2690]	4090 [450, 7870]	1630 [578, 7870]	1980 [578, 7870]	3680 [1770, 7870]	1740 [1470, 2000]	1980 [450, 7870]
active_sample
Mean (SD)	1830 (439)	3340 (2450)	2670 (1490)	4320 (2410)	NA	3550 (2310)	2440 (2200)	2660 (2510)	3700 (2260)	1160 (810)	2820 (2230)
Median [Q1, Q3]	1770 [1600, 2030]	3640 [1190, 5430]	2890 [1690, 3870]	4820 [2970, 6170]	2690 [2690, 2690]	3610 [1630, 4940]	1350 [1050, 3580]	1910 [1210, 2920]	2810 [1900, 5660]	1160 [876, 1450]	1860 [1130, 4020]
Median [min, max]	1770 [1430, 2300]	3640 [451, 6690]	2890 [930, 3980]	4820 [1270, 6380]	2690 [2690, 2690]	3610 [389, 6670]	1350 [451, 7390]	1910 [339, 7810]	2810 [1770, 6600]	1160 [590, 1740]	1860 [339, 7810]
n_event
Mean (SD)	354 (290)	275 (215)	334 (251)	170 (135)	NA	287 (222)	114 (144)	81.1 (51.2)	159 (106)	111 (16.3)	172 (181)
Median [Q1, Q3]	475 [249, 519]	231 [120, 393]	318 [245, 407]	140 [86.8, 222]	147 [147, 147]	225 [85.0, 471]	72.0 [36.3, 109]	63.0 [60.5, 93.8]	124 [78.5, 232]	111 [105, 116]	95.5 [52.5, 227]
Median [min, max]	475 [23.0, 563]	231 [34.0, 764]	318 [44.0, 658]	140 [44.0, 355]	147 [147, 147]	225 [37.0, 680]	72.0 [10.0, 696]	63.0 [21.0, 204]	124 [58.0, 315]	111 [99.0, 122]	95.5 [10.0, 764]
FI_final
Mean (SD)	16.7 (11.9)	19.2 (25.3)	32.3 (26.2)	13.8 (9.14)	NA	9.76 (11.5)	21.3 (32.2)	12.7 (15.0)	7.83 (6.05)	5.50 (4.95)	17.4 (25.5)
Median [Q1, Q3]	22.0 [12.5, 23.5]	8.00 [6.00, 20.5]	31.5 [22.8, 41.0]	12.0 [8.00, 17.8]	4.00 [4.00, 4.00]	5.00 [2.00, 17.0]	11.0 [4.00, 22.8]	6.50 [4.00, 11.5]	8.00 [2.75, 11.8]	5.50 [3.75, 7.25]	9.00 [4.00, 21.3]
Median [min, max]	22.0 [3.00, 25.0]	8.00 [4.00, 89.0]	31.5 [1.00, 65.0]	12.0 [5.00, 26.0]	4.00 [4.00, 4.00]	5.00 [1.00, 43.0]	11.0 [1.00, 171]	6.50 [1.00, 42.0]	8.00 [1.00, 16.0]	5.50 [2.00, 9.00]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00847 (0.00558)	0.00668 (0.00469)	0.0106 (0.00776)	0.00443 (0.00331)	NA	0.00282 (0.00247)	0.0110 (0.0151)	0.00448 (0.00254)	0.00290 (0.00292)	0.00429 (0.00127)	0.00782 (0.0113)
Median [Q1, Q3]	0.0109 [0.00647, 0.0117]	0.00714 [0.00236, 0.00898]	0.0122 [0.00592, 0.0169]	0.00478 [0.00204, 0.00717]	0.00149 [0.00149, 0.00149]	0.00239 [0.00101, 0.00346]	0.00634 [0.00299, 0.0136]	0.00383 [0.00298, 0.00504]	0.00168 [0.000801, 0.00514]	0.00429 [0.00384, 0.00474]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.0109 [0.00209, 0.0125]	0.00714 [0.00124, 0.0146]	0.0122 [0.00108, 0.0169]	0.00478 [0.000783, 0.00736]	0.00149 [0.00149, 0.00149]	0.00239 [0.000203, 0.00955]	0.00634 [0.000151, 0.0966]	0.00383 [0.00205, 0.0104]	0.00168 [0.000303, 0.00695]	0.00429 [0.00339, 0.00519]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	0 (0%)	1 (9.1%)	2 (50.0%)	0 (0%)	0 (0%)	1 (5.9%)	3 (5.6%)	0 (0%)	0 (0%)	1 (50.0%)	8 (7.1%)
1	1 (33.3%)	8 (72.7%)	2 (50.0%)	4 (100%)	1 (100%)	9 (52.9%)	31 (57.4%)	4 (40.0%)	3 (50.0%)	1 (50.0%)	64 (57.1%)
Missing	2 (66.7%)	2 (18.2%)	0 (0%)	0 (0%)	0 (0%)	7 (41.2%)	20 (37.0%)	6 (60.0%)	3 (50.0%)	0 (0%)	40 (35.7%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code2), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any (N=14)	Osteoporotic (N=9)	Non-Vertebrae (N=17)	Vertebrae (N=54)	Clinical Vertebrae (N=10)	Hip (N=6)	Forearm (N=2)	Overall (N=112)
no_rand
Mean (SD)	3430 (2410)	3770 (2250)	4010 (2510)	2800 (2440)	3160 (2590)	4510 (2680)	1740 (374)	3240 (2450)
Median [Q1, Q3]	2220 [1680, 4350]	4090 [2000, 4090]	4090 [1630, 5090]	1630 [1200, 4090]	1980 [1730, 3600]	3680 [2540, 6830]	1740 [1600, 1870]	1980 [1360, 4430]
Median [min, max]	2220 [578, 7740]	4090 [930, 7180]	4090 [450, 7870]	1630 [578, 7870]	1980 [578, 7870]	3680 [1770, 7870]	1740 [1470, 2000]	1980 [450, 7870]
active_sample
Mean (SD)	3020 (2250)	3410 (1940)	3550 (2310)	2440 (2200)	2660 (2510)	3700 (2260)	1160 (810)	2820 (2230)
Median [Q1, Q3]	2150 [1310, 4250]	3530 [1950, 3980]	3610 [1630, 4940]	1350 [1050, 3580]	1910 [1210, 2920]	2810 [1900, 5660]	1160 [876, 1450]	1860 [1130, 4020]
Median [min, max]	2150 [451, 6690]	3530 [930, 6380]	3610 [389, 6670]	1350 [451, 7390]	1910 [339, 7810]	2810 [1770, 6600]	1160 [590, 1740]	1860 [339, 7810]
n_event
Mean (SD)	292 (222)	240 (196)	287 (222)	114 (144)	81.1 (51.2)	159 (106)	111 (16.3)	172 (181)
Median [Q1, Q3]	239 [105, 450]	178 [101, 323]	225 [85.0, 471]	72.0 [36.3, 109]	63.0 [60.5, 93.8]	124 [78.5, 232]	111 [105, 116]	95.5 [52.5, 227]
Median [min, max]	239 [23.0, 764]	178 [44.0, 658]	225 [37.0, 680]	72.0 [10.0, 696]	63.0 [21.0, 204]	124 [58.0, 315]	111 [99.0, 122]	95.5 [10.0, 764]
FI_final
Mean (SD)	18.6 (22.7)	20.9 (20.3)	9.76 (11.5)	21.3 (32.2)	12.7 (15.0)	7.83 (6.05)	5.50 (4.95)	17.4 (25.5)
Median [Q1, Q3]	9.00 [5.50, 24.3]	15.0 [5.00, 30.0]	5.00 [2.00, 17.0]	11.0 [4.00, 22.8]	6.50 [4.00, 11.5]	8.00 [2.75, 11.8]	5.50 [3.75, 7.25]	9.00 [4.00, 21.3]
Median [min, max]	9.00 [3.00, 89.0]	15.0 [1.00, 65.0]	5.00 [1.00, 43.0]	11.0 [1.00, 171]	6.50 [1.00, 42.0]	8.00 [1.00, 16.0]	5.50 [2.00, 9.00]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00706 (0.00472)	0.00685 (0.00635)	0.00282 (0.00247)	0.0110 (0.0151)	0.00448 (0.00254)	0.00290 (0.00292)	0.00429 (0.00127)	0.00782 (0.0113)
Median [Q1, Q3]	0.00731 [0.00235, 0.0104]	0.00711 [0.00149, 0.00754]	0.00239 [0.00101, 0.00346]	0.00634 [0.00299, 0.0136]	0.00383 [0.00298, 0.00504]	0.00168 [0.000801, 0.00514]	0.00429 [0.00384, 0.00474]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00731 [0.00124, 0.0146]	0.00711 [0.000783, 0.0169]	0.00239 [0.000203, 0.00955]	0.00634 [0.000151, 0.0966]	0.00383 [0.00205, 0.0104]	0.00168 [0.000303, 0.00695]	0.00429 [0.00339, 0.00519]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	1 (7.1%)	2 (22.2%)	1 (5.9%)	3 (5.6%)	0 (0%)	0 (0%)	1 (50.0%)	8 (7.1%)
1	9 (64.3%)	7 (77.8%)	9 (52.9%)	31 (57.4%)	4 (40.0%)	3 (50.0%)	1 (50.0%)	64 (57.1%)
Missing	4 (28.6%)	0 (0%)	7 (41.2%)	20 (37.0%)	6 (60.0%)	3 (50.0%)	0 (0%)	40 (35.7%)

kruskal.test(FI_final ~ fx_code2, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by fx_code2
## Kruskal-Wallis chi-squared = 7.5755, df = 6, p-value = 0.2709

kruskal.test(FQ_final ~ fx_code2, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by fx_code2
## Kruskal-Wallis chi-squared = 17.741, df = 6, p-value = 0.006914

Box plots

p1 = ggplot(data = ori_st, aes(y = FI_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Fracture sites", y = "Fragility index")
p2 = ggplot(data = ori_st, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Fracture sites", y = "Fragility quotient")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by fracture sites", gp = gpar(fontsize = 20, font = 1)))

(2.1.3) By pharmacological interventions

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code1), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Alendronate (N=2)	Ibandronate (N=6)	Risedronate (N=5)	Minodronate (N=3)	Zoledronate (N=19)	Teriparatide (N=19)	Abaloparatide (N=3)	Romosozumab (N=26)	Denosumab (N=9)	Strontium_ranelate (N=9)	Calcium_VitD (N=11)	Overall (N=112)
no_rand
Mean (SD)	4430 (0)	1960 (0)	1490 (308)	704 (0)	3610 (2900)	1080 (309)	1650 (0)	5520 (1570)	5020 (3370)	3180 (1810)	1970 (899)	3240 (2450)
Median [Q1, Q3]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	2000 [1600, 7740]	1100 [1090, 1360]	1650 [1650, 1650]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1650, 5090]	1770 [1470, 2490]	1980 [1360, 4430]
Median [min, max]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [939, 1630]	704 [704, 704]	2000 [1200, 7740]	1100 [578, 1640]	1650 [1650, 1650]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1650, 5090]	1770 [450, 3270]	1980 [450, 7870]
active_sample
Mean (SD)	4280 (211)	1950 (0)	1270 (317)	575 (27.7)	2900 (2370)	871 (261)	1310 (75.5)	4970 (1540)	4600 (3080)	2770 (1790)	1530 (789)	2820 (2230)
Median [Q1, Q3]	4280 [4210, 4360]	1950 [1950, 1950]	1330 [1280, 1370]	582 [563, 590]	1860 [1130, 5680]	882 [843, 1050]	1280 [1270, 1340]	3910 [3620, 6640]	6600 [1350, 7390]	1440 [1390, 4930]	1770 [760, 2030]	1860 [1130, 4020]
Median [min, max]	4280 [4130, 4430]	1950 [1950, 1950]	1330 [759, 1630]	582 [544, 598]	1860 [339, 6550]	882 [451, 1430]	1280 [1270, 1400]	3910 [3240, 6910]	6600 [1350, 7810]	1440 [1150, 4940]	1770 [389, 2690]	1860 [339, 7810]
n_event
Mean (SD)	265 (204)	81.5 (23.1)	86.0 (39.3)	79.3 (20.5)	197 (222)	53.4 (27.3)	51.3 (21.9)	203 (148)	140 (180)	428 (247)	205 (180)	172 (181)
Median [Q1, Q3]	265 [193, 337]	70.5 [64.5, 101]	68.0 [65.0, 85.0]	79.0 [69.0, 89.5]	99.0 [43.5, 281]	46.0 [34.5, 84.0]	44.0 [39.0, 60.0]	168 [105, 253]	69.0 [29.0, 121]	471 [204, 671]	147 [64.0, 289]	95.5 [52.5, 227]
Median [min, max]	265 [121, 409]	70.5 [63.0, 112]	68.0 [58.0, 154]	79.0 [59.0, 100]	99.0 [13.0, 764]	46.0 [14.0, 100]	44.0 [34.0, 76.0]	168 [10.0, 658]	69.0 [15.0, 531]	471 [66.0, 696]	147 [37.0, 563]	95.5 [10.0, 764]
FI_final
Mean (SD)	10.0 (4.24)	8.50 (4.68)	5.80 (4.87)	10.0 (9.17)	26.7 (41.3)	9.84 (7.99)	8.67 (4.51)	20.8 (16.6)	25.1 (43.7)	26.6 (35.5)	8.36 (8.85)	17.4 (25.5)
Median [Q1, Q3]	10.0 [8.50, 11.5]	7.50 [4.50, 12.0]	4.00 [2.00, 11.0]	8.00 [5.00, 14.0]	10.0 [5.00, 35.5]	8.00 [2.50, 16.0]	9.00 [6.50, 11.0]	18.0 [7.00, 29.3]	4.00 [3.00, 17.0]	12.0 [5.00, 29.0]	4.00 [2.00, 13.5]	9.00 [4.00, 21.3]
Median [min, max]	10.0 [7.00, 13.0]	7.50 [4.00, 15.0]	4.00 [1.00, 11.0]	8.00 [2.00, 20.0]	10.0 [1.00, 171]	8.00 [1.00, 25.0]	9.00 [4.00, 13.0]	18.0 [1.00, 65.0]	4.00 [2.00, 137]	12.0 [1.00, 111]	4.00 [1.00, 25.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00236 (0.00111)	0.00435 (0.00240)	0.00475 (0.00356)	0.0180 (0.0171)	0.00753 (0.00714)	0.0117 (0.00946)	0.00651 (0.00311)	0.00451 (0.00413)	0.00432 (0.00546)	0.0191 (0.0311)	0.00501 (0.00387)	0.00782 (0.0113)
Median [Q1, Q3]	0.00236 [0.00197, 0.00275]	0.00384 [0.00231, 0.00615]	0.00527 [0.00156, 0.00801]	0.0137 [0.00855, 0.0253]	0.00537 [0.00309, 0.00851]	0.00887 [0.00351, 0.0177]	0.00711 [0.00512, 0.00819]	0.00330 [0.00140, 0.00598]	0.00255 [0.00222, 0.00296]	0.00795 [0.00101, 0.0137]	0.00353 [0.00244, 0.00659]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00236 [0.00158, 0.00314]	0.00384 [0.00205, 0.00768]	0.00527 [0.000615, 0.00828]	0.0137 [0.00334, 0.0368]	0.00537 [0.000887, 0.0301]	0.00887 [0.00114, 0.0288]	0.00711 [0.00314, 0.00928]	0.00330 [0.000151, 0.0169]	0.00255 [0.000303, 0.0185]	0.00795 [0.000203, 0.0966]	0.00353 [0.000567, 0.0125]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	0 (0%)	0 (0%)	5 (26.3%)	2 (10.5%)	0 (0%)	1 (3.8%)	0 (0%)	0 (0%)	0 (0%)	8 (7.1%)
1	0 (0%)	0 (0%)	4 (80.0%)	3 (100%)	14 (73.7%)	4 (21.1%)	3 (100%)	25 (96.2%)	4 (44.4%)	1 (11.1%)	6 (54.5%)	64 (57.1%)
Missing	2 (100%)	6 (100%)	1 (20.0%)	0 (0%)	0 (0%)	13 (68.4%)	0 (0%)	0 (0%)	5 (55.6%)	8 (88.9%)	5 (45.5%)	40 (35.7%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code2), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Bisphosphonates (N=35)	PTH analog (N=22)	Romosozumab (N=26)	Denosumab (N=9)	Strontium_ranelate (N=9)	Calcium_VitD (N=11)	Overall (N=112)
no_rand
Mean (SD)	2820 (2400)	1160 (347)	5520 (1570)	5020 (3370)	3180 (1810)	1970 (899)	3240 (2450)
Median [Q1, Q3]	1960 [1410, 2130]	1100 [1090, 1360]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1650, 5090]	1770 [1470, 2490]	1980 [1360, 4430]
Median [min, max]	1960 [704, 7740]	1100 [578, 1650]	4090 [4090, 7180]	7870 [1470, 7870]	1650 [1650, 5090]	1770 [450, 3270]	1980 [450, 7870]
active_sample
Mean (SD)	2380 (1960)	932 (289)	4970 (1540)	4600 (3080)	2770 (1790)	1530 (789)	2820 (2230)
Median [Q1, Q3]	1860 [1130, 1980]	892 [856, 1090]	3910 [3620, 6640]	6600 [1350, 7390]	1440 [1390, 4930]	1770 [760, 2030]	1860 [1130, 4020]
Median [min, max]	1860 [339, 6550]	892 [451, 1430]	3910 [3240, 6910]	6600 [1350, 7810]	1440 [1150, 4940]	1770 [389, 2690]	1860 [339, 7810]
n_event
Mean (SD)	155 (177)	53.1 (26.2)	203 (148)	140 (180)	428 (247)	205 (180)	172 (181)
Median [Q1, Q3]	79.0 [61.5, 147]	45.0 [34.3, 81.3]	168 [105, 253]	69.0 [29.0, 121]	471 [204, 671]	147 [64.0, 289]	95.5 [52.5, 227]
Median [min, max]	79.0 [13.0, 764]	45.0 [14.0, 100]	168 [10.0, 658]	69.0 [15.0, 531]	471 [66.0, 696]	147 [37.0, 563]	95.5 [10.0, 764]
FI_final
Mean (SD)	18.2 (31.7)	9.68 (7.54)	20.8 (16.6)	25.1 (43.7)	26.6 (35.5)	8.36 (8.85)	17.4 (25.5)
Median [Q1, Q3]	9.00 [4.00, 15.0]	8.50 [3.25, 14.5]	18.0 [7.00, 29.3]	4.00 [3.00, 17.0]	12.0 [5.00, 29.0]	4.00 [2.00, 13.5]	9.00 [4.00, 21.3]
Median [min, max]	9.00 [1.00, 171]	8.50 [1.00, 25.0]	18.0 [1.00, 65.0]	4.00 [2.00, 137]	12.0 [1.00, 111]	4.00 [1.00, 25.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00719 (0.00778)	0.0110 (0.00900)	0.00451 (0.00413)	0.00432 (0.00546)	0.0191 (0.0311)	0.00501 (0.00387)	0.00782 (0.0113)
Median [Q1, Q3]	0.00527 [0.00250, 0.00785]	0.00864 [0.00346, 0.0157]	0.00330 [0.00140, 0.00598]	0.00255 [0.00222, 0.00296]	0.00795 [0.00101, 0.0137]	0.00353 [0.00244, 0.00659]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00527 [0.000615, 0.0368]	0.00864 [0.00114, 0.0288]	0.00330 [0.000151, 0.0169]	0.00255 [0.000303, 0.0185]	0.00795 [0.000203, 0.0966]	0.00353 [0.000567, 0.0125]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	5 (14.3%)	2 (9.1%)	1 (3.8%)	0 (0%)	0 (0%)	0 (0%)	8 (7.1%)
1	21 (60.0%)	7 (31.8%)	25 (96.2%)	4 (44.4%)	1 (11.1%)	6 (54.5%)	64 (57.1%)
Missing	9 (25.7%)	13 (59.1%)	0 (0%)	5 (55.6%)	8 (88.9%)	5 (45.5%)	40 (35.7%)

kruskal.test(FI_final ~ interv_code2, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by interv_code2
## Kruskal-Wallis chi-squared = 9.2817, df = 5, p-value = 0.09834

kruskal.test(FQ_final ~ interv_code2, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by interv_code2
## Kruskal-Wallis chi-squared = 11.821, df = 5, p-value = 0.03732

Box plots

p1 = ggplot(data = ori_st, aes(y = FI_final, x = as.factor(interv_code2), fill = as.factor(interv_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Pharmacological interventions", y = "Fragility index")
p2 = ggplot(data = ori_st, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Pharmacological interventions", y = "Fragility quotine")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by intervention sites", gp = gpar(fontsize = 20, font = 1)))

#### (2.1.4) Timing of fracture assessment

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(timing), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	2 (N=20)	3 (N=10)	4 (N=36)	5 (N=28)	6 (N=6)	7 (N=5)	8 (N=7)	Overall (N=112)
no_rand
Mean (SD)	3470 (2500)	1560 (1030)	3110 (2360)	4260 (2980)	2340 (1650)	3640 (1980)	2100 (259)	3240 (2450)
Median [Q1, Q3]	2870 [1440, 4860]	1640 [610, 1650]	1720 [1100, 4090]	2220 [1770, 7740]	1650 [1120, 3740]	5090 [1470, 5090]	2000 [2000, 2000]	1980 [1360, 4430]
Median [min, max]	2870 [578, 7180]	1640 [578, 3270]	1720 [704, 7180]	2220 [450, 7870]	1650 [930, 4430]	5090 [1470, 5090]	2000 [2000, 2690]	1980 [450, 7870]
active_sample
Mean (SD)	3120 (2330)	1080 (545)	2760 (2190)	3660 (2610)	2090 (1710)	2930 (2210)	2000 (315)	2820 (2230)
Median [Q1, Q3]	2390 [1250, 4580]	1270 [484, 1420]	1650 [892, 3660]	2130 [1580, 6470]	1150 [985, 3390]	3650 [590, 4940]	1890 [1860, 1980]	1860 [1130, 4020]
Median [min, max]	2390 [476, 6910]	1270 [451, 1770]	1650 [544, 6690]	2130 [339, 7810]	1150 [759, 4430]	3650 [567, 4940]	1890 [1740, 2690]	1860 [339, 7810]
n_event
Mean (SD)	94.5 (76.5)	59.3 (40.9)	141 (145)	242 (215)	257 (252)	418 (301)	186 (127)	172 (181)
Median [Q1, Q3]	70.5 [48.5, 142]	46.0 [34.5, 71.5]	88.5 [44.0, 189]	131 [72.0, 391]	163 [81.3, 358]	537 [122, 671]	147 [85.5, 281]	95.5 [52.5, 227]
Median [min, max]	70.5 [10.0, 323]	46.0 [21.0, 163]	88.5 [14.0, 658]	131 [23.0, 764]	163 [44.0, 696]	537 [70.0, 691]	147 [48.0, 377]	95.5 [10.0, 764]
FI_final
Mean (SD)	8.75 (8.95)	7.10 (4.38)	17.2 (15.3)	28.5 (40.9)	24.7 (42.5)	8.20 (11.7)	13.6 (9.85)	17.4 (25.5)
Median [Q1, Q3]	5.00 [2.75, 9.50]	7.00 [4.00, 10.5]	14.5 [5.75, 23.5]	14.0 [4.00, 38.3]	9.50 [4.75, 12.8]	3.00 [2.00, 5.00]	10.0 [7.50, 16.5]	9.00 [4.00, 21.3]
Median [min, max]	5.00 [1.00, 30.0]	7.00 [1.00, 13.0]	14.5 [1.00, 65.0]	14.0 [1.00, 171]	9.50 [1.00, 111]	3.00 [2.00, 29.0]	10.0 [4.00, 33.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00362 (0.00342)	0.00871 (0.00801)	0.00864 (0.00885)	0.00792 (0.00850)	0.0197 (0.0378)	0.00330 (0.00292)	0.00703 (0.00510)	0.00782 (0.0113)
Median [Q1, Q3]	0.00240 [0.00136, 0.00419]	0.00741 [0.00366, 0.00918]	0.00535 [0.00283, 0.0119]	0.00638 [0.00225, 0.00872]	0.00421 [0.00197, 0.00915]	0.00339 [0.00101, 0.00353]	0.00537 [0.00421, 0.00851]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00240 [0.000151, 0.0137]	0.00741 [0.000567, 0.0288]	0.00535 [0.000554, 0.0368]	0.00638 [0.000203, 0.0361]	0.00421 [0.00108, 0.0966]	0.00339 [0.000608, 0.00795]	0.00537 [0.00149, 0.0169]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	1 (5.0%)	0 (0%)	2 (5.6%)	0 (0%)	0 (0%)	0 (0%)	5 (71.4%)	8 (7.1%)
1	16 (80.0%)	7 (70.0%)	23 (63.9%)	13 (46.4%)	1 (16.7%)	2 (40.0%)	2 (28.6%)	64 (57.1%)
Missing	3 (15.0%)	3 (30.0%)	11 (30.6%)	15 (53.6%)	5 (83.3%)	3 (60.0%)	0 (0%)	40 (35.7%)

kruskal.test(FI_final ~ timing, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by timing
## Kruskal-Wallis chi-squared = 9.8301, df = 6, p-value = 0.132

kruskal.test(FQ_final ~ timing, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by timing
## Kruskal-Wallis chi-squared = 9.9307, df = 6, p-value = 0.1276

Box plots

p1 = ggplot(data = ori_st, aes(y = FI_final, x = as.factor(timing), fill = as.factor(timing))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index")
p1

(2.1.5) By journal

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(journal_code2), data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	NEJM (N=69)	Lancet (N=5)	BMJ (N=5)	JAMA (N=10)	JBMR (N=6)	JCEM (N=5)	Other (N=12)	Overall (N=112)
no_rand
Mean (SD)	4040 (2660)	1360 (0)	2160 (397)	2190 (1180)	1960 (0)	1480 (2020)	2120 (1820)	3240 (2450)
Median [Q1, Q3]	4090 [1470, 7180]	1360 [1360, 1360]	2300 [1770, 2300]	1640 [1630, 1650]	1960 [1960, 1960]	578 [578, 578]	1470 [874, 2510]	1980 [1360, 4430]
Median [min, max]	4090 [450, 7870]	1360 [1360, 1360]	2300 [1770, 2690]	1640 [1630, 4430]	1960 [1960, 1960]	578 [578, 5090]	1470 [704, 5090]	1980 [450, 7870]
active_sample
Mean (SD)	3500 (2430)	1080 (48.9)	2160 (397)	1950 (1230)	1950 (0)	1350 (2000)	1700 (1740)	2820 (2230)
Median [Q1, Q3]	3400 [1350, 6430]	1050 [1050, 1100]	2300 [1770, 2300]	1390 [1290, 1580]	1950 [1950, 1950]	451 [451, 476]	845 [588, 1770]	1860 [1130, 4020]
Median [min, max]	3400 [339, 7810]	1050 [1050, 1160]	2300 [1770, 2690]	1390 [1270, 4430]	1950 [1950, 1950]	451 [451, 4930]	845 [544, 4940]	1860 [339, 7810]
n_event
Mean (SD)	168 (170)	70.0 (36.2)	352 (167)	108 (112)	81.5 (23.1)	122 (195)	278 (279)	172 (181)
Median [Q1, Q3]	103 [48.0, 231]	91.0 [53.0, 92.0]	315 [262, 475]	70.5 [47.5, 112]	70.5 [64.5, 101]	35.0 [34.0, 48.0]	111 [69.5, 571]	95.5 [52.5, 227]
Median [min, max]	103 [10.0, 764]	91.0 [14.0, 100]	315 [147, 563]	70.5 [34.0, 409]	70.5 [63.0, 112]	35.0 [21.0, 471]	111 [44.0, 696]	95.5 [10.0, 764]
FI_final
Mean (SD)	21.3 (29.0)	9.40 (6.80)	15.6 (8.44)	8.20 (4.47)	8.50 (4.68)	4.80 (4.76)	16.6 (30.9)	17.4 (25.5)
Median [Q1, Q3]	10.0 [5.00, 26.0]	10.0 [3.00, 15.0]	16.0 [11.0, 22.0]	10.0 [4.75, 11.0]	7.50 [4.50, 12.0]	4.00 [2.00, 4.00]	4.50 [2.00, 14.0]	9.00 [4.00, 21.3]
Median [min, max]	10.0 [1.00, 171]	10.0 [2.00, 17.0]	16.0 [4.00, 25.0]	10.0 [1.00, 13.0]	7.50 [4.00, 15.0]	4.00 [1.00, 13.0]	4.50 [1.00, 111]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00700 (0.00778)	0.00882 (0.00654)	0.00760 (0.00430)	0.00504 (0.00332)	0.00435 (0.00240)	0.0101 (0.0110)	0.0153 (0.0275)	0.00782 (0.0113)
Median [Q1, Q3]	0.00391 [0.00222, 0.00748]	0.00908 [0.00259, 0.0143]	0.00695 [0.00623, 0.0109]	0.00513 [0.00197, 0.00793]	0.00384 [0.00231, 0.00615]	0.00840 [0.00443, 0.00887]	0.00440 [0.00278, 0.0113]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00391 [0.000151, 0.0361]	0.00908 [0.00191, 0.0162]	0.00695 [0.00149, 0.0125]	0.00513 [0.000615, 0.00928]	0.00384 [0.00205, 0.00768]	0.00840 [0.000203, 0.0288]	0.00440 [0.000608, 0.0966]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	6 (8.7%)	2 (40.0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	8 (7.1%)
1	45 (65.2%)	3 (60.0%)	1 (20.0%)	8 (80.0%)	0 (0%)	1 (20.0%)	6 (50.0%)	64 (57.1%)
Missing	18 (26.1%)	0 (0%)	4 (80.0%)	2 (20.0%)	6 (100%)	4 (80.0%)	6 (50.0%)	40 (35.7%)

kruskal.test(FI_final ~ journal_code2, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by journal_code2
## Kruskal-Wallis chi-squared = 8.2654, df = 6, p-value = 0.2193

kruskal.test(FQ_final ~ journal_code2, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by journal_code2
## Kruskal-Wallis chi-squared = 2.733, df = 6, p-value = 0.8415

Box plots

p1 = ggplot(data = ori_st, aes(y = FI_final, x = as.factor(timing), fill = as.factor(journal_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index") 
p1

(2.1.6) By sex

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | sex, data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Both (N=9)	Men (N=9)	Women (N=94)	Overall (N=112)
no_rand
Mean (SD)	1180 (874)	1320 (142)	3630 (2490)	3240 (2450)
Median [Q1, Q3]	578 [578, 2130]	1200 [1200, 1470]	2150 [1630, 5090]	1980 [1360, 4430]
Median [min, max]	578 [450, 2690]	1200 [1200, 1470]	2150 [704, 7870]	1980 [450, 7870]
active_sample
Mean (SD)	739 (750)	1240 (132)	3180 (2260)	2820 (2230)
Median [Q1, Q3]	451 [451, 479]	1130 [1130, 1350]	1950 [1280, 4940]	1860 [1130, 4020]
Median [min, max]	451 [339, 2690]	1130 [1130, 1430]	1950 [544, 7810]	1860 [339, 7810]
n_event
Mean (SD)	73.0 (69.9)	26.2 (9.56)	195 (188)	172 (181)
Median [Q1, Q3]	44.0 [35.0, 60.0]	23.0 [21.0, 36.0]	107 [69.0, 260]	95.5 [52.5, 227]
Median [min, max]	44.0 [21.0, 231]	23.0 [13.0, 39.0]	107 [10.0, 764]	95.5 [10.0, 764]
FI_final
Mean (SD)	4.22 (3.80)	3.11 (1.62)	20.0 (27.0)	17.4 (25.5)
Median [Q1, Q3]	4.00 [2.00, 4.00]	3.00 [2.00, 4.00]	11.5 [5.00, 23.8]	9.00 [4.00, 21.3]
Median [min, max]	4.00 [1.00, 13.0]	3.00 [1.00, 6.00]	11.5 [1.00, 171]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00842 (0.00876)	0.00252 (0.00139)	0.00827 (0.0119)	0.00782 (0.0113)
Median [Q1, Q3]	0.00514 [0.00295, 0.00887]	0.00222 [0.00177, 0.00296]	0.00523 [0.00237, 0.00908]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00514 [0.00108, 0.0288]	0.00222 [0.000887, 0.00532]	0.00523 [0.000151, 0.0966]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	8 (8.5%)	8 (7.1%)
1	4 (44.4%)	9 (100%)	51 (54.3%)	64 (57.1%)
Missing	5 (55.6%)	0 (0%)	35 (37.2%)	40 (35.7%)

kruskal.test(FI_final ~ sex, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by sex
## Kruskal-Wallis chi-squared = 19.906, df = 2, p-value = 4.759e-05

kruskal.test(FQ_final ~ sex, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by sex
## Kruskal-Wallis chi-squared = 5.6754, df = 2, p-value = 0.05856

Box plots

p1 = ggplot(data = ori_st, aes(y = FI_final, x = as.factor(sex), fill = as.factor(sex))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by sex", x = "Sex", y = "Fragility index") 
p1

(2.1.7) By placebo

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | placebo, data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Active (N=23)	Placebo (N=89)	Overall (N=112)
no_rand
Mean (SD)	3070 (1300)	3290 (2670)	3240 (2450)
Median [Q1, Q3]	4090 [1640, 4090]	1960 [1200, 7180]	1980 [1360, 4430]
Median [min, max]	4090 [1360, 4090]	1960 [450, 7870]	1980 [450, 7870]
active_sample
Mean (SD)	2650 (1210)	2870 (2430)	2820 (2230)
Median [Q1, Q3]	3400 [1270, 3650]	1770 [930, 5680]	1860 [1130, 4020]
Median [min, max]	3400 [1050, 3980]	1770 [339, 7810]	1860 [339, 7810]
n_event
Mean (SD)	190 (165)	167 (186)	172 (181)
Median [Q1, Q3]	140 [69.0, 289]	85.0 [48.0, 204]	95.5 [52.5, 227]
Median [min, max]	140 [14.0, 658]	85.0 [10.0, 764]	95.5 [10.0, 764]
FI_final
Mean (SD)	16.4 (16.3)	17.6 (27.5)	17.4 (25.5)
Median [Q1, Q3]	10.0 [5.00, 21.5]	8.00 [4.00, 21.0]	9.00 [4.00, 21.3]
Median [min, max]	10.0 [2.00, 65.0]	8.00 [1.00, 171]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.00658 (0.00507)	0.00814 (0.0124)	0.00782 (0.0113)
Median [Q1, Q3]	0.00711 [0.00232, 0.00918]	0.00461 [0.00222, 0.00828]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00711 [0.000554, 0.0169]	0.00461 [0.000151, 0.0966]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	3 (13.0%)	5 (5.6%)	8 (7.1%)
1	20 (87.0%)	44 (49.4%)	64 (57.1%)
Missing	0 (0%)	40 (44.9%)	40 (35.7%)

kruskal.test(FI_final ~ placebo, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by placebo
## Kruskal-Wallis chi-squared = 0.86592, df = 1, p-value = 0.3521

kruskal.test(FQ_final ~ placebo, data = ori_st)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by placebo
## Kruskal-Wallis chi-squared = 0.17754, df = 1, p-value = 0.6735

Box plots

p1 = ggplot(data = ori_st, aes(y = FI_final, x = as.factor(control), fill = as.factor(control))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by types of control", x = "Types of control", y = "Fragility index") 
p1

(2.2) Fracture as the predefined primary endpoint

(2.2.1) Overall

# Comparison:
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | fx_primary , data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Primary endpoint (N=24)	Secondary endpoint (N=88)	Overall (N=112)
no_rand
Mean (SD)	3300 (2520)	3230 (2450)	3240 (2450)
Median [Q1, Q3]	1980 [1560, 4600]	1980 [1360, 4180]	1980 [1360, 4430]
Median [min, max]	1980 [578, 7870]	1980 [450, 7870]	1980 [450, 7870]
active_sample
Mean (SD)	2830 (2290)	2820 (2230)	2820 (2230)
Median [Q1, Q3]	1860 [1110, 4330]	1860 [1130, 3870]	1860 [1130, 4020]
Median [min, max]	1860 [451, 7390]	1860 [339, 7810]	1860 [339, 7810]
n_event
Mean (SD)	185 (165)	168 (187)	172 (181)
Median [Q1, Q3]	111 [81.0, 251]	83.5 [47.5, 209]	95.5 [52.5, 227]
Median [min, max]	111 [34.0, 671]	83.5 [10.0, 764]	95.5 [10.0, 764]
FI_final
Mean (SD)	30.3 (40.4)	13.9 (18.4)	17.4 (25.5)
Median [Q1, Q3]	15.0 [11.8, 27.8]	7.00 [3.00, 17.0]	9.00 [4.00, 21.3]
Median [min, max]	15.0 [1.00, 171]	7.00 [1.00, 111]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.0137 (0.0114)	0.00621 (0.0108)	0.00782 (0.0113)
Median [Q1, Q3]	0.00864 [0.00584, 0.0203]	0.00343 [0.00205, 0.00717]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00864 [0.000567, 0.0368]	0.00343 [0.000151, 0.0966]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	2 (8.3%)	6 (6.8%)	8 (7.1%)
1	13 (54.2%)	51 (58.0%)	64 (57.1%)
Missing	9 (37.5%)	31 (35.2%)	40 (35.7%)

createTable(compareGroups(fx_primary ~ no_rand + active_sample + n_event + FI_final + FQ_final + missing_fi, data = ori_st, method = c(no_rand = 2, active_sample = 2, n_event = 2, FI_final = 2, FQ_final = 2)))

## Warning in chisq.test(xx, correct = FALSE): Chi-squared approximation may be
## incorrect

## 
## --------Summary descriptives table by 'fx_primary'---------
## 
## ___________________________________________________________ 
##               Primary endpoint Secondary endpoint p.overall 
##                     N=24              N=88                  
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 
## no_rand       1982 [1561;4597]  1982 [1360;4178]    0.817   
## active_sample 1856 [1108;4334]  1861 [1127;3872]    0.938   
## n_event        111 [81.0;251]   83.5 [47.5;209]     0.202   
## FI_final      15.0 [11.8;27.8]  7.00 [3.00;17.0]    0.001   
## FQ_final      0.01 [0.01;0.02]  0.00 [0.00;0.01]   <0.001   
## missing_fi:                                         0.669   
##     0            2 (13.3%)         6 (10.5%)                
##     1            13 (86.7%)        51 (89.5%)               
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

# Description:
fx_prim2 = subset(ori_st, pri_endpoint == 1)
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi), data = fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Overall (N=24)
no_rand
Mean (SD)	3300 (2520)
Median [Q1, Q3]	1980 [1560, 4600]
Median [min, max]	1980 [578, 7870]
active_sample
Mean (SD)	2830 (2290)
Median [Q1, Q3]	1860 [1110, 4330]
Median [min, max]	1860 [451, 7390]
n_event
Mean (SD)	185 (165)
Median [Q1, Q3]	111 [81.0, 251]
Median [min, max]	111 [34.0, 671]
FI_final
Mean (SD)	30.3 (40.4)
Median [Q1, Q3]	15.0 [11.8, 27.8]
Median [min, max]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.0137 (0.0114)
Median [Q1, Q3]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	2 (8.3%)
1	13 (54.2%)
Missing	9 (37.5%)

Relationship between sample size/active sample/no. events and FI

p = ggplot(data = fx_prim2, aes(x = no_rand, y = FI_final))
p1 = p + geom_point() + geom_smooth() + labs(x = "Number of participants at randomisation", y = "Fragility index") + theme_bw()

p0 = ggplot(data = fx_prim2, aes(x = active_sample, y = FI_final))
p2 = p0 + geom_point() + geom_smooth() + labs(x = "Number of participants included in the analyses", y = "Fragility index") + theme_bw()

p.0 = ggplot(data =  fx_prim2, aes(x = n_event, y = FI_final))
p3 = p.0 + geom_point() + geom_smooth() + labs(x = "Number of participants with fracture events", y = "Fragility index") + theme_bw()

#grid.arrange(p1, p2, p3, nrow = 1)
grid.arrange(p1, p3, nrow = 1, top = textGrob("Relationship between Number of participants and Fragility index", gp = gpar(fontsize = 20, font = 3)))

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

(2.2.2) By fracture sites

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code1), data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Clin_fx (N=2)	OFx (N=1)	NonVert_fx (N=1)	Vert_fx (N=18)	Hip (N=2)	Overall (N=24)
no_rand
Mean (SD)	3110 (1390)	NA	NA	3060 (2640)	5500 (3160)	3300 (2520)
Median [Q1, Q3]	3110 [2620, 3600]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [1240, 4350]	5500 [4390, 6620]	1980 [1560, 4600]
Median [min, max]	3110 [2130, 4090]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [578, 7870]	5500 [3270, 7740]	1980 [578, 7870]
active_sample
Mean (SD)	2060 (2240)	NA	NA	2700 (2350)	4110 (3310)	2830 (2290)
Median [Q1, Q3]	2060 [1270, 2850]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [1070, 4020]	4110 [2940, 5280]	1860 [1110, 4330]
Median [min, max]	2060 [479, 3640]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [451, 7390]	4110 [1770, 6450]	1860 [451, 7390]
n_event
Mean (SD)	348 (165)	NA	NA	142 (119)	99.0 (58.0)	185 (165)
Median [Q1, Q3]	348 [289, 406]	312 [312, 312]	671 [671, 671]	103 [77.0, 146]	99.0 [78.5, 120]	111 [81.0, 251]
Median [min, max]	348 [231, 464]	312 [312, 312]	671 [671, 671]	103 [34.0, 402]	99.0 [58.0, 140]	111 [34.0, 671]
FI_final
Mean (SD)	16.5 (13.4)	NA	NA	35.8 (45.1)	6.50 (7.78)	30.3 (40.4)
Median [Q1, Q3]	16.5 [11.8, 21.3]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [13.0, 36.3]	6.50 [3.75, 9.25]	15.0 [11.8, 27.8]
Median [min, max]	16.5 [7.00, 26.0]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [6.00, 171]	6.50 [1.00, 12.0]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.0109 (0.00529)	NA	NA	0.0160 (0.0117)	0.00121 (0.000916)	0.0137 (0.0114)
Median [Q1, Q3]	0.0109 [0.00901, 0.0127]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0104 [0.00692, 0.0277]	0.00121 [0.000890, 0.00154]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.0109 [0.00714, 0.0146]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0104 [0.00314, 0.0368]	0.00121 [0.000567, 0.00186]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	1 (100%)	0 (0%)	1 (5.6%)	0 (0%)	2 (8.3%)
1	2 (100%)	0 (0%)	0 (0%)	9 (50.0%)	2 (100%)	13 (54.2%)
Missing	0 (0%)	0 (0%)	1 (100%)	8 (44.4%)	0 (0%)	9 (37.5%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code2), data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any (N=2)	Osteoporotic (N=1)	Non-Vertebrae (N=1)	Vertebrae (N=18)	Hip (N=2)	Overall (N=24)
no_rand
Mean (SD)	3110 (1390)	NA	NA	3060 (2640)	5500 (3160)	3300 (2520)
Median [Q1, Q3]	3110 [2620, 3600]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [1240, 4350]	5500 [4390, 6620]	1980 [1560, 4600]
Median [min, max]	3110 [2130, 4090]	2000 [2000, 2000]	5090 [5090, 5090]	1650 [578, 7870]	5500 [3270, 7740]	1980 [578, 7870]
active_sample
Mean (SD)	2060 (2240)	NA	NA	2700 (2350)	4110 (3310)	2830 (2290)
Median [Q1, Q3]	2060 [1270, 2850]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [1070, 4020]	4110 [2940, 5280]	1860 [1110, 4330]
Median [min, max]	2060 [479, 3640]	1950 [1950, 1950]	4940 [4940, 4940]	1440 [451, 7390]	4110 [1770, 6450]	1860 [451, 7390]
n_event
Mean (SD)	348 (165)	NA	NA	142 (119)	99.0 (58.0)	185 (165)
Median [Q1, Q3]	348 [289, 406]	312 [312, 312]	671 [671, 671]	103 [77.0, 146]	99.0 [78.5, 120]	111 [81.0, 251]
Median [min, max]	348 [231, 464]	312 [312, 312]	671 [671, 671]	103 [34.0, 402]	99.0 [58.0, 140]	111 [34.0, 671]
FI_final
Mean (SD)	16.5 (13.4)	NA	NA	35.8 (45.1)	6.50 (7.78)	30.3 (40.4)
Median [Q1, Q3]	16.5 [11.8, 21.3]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [13.0, 36.3]	6.50 [3.75, 9.25]	15.0 [11.8, 27.8]
Median [min, max]	16.5 [7.00, 26.0]	33.0 [33.0, 33.0]	3.00 [3.00, 3.00]	17.5 [6.00, 171]	6.50 [1.00, 12.0]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.0109 (0.00529)	NA	NA	0.0160 (0.0117)	0.00121 (0.000916)	0.0137 (0.0114)
Median [Q1, Q3]	0.0109 [0.00901, 0.0127]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0104 [0.00692, 0.0277]	0.00121 [0.000890, 0.00154]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.0109 [0.00714, 0.0146]	0.0169 [0.0169, 0.0169]	0.000608 [0.000608, 0.000608]	0.0104 [0.00314, 0.0368]	0.00121 [0.000567, 0.00186]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	1 (100%)	0 (0%)	1 (5.6%)	0 (0%)	2 (8.3%)
1	2 (100%)	0 (0%)	0 (0%)	9 (50.0%)	2 (100%)	13 (54.2%)
Missing	0 (0%)	0 (0%)	1 (100%)	8 (44.4%)	0 (0%)	9 (37.5%)

kruskal.test(FI_final ~ fx_code2, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by fx_code2
## Kruskal-Wallis chi-squared = 6.705, df = 4, p-value = 0.1523

kruskal.test(FQ_final ~ fx_code2, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by fx_code2
## Kruskal-Wallis chi-squared = 7.83, df = 4, p-value = 0.09801

Box plots

p1 = ggplot(data = fx_prim2, aes(y = FI_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Fracture sites", y = "Fragility index")
p2 = ggplot(data =  fx_prim2, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Fracture sites", y = "Fragility quotient")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by fracture sites", gp = gpar(fontsize = 20, font = 1)))

(2.2.3) By pharmacological interventions

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code1), data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Alendronate (N=1)	Ibandronate (N=2)	Risedronate (N=1)	Minodronate (N=1)	Zoledronate (N=5)	Teriparatide (N=5)	Abaloparatide (N=1)	Romosozumab (N=4)	Denosumab (N=1)	Strontium_ranelate (N=2)	Calcium_VitD (N=1)	Overall (N=24)
no_rand
Mean (SD)	NA	1960 (0)	NA	NA	4160 (3280)	1150 (393)	NA	5640 (1780)	NA	3370 (2430)	NA	3300 (2520)
Median [Q1, Q3]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	2130 [2000, 7740]	1100 [1090, 1360]	1650 [1650, 1650]	5640 [4090, 7180]	7870 [7870, 7870]	3370 [2510, 4230]	3270 [3270, 3270]	1980 [1560, 4600]
Median [min, max]	4430 [4430, 4430]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	2130 [1200, 7740]	1100 [578, 1640]	1650 [1650, 1650]	5640 [4090, 7180]	7870 [7870, 7870]	3370 [1650, 5090]	3270 [3270, 3270]	1980 [578, 7870]
active_sample
Mean (SD)	NA	1950 (0)	NA	NA	3130 (2730)	940 (352)	NA	5150 (1730)	NA	3190 (2470)	NA	2830 (2290)
Median [Q1, Q3]	4130 [4130, 4130]	1950 [1950, 1950]	1370 [1370, 1370]	544 [544, 544]	1950 [1130, 5680]	892 [882, 1050]	1400 [1400, 1400]	5150 [3660, 6650]	7390 [7390, 7390]	3190 [2320, 4060]	1770 [1770, 1770]	1860 [1110, 4330]
Median [min, max]	4130 [4130, 4130]	1950 [1950, 1950]	1370 [1370, 1370]	544 [544, 544]	1950 [479, 6450]	892 [451, 1430]	1400 [1400, 1400]	5150 [3640, 6650]	7390 [7390, 7390]	3190 [1440, 4940]	1770 [1770, 1770]	1860 [451, 7390]
n_event
Mean (SD)	NA	111 (1.41)	NA	NA	224 (143)	69.0 (25.2)	NA	216 (177)	NA	529 (201)	NA	185 (165)
Median [Q1, Q3]	121 [121, 121]	111 [111, 112]	154 [154, 154]	100 [100, 100]	231 [140, 312]	83.0 [48.0, 86.0]	34.0 [34.0, 34.0]	163 [97.5, 282]	350 [350, 350]	529 [458, 600]	58.0 [58.0, 58.0]	111 [81.0, 251]
Median [min, max]	121 [121, 121]	111 [110, 112]	154 [154, 154]	100 [100, 100]	231 [37.0, 402]	83.0 [36.0, 92.0]	34.0 [34.0, 34.0]	163 [75.0, 464]	350 [350, 350]	529 [387, 671]	58.0 [58.0, 58.0]	111 [34.0, 671]
FI_final
Mean (SD)	NA	14.0 (1.41)	NA	NA	45.8 (70.8)	17.4 (6.23)	NA	33.0 (9.31)	NA	27.5 (34.6)	NA	30.3 (40.4)
Median [Q1, Q3]	13.0 [13.0, 13.0]	14.0 [13.5, 14.5]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	12.0 [7.00, 33.0]	15.0 [13.0, 23.0]	13.0 [13.0, 13.0]	33.0 [25.5, 40.5]	137 [137, 137]	27.5 [15.3, 39.8]	1.00 [1.00, 1.00]	15.0 [11.8, 27.8]
Median [min, max]	13.0 [13.0, 13.0]	14.0 [13.0, 15.0]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	12.0 [6.00, 171]	15.0 [11.0, 25.0]	13.0 [13.0, 13.0]	33.0 [24.0, 42.0]	137 [137, 137]	27.5 [3.00, 52.0]	1.00 [1.00, 1.00]	15.0 [1.00, 171]
FQ_final
Mean (SD)	NA	0.00717 (0.000724)	NA	NA	0.0138 (0.0111)	0.0210 (0.00948)	NA	0.00706 (0.00329)	NA	0.0183 (0.0251)	NA	0.0137 (0.0114)
Median [Q1, Q3]	0.00314 [0.00314, 0.00314]	0.00717 [0.00692, 0.00743]	0.00801 [0.00801, 0.00801]	0.0368 [0.0368, 0.0368]	0.0146 [0.00532, 0.0169]	0.0258 [0.0143, 0.0283]	0.00928 [0.00928, 0.00928]	0.00658 [0.00541, 0.00822]	0.0185 [0.0185, 0.0185]	0.0183 [0.00947, 0.0272]	0.000567 [0.000567, 0.000567]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.00314 [0.00314, 0.00314]	0.00717 [0.00666, 0.00768]	0.00801 [0.00801, 0.00801]	0.0368 [0.0368, 0.0368]	0.0146 [0.00186, 0.0301]	0.0258 [0.00770, 0.0288]	0.00928 [0.00928, 0.00928]	0.00658 [0.00361, 0.0115]	0.0185 [0.0185, 0.0185]	0.0183 [0.000608, 0.0361]	0.000567 [0.000567, 0.000567]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	0 (0%)	0 (0%)	1 (20.0%)	1 (20.0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	2 (8.3%)
1	0 (0%)	0 (0%)	1 (100%)	1 (100%)	4 (80.0%)	1 (20.0%)	1 (100%)	4 (100%)	0 (0%)	0 (0%)	1 (100%)	13 (54.2%)
Missing	1 (100%)	2 (100%)	0 (0%)	0 (0%)	0 (0%)	3 (60.0%)	0 (0%)	0 (0%)	1 (100%)	2 (100%)	0 (0%)	9 (37.5%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code2), data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Bisphosphonates (N=10)	PTH analog (N=6)	Romosozumab (N=4)	Denosumab (N=1)	Strontium_ranelate (N=2)	Calcium_VitD (N=1)	Overall (N=24)
no_rand
Mean (SD)	3150 (2600)	1230 (405)	5640 (1780)	NA	3370 (2430)	NA	3300 (2520)
Median [Q1, Q3]	1980 [1710, 3860]	1230 [1090, 1570]	5640 [4090, 7180]	7870 [7870, 7870]	3370 [2510, 4230]	3270 [3270, 3270]	1980 [1560, 4600]
Median [min, max]	1980 [704, 7740]	1230 [578, 1650]	5640 [4090, 7180]	7870 [7870, 7870]	3370 [1650, 5090]	3270 [3270, 3270]	1980 [578, 7870]
active_sample
Mean (SD)	2560 (2110)	1020 (366)	5150 (1730)	NA	3190 (2470)	NA	2830 (2290)
Median [Q1, Q3]	1950 [1190, 3590]	971 [885, 1310]	5150 [3660, 6650]	7390 [7390, 7390]	3190 [2320, 4060]	1770 [1770, 1770]	1860 [1110, 4330]
Median [min, max]	1950 [479, 6450]	971 [451, 1430]	5150 [3640, 6650]	7390 [7390, 7390]	3190 [1440, 4940]	1770 [1770, 1770]	1860 [451, 7390]
n_event
Mean (SD)	172 (111)	63.2 (26.7)	216 (177)	NA	529 (201)	NA	185 (165)
Median [Q1, Q3]	131 [111, 212]	65.5 [39.0, 85.3]	163 [97.5, 282]	350 [350, 350]	529 [458, 600]	58.0 [58.0, 58.0]	111 [81.0, 251]
Median [min, max]	131 [37.0, 402]	65.5 [34.0, 92.0]	163 [75.0, 464]	350 [350, 350]	529 [387, 671]	58.0 [58.0, 58.0]	111 [34.0, 671]
FI_final
Mean (SD)	30.1 (50.1)	16.7 (5.85)	33.0 (9.31)	NA	27.5 (34.6)	NA	30.3 (40.4)
Median [Q1, Q3]	13.0 [11.3, 18.8]	14.0 [13.0, 21.0]	33.0 [25.5, 40.5]	137 [137, 137]	27.5 [15.3, 39.8]	1.00 [1.00, 1.00]	15.0 [11.8, 27.8]
Median [min, max]	13.0 [6.00, 171]	14.0 [11.0, 25.0]	33.0 [24.0, 42.0]	137 [137, 137]	27.5 [3.00, 52.0]	1.00 [1.00, 1.00]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.0131 (0.0118)	0.0190 (0.00974)	0.00706 (0.00329)	NA	0.0183 (0.0251)	NA	0.0137 (0.0114)
Median [Q1, Q3]	0.00785 [0.00566, 0.0164]	0.0200 [0.0105, 0.0277]	0.00658 [0.00541, 0.00822]	0.0185 [0.0185, 0.0185]	0.0183 [0.00947, 0.0272]	0.000567 [0.000567, 0.000567]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.00785 [0.00186, 0.0368]	0.0200 [0.00770, 0.0288]	0.00658 [0.00361, 0.0115]	0.0185 [0.0185, 0.0185]	0.0183 [0.000608, 0.0361]	0.000567 [0.000567, 0.000567]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	1 (10.0%)	1 (16.7%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	2 (8.3%)
1	6 (60.0%)	2 (33.3%)	4 (100%)	0 (0%)	0 (0%)	1 (100%)	13 (54.2%)
Missing	3 (30.0%)	3 (50.0%)	0 (0%)	1 (100%)	2 (100%)	0 (0%)	9 (37.5%)

kruskal.test(FI_final ~ interv_code2, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by interv_code2
## Kruskal-Wallis chi-squared = 8.7285, df = 5, p-value = 0.1204

kruskal.test(FQ_final ~ interv_code2, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by interv_code2
## Kruskal-Wallis chi-squared = 6.313, df = 5, p-value = 0.2769

Box plots

p1 = ggplot(data =  fx_prim2, aes(y = FI_final, x = as.factor(interv_code2), fill = as.factor(interv_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Pharmacological interventions", y = "Fragility index")
p2 = ggplot(data =  fx_prim2, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Pharmacological interventions", y = "Fragility quotine")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by intervention sites", gp = gpar(fontsize = 20, font = 1)))

(2.2.4) Timing of fracture assessment

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(timing), data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	2 (N=1)	3 (N=4)	4 (N=8)	5 (N=8)	6 (N=1)	7 (N=1)	8 (N=1)	Overall (N=24)
no_rand
Mean (SD)	NA	1780 (1110)	2600 (2300)	4080 (3070)	NA	NA	NA	3300 (2520)
Median [Q1, Q3]	7180 [7180, 7180]	1640 [1370, 2050]	1280 [1090, 4090]	2050 [1890, 7740]	4430 [4430, 4430]	5090 [5090, 5090]	2000 [2000, 2000]	1980 [1560, 4600]
Median [min, max]	7180 [7180, 7180]	1640 [578, 3270]	1280 [704, 7180]	2050 [1630, 7870]	4430 [4430, 4430]	5090 [5090, 5090]	2000 [2000, 2000]	1980 [578, 7870]
active_sample
Mean (SD)	NA	1260 (565)	2310 (2160)	3340 (2700)	NA	NA	NA	2830 (2290)
Median [Q1, Q3]	6640 [6640, 6640]	1410 [1160, 1510]	1090 [890, 3650]	1950 [1430, 5870]	4130 [4130, 4130]	4940 [4940, 4940]	1950 [1950, 1950]	1860 [1110, 4330]
Median [min, max]	6640 [6640, 6640]	1410 [451, 1770]	1090 [544, 6650]	1950 [479, 7390]	4130 [4130, 4130]	4940 [4940, 4940]	1950 [1950, 1950]	1860 [451, 7390]
n_event
Mean (SD)	NA	44.0 (11.2)	149 (138)	236 (126)	NA	NA	NA	185 (165)
Median [Q1, Q3]	75.0 [75.0, 75.0]	42.0 [35.5, 50.5]	96.0 [85.3, 134]	193 [133, 359]	121 [121, 121]	671 [671, 671]	312 [312, 312]	111 [81.0, 251]
Median [min, max]	75.0 [75.0, 75.0]	42.0 [34.0, 58.0]	96.0 [37.0, 464]	193 [110, 402]	121 [121, 121]	671 [671, 671]	312 [312, 312]	111 [34.0, 671]
FI_final
Mean (SD)	NA	9.50 (5.74)	24.6 (12.0)	52.3 (65.0)	NA	NA	NA	30.3 (40.4)
Median [Q1, Q3]	24.0 [24.0, 24.0]	12.0 [8.50, 13.0]	24.0 [18.8, 29.5]	14.0 [11.8, 73.3]	13.0 [13.0, 13.0]	3.00 [3.00, 3.00]	33.0 [33.0, 33.0]	15.0 [11.8, 27.8]
Median [min, max]	24.0 [24.0, 24.0]	12.0 [1.00, 13.0]	24.0 [6.00, 42.0]	14.0 [7.00, 171]	13.0 [13.0, 13.0]	3.00 [3.00, 3.00]	33.0 [33.0, 33.0]	15.0 [1.00, 171]
FQ_final
Mean (SD)	NA	0.0116 (0.0121)	0.0169 (0.0119)	0.0154 (0.0121)	NA	NA	NA	0.0137 (0.0114)
Median [Q1, Q3]	0.00361 [0.00361, 0.00361]	0.00849 [0.00592, 0.0142]	0.0129 [0.00686, 0.0264]	0.0113 [0.00743, 0.0214]	0.00314 [0.00314, 0.00314]	0.000608 [0.000608, 0.000608]	0.0169 [0.0169, 0.0169]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.00361 [0.00361, 0.00361]	0.00849 [0.000567, 0.0288]	0.0129 [0.00532, 0.0368]	0.0113 [0.00186, 0.0361]	0.00314 [0.00314, 0.00314]	0.000608 [0.000608, 0.000608]	0.0169 [0.0169, 0.0169]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	1 (12.5%)	0 (0%)	0 (0%)	0 (0%)	1 (100%)	2 (8.3%)
1	1 (100%)	3 (75.0%)	5 (62.5%)	4 (50.0%)	0 (0%)	0 (0%)	0 (0%)	13 (54.2%)
Missing	0 (0%)	1 (25.0%)	2 (25.0%)	4 (50.0%)	1 (100%)	1 (100%)	0 (0%)	9 (37.5%)

kruskal.test(FI_final ~ timing, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by timing
## Kruskal-Wallis chi-squared = 7.7077, df = 6, p-value = 0.2603

kruskal.test(FQ_final ~ timing, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by timing
## Kruskal-Wallis chi-squared = 6.11, df = 6, p-value = 0.411

Box plots

p1 = ggplot(data =  fx_prim2, aes(y = FI_final, x = as.factor(timing), fill = as.factor(timing))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index")
p1

(2.2.5) By journal

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(journal_code2), data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	NEJM (N=14)	Lancet (N=1)	JAMA (N=4)	JBMR (N=2)	JCEM (N=1)	Other (N=2)	Overall (N=24)
no_rand
Mean (SD)	4170 (2790)	NA	2340 (1400)	1960 (0)	NA	2900 (3100)	3300 (2520)
Median [Q1, Q3]	3680 [1740, 7180]	1360 [1360, 1360]	1640 [1640, 2340]	1960 [1960, 1960]	578 [578, 578]	2900 [1800, 3990]	1980 [1560, 4600]
Median [min, max]	3680 [1090, 7870]	1360 [1360, 1360]	1640 [1630, 4430]	1960 [1960, 1960]	578 [578, 578]	2900 [704, 5090]	1980 [578, 7870]
active_sample
Mean (SD)	3470 (2580)	NA	2080 (1370)	1950 (0)	NA	2740 (3100)	2830 (2290)
Median [Q1, Q3]	2800 [1210, 6250]	1050 [1050, 1050]	1410 [1390, 2100]	1950 [1950, 1950]	451 [451, 451]	2740 [1640, 3840]	1860 [1110, 4330]
Median [min, max]	2800 [479, 7390]	1050 [1050, 1050]	1410 [1370, 4130]	1950 [1950, 1950]	451 [451, 451]	2740 [544, 4940]	1860 [451, 7390]
n_event
Mean (SD)	211 (147)	NA	86.3 (60.7)	111 (1.41)	NA	386 (404)	185 (165)
Median [Q1, Q3]	181 [83.8, 341]	92.0 [92.0, 92.0]	78.5 [35.5, 129]	111 [111, 112]	48.0 [48.0, 48.0]	386 [243, 528]	111 [81.0, 251]
Median [min, max]	181 [37.0, 464]	92.0 [92.0, 92.0]	78.5 [34.0, 154]	111 [110, 112]	48.0 [48.0, 48.0]	386 [100, 671]	111 [34.0, 671]
FI_final
Mean (SD)	42.8 (49.7)	NA	12.0 (1.15)	14.0 (1.41)	NA	11.5 (12.0)	30.3 (40.4)
Median [Q1, Q3]	25.5 [14.8, 41.5]	15.0 [15.0, 15.0]	12.0 [11.0, 13.0]	14.0 [13.5, 14.5]	13.0 [13.0, 13.0]	11.5 [7.25, 15.8]	15.0 [11.8, 27.8]
Median [min, max]	25.5 [1.00, 171]	15.0 [15.0, 15.0]	12.0 [11.0, 13.0]	14.0 [13.0, 15.0]	13.0 [13.0, 13.0]	11.5 [3.00, 20.0]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.0147 (0.0116)	NA	0.00703 (0.00268)	0.00717 (0.000724)	NA	0.0187 (0.0256)	0.0137 (0.0114)
Median [Q1, Q3]	0.0130 [0.00550, 0.0240]	0.0143 [0.0143, 0.0143]	0.00785 [0.00656, 0.00832]	0.00717 [0.00692, 0.00743]	0.0288 [0.0288, 0.0288]	0.0187 [0.00965, 0.0277]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.0130 [0.000567, 0.0361]	0.0143 [0.0143, 0.0143]	0.00785 [0.00314, 0.00928]	0.00717 [0.00666, 0.00768]	0.0288 [0.0288, 0.0288]	0.0187 [0.000608, 0.0368]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	1 (7.1%)	1 (100%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	2 (8.3%)
1	9 (64.3%)	0 (0%)	3 (75.0%)	0 (0%)	0 (0%)	1 (50.0%)	13 (54.2%)
Missing	4 (28.6%)	0 (0%)	1 (25.0%)	2 (100%)	1 (100%)	1 (50.0%)	9 (37.5%)

kruskal.test(FI_final ~ journal_code2, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by journal_code2
## Kruskal-Wallis chi-squared = 4.8553, df = 5, p-value = 0.4338

kruskal.test(FQ_final ~ journal_code2, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by journal_code2
## Kruskal-Wallis chi-squared = 2.6057, df = 5, p-value = 0.7605

Box plots

p1 = ggplot(data =  fx_prim2, aes(y = FI_final, x = as.factor(timing), fill = as.factor(journal_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index") 
p1

(2.2.6) By sex

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | sex, data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Both (N=2)	Men (N=1)	Women (N=21)	Overall (N=24)
no_rand
Mean (SD)	1350 (1100)	NA	3590 (2560)	3300 (2520)
Median [Q1, Q3]	1350 [965, 1740]	1200 [1200, 1200]	2000 [1640, 5090]	1980 [1560, 4600]
Median [min, max]	1350 [578, 2130]	1200 [1200, 1200]	2000 [704, 7870]	1980 [578, 7870]
active_sample
Mean (SD)	465 (19.8)	NA	3130 (2280)	2830 (2290)
Median [Q1, Q3]	465 [458, 472]	1130 [1130, 1130]	1950 [1400, 4940]	1860 [1110, 4330]
Median [min, max]	465 [451, 479]	1130 [1130, 1130]	1950 [544, 7390]	1860 [451, 7390]
n_event
Mean (SD)	140 (129)	NA	196 (170)	185 (165)
Median [Q1, Q3]	140 [93.8, 185]	37.0 [37.0, 37.0]	112 [86.0, 312]	111 [81.0, 251]
Median [min, max]	140 [48.0, 231]	37.0 [37.0, 37.0]	112 [34.0, 671]	111 [34.0, 671]
FI_final
Mean (SD)	10.0 (4.24)	NA	33.3 (42.4)	30.3 (40.4)
Median [Q1, Q3]	10.0 [8.50, 11.5]	6.00 [6.00, 6.00]	20.0 [13.0, 33.0]	15.0 [11.8, 27.8]
Median [min, max]	10.0 [7.00, 13.0]	6.00 [6.00, 6.00]	20.0 [1.00, 171]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.0217 (0.0100)	NA	0.0134 (0.0116)	0.0137 (0.0114)
Median [Q1, Q3]	0.0217 [0.0182, 0.0253]	0.00532 [0.00532, 0.00532]	0.00801 [0.00601, 0.0185]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.0217 [0.0146, 0.0288]	0.00532 [0.00532, 0.00532]	0.00801 [0.000567, 0.0368]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	2 (9.5%)	2 (8.3%)
1	1 (50.0%)	1 (100%)	11 (52.4%)	13 (54.2%)
Missing	1 (50.0%)	0 (0%)	8 (38.1%)	9 (37.5%)

kruskal.test(FI_final ~ sex, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by sex
## Kruskal-Wallis chi-squared = 3.5661, df = 2, p-value = 0.1681

kruskal.test(FQ_final ~ sex, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by sex
## Kruskal-Wallis chi-squared = 2.3138, df = 2, p-value = 0.3145

Box plots

p1 = ggplot(data =  fx_prim2, aes(y = FI_final, x = as.factor(sex), fill = as.factor(sex))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by sex", x = "Sex", y = "Fragility index") 
p1

(2.2.7) By placebo

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | placebo, data =  fx_prim2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Active (N=5)	Placebo (N=19)	Overall (N=24)
no_rand
Mean (SD)	2570 (1400)	3500 (2730)	3300 (2520)
Median [Q1, Q3]	1650 [1640, 4090]	2000 [1410, 6140]	1980 [1560, 4600]
Median [min, max]	1650 [1360, 4090]	2000 [578, 7870]	1980 [578, 7870]
active_sample
Mean (SD)	2240 (1300)	2980 (2490)	2830 (2290)
Median [Q1, Q3]	1430 [1400, 3640]	1950 [1010, 5310]	1860 [1110, 4330]
Median [min, max]	1430 [1050, 3660]	1950 [451, 7390]	1860 [451, 7390]
n_event
Mean (SD)	169 (181)	189 (165)	185 (165)
Median [Q1, Q3]	92.0 [36.0, 221]	112 [84.5, 272]	111 [81.0, 251]
Median [min, max]	92.0 [34.0, 464]	112 [37.0, 671]	111 [34.0, 671]
FI_final
Mean (SD)	21.4 (12.9)	32.6 (45.0)	30.3 (40.4)
Median [Q1, Q3]	15.0 [13.0, 26.0]	15.0 [11.5, 29.0]	15.0 [11.8, 27.8]
Median [min, max]	15.0 [11.0, 42.0]	15.0 [1.00, 171]	15.0 [1.00, 171]
FQ_final
Mean (SD)	0.00998 (0.00294)	0.0147 (0.0126)	0.0137 (0.0114)
Median [Q1, Q3]	0.00928 [0.00770, 0.0115]	0.00801 [0.00447, 0.0271]	0.00864 [0.00584, 0.0203]
Median [min, max]	0.00928 [0.00714, 0.0143]	0.00801 [0.000567, 0.0368]	0.00864 [0.000567, 0.0368]
as.factor(missing_fi)
0	1 (20.0%)	1 (5.3%)	2 (8.3%)
1	4 (80.0%)	9 (47.4%)	13 (54.2%)
Missing	0 (0%)	9 (47.4%)	9 (37.5%)

kruskal.test(FI_final ~ placebo, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by placebo
## Kruskal-Wallis chi-squared = 0.081266, df = 1, p-value = 0.7756

kruskal.test(FQ_final ~ placebo, data = fx_prim2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by placebo
## Kruskal-Wallis chi-squared = 0.0012632, df = 1, p-value = 0.9716

Box plots

p1 = ggplot(data =  fx_prim2, aes(y = FI_final, x = as.factor(control), fill = as.factor(control))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by types of control", x = "Types of control", y = "Fragility index") 
p1

(2.3) Analyses with P< 0.001

(2.3.1) Overall

# Comparison of different P values:
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | p_sig2 , data = ori_st, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Highly significant (N=37)	Significant (N=75)	Overall (N=112)
no_rand
Mean (SD)	4240 (2890)	2750 (2050)	3240 (2450)
Median [Q1, Q3]	4090 [1640, 7180]	1960 [1360, 4090]	1980 [1360, 4430]
Median [min, max]	4090 [578, 7870]	1960 [450, 7870]	1980 [450, 7870]
active_sample
Mean (SD)	3750 (2630)	2370 (1850)	2820 (2230)
Median [Q1, Q3]	3660 [1270, 6640]	1770 [1110, 3480]	1860 [1130, 4020]
Median [min, max]	3660 [451, 7810]	1770 [339, 6670]	1860 [339, 7810]
n_event
Mean (SD)	211 (204)	153 (168)	172 (181)
Median [Q1, Q3]	106 [76.0, 312]	76.0 [44.0, 173]	95.5 [52.5, 227]
Median [min, max]	106 [34.0, 764]	76.0 [10.0, 691]	95.5 [10.0, 764]
FI_final
Mean (SD)	38.5 (35.3)	7.00 (6.23)	17.4 (25.5)
Median [Q1, Q3]	26.0 [17.0, 42.0]	5.00 [2.00, 9.50]	9.00 [4.00, 21.3]
Median [min, max]	26.0 [9.00, 171]	5.00 [1.00, 29.0]	9.00 [1.00, 171]
FQ_final
Mean (SD)	0.0155 (0.0167)	0.00402 (0.00337)	0.00782 (0.0113)
Median [Q1, Q3]	0.00928 [0.00653, 0.0185]	0.00296 [0.00153, 0.00535]	0.00480 [0.00219, 0.00852]
Median [min, max]	0.00928 [0.00230, 0.0966]	0.00296 [0.000151, 0.0146]	0.00480 [0.000151, 0.0966]
as.factor(missing_fi)
0	4 (10.8%)	4 (5.3%)	8 (7.1%)
1	21 (56.8%)	43 (57.3%)	64 (57.1%)
Missing	12 (32.4%)	28 (37.3%)	40 (35.7%)

createTable(compareGroups(p_sig2 ~ no_rand + active_sample + n_event + FI_final + FQ_final + missing_fi, data = ori_st, method = c(no_rand = 2, active_sample = 2, n_event = 2, FI_final = 2, FQ_final = 2)))

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning in chisq.test(xx, correct = FALSE): Chi-squared approximation may be
## incorrect

## 
## --------Summary descriptives table by 'p_sig2'---------
## 
## ___________________________________________________________ 
##               Highly significant   Significant    p.overall 
##                      N=37              N=75                 
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 
## no_rand        4093 [1639;7180]  1964 [1360;4093]   0.030   
## active_sample  3659 [1266;6643]  1765 [1114;3479]   0.013   
## n_event         106 [76.0;312]   76.0 [44.0;173]    0.029   
## FI_final       26.0 [17.0;42.0]  5.00 [2.00;9.50]  <0.001   
## FQ_final       0.01 [0.01;0.02]  0.00 [0.00;0.01]  <0.001   
## missing_fi:                                         0.436   
##     0             4 (16.0%)         4 (8.51%)               
##     1             21 (84.0%)        43 (91.5%)              
## ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

# Subset of analyses whose P-value<= 0.001

p_sig2 = subset(ori_st, Pval_screen<=0.001)
table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Overall (N=37)
no_rand
Mean (SD)	4240 (2890)
Median [Q1, Q3]	4090 [1640, 7180]
Median [min, max]	4090 [578, 7870]
active_sample
Mean (SD)	3750 (2630)
Median [Q1, Q3]	3660 [1270, 6640]
Median [min, max]	3660 [451, 7810]
n_event
Mean (SD)	211 (204)
Median [Q1, Q3]	106 [76.0, 312]
Median [min, max]	106 [34.0, 764]
FI_final
Mean (SD)	38.5 (35.3)
Median [Q1, Q3]	26.0 [17.0, 42.0]
Median [min, max]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.0155 (0.0167)
Median [Q1, Q3]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	4 (10.8%)
1	21 (56.8%)
Missing	12 (32.4%)

Relationship between sample size/active sample/no. events and FI

p = ggplot(data = p_sig2, aes(x = no_rand, y = FI_final))
p1 = p + geom_point() + geom_smooth() + labs(x = "Number of participants at randomisation", y = "Fragility index") + theme_bw()

p0 = ggplot(data = p_sig2, aes(x = active_sample, y = FI_final))
p2 = p0 + geom_point() + geom_smooth() + labs(x = "Number of participants included in the analyses", y = "Fragility index") + theme_bw()

p.0 = ggplot(data = p_sig2, aes(x = n_event, y = FI_final))
p3 = p.0 + geom_point() + geom_smooth() + labs(x = "Number of participants with fracture events", y = "Fragility index") + theme_bw()

#grid.arrange(p1, p2, p3, nrow = 1)
grid.arrange(p1, p3, nrow = 1, top = textGrob("Relationship between Number of participants and Fragility index", gp = gpar(fontsize = 20, font = 3)))

## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

(2.3.2) By fracture sites

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code1), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Clin_fx (N=2)	OFx (N=3)	MOF (N=2)	NonVert_fx (N=3)	Vert_fx (N=25)	ClinVert_fx (N=2)	Overall (N=37)
no_rand
Mean (SD)	7460 (393)	3400 (1210)	2870 (1730)	7370 (321)	3530 (2890)	7800 (93.3)	4240 (2890)
Median [Q1, Q3]	7460 [7320, 7600]	4090 [3050, 4090]	2870 [2260, 3480]	7180 [7180, 7460]	1650 [1360, 7180]	7800 [7770, 7840]	4090 [1640, 7180]
Median [min, max]	7460 [7180, 7740]	4090 [2000, 4090]	2870 [1650, 4090]	7180 [7180, 7740]	1650 [578, 7870]	7800 [7740, 7870]	4090 [578, 7870]
active_sample
Mean (SD)	6620 (100)	3250 (1130)	2400 (1600)	6620 (76.9)	3080 (2620)	7120 (975)	3750 (2630)
Median [Q1, Q3]	6620 [6580, 6660]	3840 [2890, 3910]	2400 [1830, 2970]	6650 [6590, 6660]	1430 [1050, 5680]	7120 [6770, 7460]	3660 [1270, 6640]
Median [min, max]	6620 [6550, 6690]	3840 [1950, 3980]	2400 [1270, 3530]	6650 [6530, 6670]	1430 [451, 7390]	7120 [6430, 7810]	3660 [451, 7810]
n_event
Mean (SD)	505 (366)	431 (197)	200 (220)	358 (281)	152 (156)	112 (12.7)	211 (204)
Median [Q1, Q3]	505 [376, 635]	323 [318, 491]	200 [122, 277]	225 [197, 453]	92.0 [73.0, 128]	112 [108, 117]	106 [76.0, 312]
Median [min, max]	505 [246, 764]	323 [312, 658]	200 [44.0, 355]	225 [168, 680]	92.0 [34.0, 696]	112 [103, 121]	106 [34.0, 764]
FI_final
Mean (SD)	62.5 (37.5)	42.7 (19.4)	17.5 (12.0)	29.0 (12.2)	38.7 (40.8)	40.5 (2.12)	38.5 (35.3)
Median [Q1, Q3]	62.5 [49.3, 75.8]	33.0 [31.5, 49.0]	17.5 [13.3, 21.8]	23.0 [22.0, 33.0]	23.0 [17.0, 40.0]	40.5 [39.8, 41.3]	26.0 [17.0, 42.0]
Median [min, max]	62.5 [36.0, 89.0]	33.0 [30.0, 65.0]	17.5 [9.00, 26.0]	23.0 [21.0, 43.0]	23.0 [11.0, 171]	40.5 [39.0, 42.0]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.00949 (0.00580)	0.0138 (0.00543)	0.00723 (0.000175)	0.00440 (0.00190)	0.0190 (0.0192)	0.00576 (0.00109)	0.0155 (0.0167)
Median [Q1, Q3]	0.00949 [0.00743, 0.0115]	0.0169 [0.0122, 0.0169]	0.00723 [0.00717, 0.00730]	0.00346 [0.00330, 0.00502]	0.0137 [0.00768, 0.0258]	0.00576 [0.00538, 0.00615]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00949 [0.00538, 0.0136]	0.0169 [0.00754, 0.0169]	0.00723 [0.00711, 0.00736]	0.00346 [0.00315, 0.00659]	0.0137 [0.00230, 0.0966]	0.00576 [0.00499, 0.00653]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	2 (66.7%)	0 (0%)	0 (0%)	2 (8.0%)	0 (0%)	4 (10.8%)
1	2 (100%)	1 (33.3%)	2 (100%)	3 (100%)	12 (48.0%)	1 (50.0%)	21 (56.8%)
Missing	0 (0%)	0 (0%)	0 (0%)	0 (0%)	11 (44.0%)	1 (50.0%)	12 (32.4%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(fx_code2), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Any (N=2)	Osteoporotic (N=5)	Non-Vertebrae (N=3)	Vertebrae (N=25)	Clinical Vertebrae (N=2)	Overall (N=37)
no_rand
Mean (SD)	7460 (393)	3180 (1250)	7370 (321)	3530 (2890)	7800 (93.3)	4240 (2890)
Median [Q1, Q3]	7460 [7320, 7600]	4090 [2000, 4090]	7180 [7180, 7460]	1650 [1360, 7180]	7800 [7770, 7840]	4090 [1640, 7180]
Median [min, max]	7460 [7180, 7740]	4090 [1650, 4090]	7180 [7180, 7740]	1650 [578, 7870]	7800 [7740, 7870]	4090 [578, 7870]
active_sample
Mean (SD)	6620 (100)	2910 (1230)	6620 (76.9)	3080 (2620)	7120 (975)	3750 (2630)
Median [Q1, Q3]	6620 [6580, 6660]	3530 [1950, 3840]	6650 [6590, 6660]	1430 [1050, 5680]	7120 [6770, 7460]	3660 [1270, 6640]
Median [min, max]	6620 [6550, 6690]	3530 [1270, 3980]	6650 [6530, 6670]	1430 [451, 7390]	7120 [6430, 7810]	3660 [451, 7810]
n_event
Mean (SD)	505 (366)	338 (218)	358 (281)	152 (156)	112 (12.7)	211 (204)
Median [Q1, Q3]	505 [376, 635]	323 [312, 355]	225 [197, 453]	92.0 [73.0, 128]	112 [108, 117]	106 [76.0, 312]
Median [min, max]	505 [246, 764]	323 [44.0, 658]	225 [168, 680]	92.0 [34.0, 696]	112 [103, 121]	106 [34.0, 764]
FI_final
Mean (SD)	62.5 (37.5)	32.6 (20.4)	29.0 (12.2)	38.7 (40.8)	40.5 (2.12)	38.5 (35.3)
Median [Q1, Q3]	62.5 [49.3, 75.8]	30.0 [26.0, 33.0]	23.0 [22.0, 33.0]	23.0 [17.0, 40.0]	40.5 [39.8, 41.3]	26.0 [17.0, 42.0]
Median [min, max]	62.5 [36.0, 89.0]	30.0 [9.00, 65.0]	23.0 [21.0, 43.0]	23.0 [11.0, 171]	40.5 [39.0, 42.0]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.00949 (0.00580)	0.0112 (0.00526)	0.00440 (0.00190)	0.0190 (0.0192)	0.00576 (0.00109)	0.0155 (0.0167)
Median [Q1, Q3]	0.00949 [0.00743, 0.0115]	0.00754 [0.00736, 0.0169]	0.00346 [0.00330, 0.00502]	0.0137 [0.00768, 0.0258]	0.00576 [0.00538, 0.00615]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00949 [0.00538, 0.0136]	0.00754 [0.00711, 0.0169]	0.00346 [0.00315, 0.00659]	0.0137 [0.00230, 0.0966]	0.00576 [0.00499, 0.00653]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	2 (40.0%)	0 (0%)	2 (8.0%)	0 (0%)	4 (10.8%)
1	2 (100%)	3 (60.0%)	3 (100%)	12 (48.0%)	1 (50.0%)	21 (56.8%)
Missing	0 (0%)	0 (0%)	0 (0%)	11 (44.0%)	1 (50.0%)	12 (32.4%)

kruskal.test(FI_final ~ fx_code2, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by fx_code2
## Kruskal-Wallis chi-squared = 3.1249, df = 4, p-value = 0.5371

kruskal.test(FQ_final ~ fx_code2, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by fx_code2
## Kruskal-Wallis chi-squared = 8.9632, df = 4, p-value = 0.06202

Box plots

p1 = ggplot(data = p_sig2, aes(y = FI_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Fracture sites", y = "Fragility index")
p2 = ggplot(data = p_sig2, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Fracture sites", y = "Fragility quotient")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by fracture sites", gp = gpar(fontsize = 20, font = 1)))

(2.3.3) By pharmacological interventions

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code1), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Ibandronate (N=1)	Risedronate (N=1)	Minodronate (N=1)	Zoledronate (N=6)	Teriparatide (N=8)	Abaloparatide (N=2)	Romosozumab (N=12)	Denosumab (N=3)	Strontium_ranelate (N=3)	Overall (N=37)
no_rand
Mean (SD)	NA	NA	NA	6780 (2340)	1160 (309)	1650 (0)	5890 (1590)	7870 (0)	1650 (0)	4240 (2890)
Median [Q1, Q3]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	7740 [7740, 7740]	1100 [1090, 1360]	1650 [1650, 1650]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 1650]	4090 [1640, 7180]
Median [min, max]	1960 [1960, 1960]	1630 [1630, 1630]	704 [704, 704]	7740 [2000, 7740]	1100 [578, 1640]	1650 [1650, 1650]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 1650]	4090 [578, 7870]
active_sample
Mean (SD)	NA	NA	NA	5470 (1770)	941 (271)	1330 (95.5)	5460 (1530)	7530 (240)	1330 (155)	3750 (2630)
Median [Q1, Q3]	1950 [1950, 1950]	1330 [1330, 1330]	544 [544, 544]	6050 [5680, 6500]	892 [882, 1050]	1330 [1300, 1370]	6640 [3790, 6660]	7390 [7390, 7600]	1390 [1270, 1410]	3660 [1270, 6640]
Median [min, max]	1950 [1950, 1950]	1330 [1330, 1330]	544 [544, 544]	6050 [1950, 6550]	892 [451, 1430]	1330 [1270, 1400]	6640 [3530, 6910]	7390 [7390, 7810]	1390 [1150, 1440]	3660 [451, 7810]
n_event
Mean (SD)	NA	NA	NA	389 (287)	67.8 (24.9)	39.0 (7.07)	234 (163)	184 (145)	404 (284)	211 (204)
Median [Q1, Q3]	110 [110, 110]	58.0 [58.0, 58.0]	100 [100, 100]	357 [155, 611]	67.0 [47.5, 87.5]	39.0 [36.5, 41.5]	223 [106, 272]	121 [102, 236]	387 [258, 542]	106 [76.0, 312]
Median [min, max]	110 [110, 110]	58.0 [58.0, 58.0]	100 [100, 100]	357 [73.0, 764]	67.0 [36.0, 100]	39.0 [34.0, 44.0]	223 [75.0, 658]	121 [82.0, 350]	387 [128, 696]	106 [34.0, 764]
FI_final
Mean (SD)	NA	NA	NA	69.3 (53.8)	17.9 (5.00)	11.0 (2.83)	35.1 (12.8)	64.3 (63.9)	60.7 (46.6)	38.5 (35.3)
Median [Q1, Q3]	15.0 [15.0, 15.0]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	42.5 [39.0, 77.5]	17.0 [14.5, 22.3]	11.0 [10.0, 12.0]	33.0 [25.5, 40.5]	39.0 [28.0, 88.0]	52.0 [35.5, 81.5]	26.0 [17.0, 42.0]
Median [min, max]	15.0 [15.0, 15.0]	11.0 [11.0, 11.0]	20.0 [20.0, 20.0]	42.5 [33.0, 171]	17.0 [11.0, 25.0]	11.0 [9.00, 13.0]	33.0 [21.0, 65.0]	39.0 [17.0, 137]	52.0 [19.0, 111]	26.0 [9.00, 171]
FQ_final
Mean (SD)	NA	NA	NA	0.0134 (0.00928)	0.0206 (0.00754)	0.00819 (0.00153)	0.00732 (0.00436)	0.00861 (0.00870)	0.0488 (0.0429)	0.0155 (0.0167)
Median [Q1, Q3]	0.00768 [0.00768, 0.00768]	0.00828 [0.00828, 0.00828]	0.0368 [0.0368, 0.0368]	0.0101 [0.00661, 0.0161]	0.0220 [0.0157, 0.0264]	0.00819 [0.00765, 0.00874]	0.00594 [0.00383, 0.00853]	0.00499 [0.00365, 0.0118]	0.0361 [0.0249, 0.0663]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00768 [0.00768, 0.00768]	0.00828 [0.00828, 0.00828]	0.0368 [0.0368, 0.0368]	0.0101 [0.00653, 0.0301]	0.0220 [0.00770, 0.0288]	0.00819 [0.00711, 0.00928]	0.00594 [0.00315, 0.0169]	0.00499 [0.00230, 0.0185]	0.0361 [0.0137, 0.0966]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	0 (0%)	0 (0%)	1 (16.7%)	2 (25.0%)	0 (0%)	1 (8.3%)	0 (0%)	0 (0%)	4 (10.8%)
1	0 (0%)	1 (100%)	1 (100%)	5 (83.3%)	1 (12.5%)	2 (100%)	11 (91.7%)	0 (0%)	0 (0%)	21 (56.8%)
Missing	1 (100%)	0 (0%)	0 (0%)	0 (0%)	5 (62.5%)	0 (0%)	0 (0%)	3 (100%)	3 (100%)	12 (32.4%)

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(interv_code2), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]"))

	Bisphosphonates (N=9)	PTH analog (N=10)	Romosozumab (N=12)	Denosumab (N=3)	Strontium_ranelate (N=3)	Overall (N=37)
no_rand
Mean (SD)	5000 (3270)	1260 (340)	5890 (1590)	7870 (0)	1650 (0)	4240 (2890)
Median [Q1, Q3]	7740 [1960, 7740]	1230 [1090, 1570]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 1650]	4090 [1640, 7180]
Median [min, max]	7740 [704, 7740]	1230 [578, 1650]	7180 [4090, 7180]	7870 [7870, 7870]	1650 [1650, 1650]	4090 [578, 7870]
active_sample
Mean (SD)	4070 (2550)	1020 (292)	5460 (1530)	7530 (240)	1330 (155)	3750 (2630)
Median [Q1, Q3]	5680 [1950, 6430]	971 [885, 1210]	6640 [3790, 6660]	7390 [7390, 7600]	1390 [1270, 1410]	3660 [1270, 6640]
Median [min, max]	5680 [544, 6550]	971 [451, 1430]	6640 [3530, 6910]	7390 [7390, 7810]	1390 [1150, 1440]	3660 [451, 7810]
n_event
Mean (SD)	289 (273)	62.0 (25.2)	234 (163)	184 (145)	404 (284)	211 (204)
Median [Q1, Q3]	110 [100, 402]	49.5 [44.5, 85.3]	223 [106, 272]	121 [102, 236]	387 [258, 542]	106 [76.0, 312]
Median [min, max]	110 [58.0, 764]	49.5 [34.0, 100]	223 [75.0, 658]	121 [82.0, 350]	387 [128, 696]	106 [34.0, 764]
FI_final
Mean (SD)	51.3 (50.4)	16.5 (5.36)	35.1 (12.8)	64.3 (63.9)	60.7 (46.6)	38.5 (35.3)
Median [Q1, Q3]	38.0 [20.0, 43.0]	16.0 [13.0, 20.8]	33.0 [25.5, 40.5]	39.0 [28.0, 88.0]	52.0 [35.5, 81.5]	26.0 [17.0, 42.0]
Median [min, max]	38.0 [11.0, 171]	16.0 [9.00, 25.0]	33.0 [21.0, 65.0]	39.0 [17.0, 137]	52.0 [19.0, 111]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.0148 (0.0113)	0.0181 (0.00849)	0.00732 (0.00436)	0.00861 (0.00870)	0.0488 (0.0429)	0.0155 (0.0167)
Median [Q1, Q3]	0.00828 [0.00670, 0.0169]	0.0177 [0.0105, 0.0255]	0.00594 [0.00383, 0.00853]	0.00499 [0.00365, 0.0118]	0.0361 [0.0249, 0.0663]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00828 [0.00653, 0.0368]	0.0177 [0.00711, 0.0288]	0.00594 [0.00315, 0.0169]	0.00499 [0.00230, 0.0185]	0.0361 [0.0137, 0.0966]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	1 (11.1%)	2 (20.0%)	1 (8.3%)	0 (0%)	0 (0%)	4 (10.8%)
1	7 (77.8%)	3 (30.0%)	11 (91.7%)	0 (0%)	0 (0%)	21 (56.8%)
Missing	1 (11.1%)	5 (50.0%)	0 (0%)	3 (100%)	3 (100%)	12 (32.4%)

kruskal.test(FI_final ~ interv_code2, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by interv_code2
## Kruskal-Wallis chi-squared = 13.378, df = 4, p-value = 0.009571

kruskal.test(FQ_final ~ interv_code2, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by interv_code2
## Kruskal-Wallis chi-squared = 15.37, df = 4, p-value = 0.003992

Box plots

p1 = ggplot(data = p_sig2, aes(y = FI_final, x = as.factor(interv_code2), fill = as.factor(interv_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index", x = "Pharmacological interventions", y = "Fragility index")
p2 = ggplot(data = p_sig2, aes(y = FQ_final, x = as.factor(fx_code2), fill = as.factor(fx_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility quotient", x = "Pharmacological interventions", y = "Fragility quotine")

grid.arrange(p1, p2, nrow = 1, top = textGrob("Fragility of evidence for anti-fracture efficacy by intervention sites", gp = gpar(fontsize = 20, font = 1)))

(2.3.4) Timing of fracture assessment

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(timing), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	2 (N=5)	3 (N=4)	4 (N=16)	5 (N=10)	6 (N=1)	8 (N=1)	Overall (N=37)
no_rand
Mean (SD)	4350 (2770)	1380 (533)	3750 (2690)	6590 (2520)	NA	NA	4240 (2890)
Median [Q1, Q3]	4090 [1650, 7180]	1640 [1370, 1650]	4090 [1100, 7180]	7740 [7740, 7840]	1650 [1650, 1650]	2000 [2000, 2000]	4090 [1640, 7180]
Median [min, max]	4090 [1630, 7180]	1640 [578, 1650]	4090 [704, 7180]	7740 [1650, 7870]	1650 [1650, 1650]	2000 [2000, 2000]	4090 [578, 7870]
active_sample
Mean (SD)	4050 (2710)	1140 (462)	3390 (2560)	5680 (2220)	NA	NA	3750 (2630)
Median [Q1, Q3]	3980 [1390, 6640]	1330 [1060, 1410]	3600 [892, 6650]	6480 [5680, 7180]	1150 [1150, 1150]	1950 [1950, 1950]	3660 [1270, 6640]
Median [min, max]	3980 [1330, 6910]	1330 [451, 1430]	3600 [544, 6690]	6480 [1440, 7810]	1150 [1150, 1150]	1950 [1950, 1950]	3660 [451, 7810]
n_event
Mean (SD)	132 (110)	40.5 (6.61)	181 (154)	307 (255)	NA	NA	211 (204)
Median [Q1, Q3]	76.0 [75.0, 128]	40.0 [35.5, 45.0]	106 [90.5, 230]	236 [105, 398]	696 [696, 696]	312 [312, 312]	106 [76.0, 312]
Median [min, max]	76.0 [58.0, 323]	40.0 [34.0, 48.0]	106 [46.0, 658]	236 [73.0, 764]	696 [696, 696]	312 [312, 312]	106 [34.0, 764]
FI_final
Mean (SD)	22.2 (7.46)	11.5 (1.91)	29.9 (13.8)	64.3 (52.0)	NA	NA	38.5 (35.3)
Median [Q1, Q3]	24.0 [19.0, 27.0]	12.0 [10.5, 13.0]	24.0 [20.8, 39.3]	42.5 [38.3, 79.8]	111 [111, 111]	33.0 [33.0, 33.0]	26.0 [17.0, 42.0]
Median [min, max]	24.0 [11.0, 30.0]	12.0 [9.00, 13.0]	24.0 [15.0, 65.0]	42.5 [15.0, 171]	111 [111, 111]	33.0 [33.0, 33.0]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.00741 (0.00410)	0.0132 (0.0104)	0.0149 (0.00997)	0.0133 (0.0115)	NA	NA	0.0155 (0.0167)
Median [Q1, Q3]	0.00754 [0.00391, 0.00828]	0.00849 [0.00755, 0.0142]	0.0137 [0.00598, 0.0206]	0.00719 [0.00655, 0.0173]	0.0966 [0.0966, 0.0966]	0.0169 [0.0169, 0.0169]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00754 [0.00361, 0.0137]	0.00849 [0.00711, 0.0288]	0.0137 [0.00315, 0.0368]	0.00719 [0.00230, 0.0361]	0.0966 [0.0966, 0.0966]	0.0169 [0.0169, 0.0169]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	1 (20.0%)	0 (0%)	2 (12.5%)	0 (0%)	0 (0%)	1 (100%)	4 (10.8%)
1	3 (60.0%)	3 (75.0%)	10 (62.5%)	5 (50.0%)	0 (0%)	0 (0%)	21 (56.8%)
Missing	1 (20.0%)	1 (25.0%)	4 (25.0%)	5 (50.0%)	1 (100%)	0 (0%)	12 (32.4%)

kruskal.test(FI_final ~ timing, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by timing
## Kruskal-Wallis chi-squared = 16.324, df = 5, p-value = 0.005977

kruskal.test(FQ_final ~ timing, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by timing
## Kruskal-Wallis chi-squared = 5.2068, df = 5, p-value = 0.3912

Box plots

p1 = ggplot(data = p_sig2, aes(y = FI_final, x = as.factor(timing), fill = as.factor(timing))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index")
p1

(2.3.5) By journal

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | as.factor(journal_code2), data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	NEJM (N=27)	Lancet (N=2)	JAMA (N=4)	JBMR (N=1)	JCEM (N=1)	Other (N=2)	Overall (N=37)
no_rand
Mean (SD)	5280 (2700)	1360 (0)	1640 (8.02)	NA	NA	1180 (668)	4240 (2890)
Median [Q1, Q3]	7180 [3050, 7740]	1360 [1360, 1360]	1640 [1640, 1650]	1960 [1960, 1960]	578 [578, 578]	1180 [940, 1410]	4090 [1640, 7180]
Median [min, max]	7180 [1090, 7870]	1360 [1360, 1360]	1640 [1630, 1650]	1960 [1960, 1960]	578 [578, 578]	1180 [704, 1650]	4090 [578, 7870]
active_sample
Mean (SD)	4720 (2450)	1050 (0)	1360 (73.1)	NA	NA	847 (428)	3750 (2630)
Median [Q1, Q3]	5680 [2740, 6650]	1050 [1050, 1050]	1370 [1310, 1410]	1950 [1950, 1950]	451 [451, 451]	847 [695, 998]	3660 [1270, 6640]
Median [min, max]	5680 [882, 7810]	1050 [1050, 1050]	1370 [1270, 1430]	1950 [1950, 1950]	451 [451, 451]	847 [544, 1150]	3660 [451, 7810]
n_event
Mean (SD)	240 (200)	96.0 (5.66)	43.0 (10.9)	NA	NA	398 (421)	211 (204)
Median [Q1, Q3]	168 [84.5, 337]	96.0 [94.0, 98.0]	40.0 [35.5, 47.5]	110 [110, 110]	48.0 [48.0, 48.0]	398 [249, 547]	106 [76.0, 312]
Median [min, max]	168 [46.0, 764]	96.0 [92.0, 100]	40.0 [34.0, 58.0]	110 [110, 110]	48.0 [48.0, 48.0]	398 [100, 696]	106 [34.0, 764]
FI_final
Mean (SD)	44.0 (35.7)	16.0 (1.41)	11.0 (1.63)	NA	NA	65.5 (64.3)	38.5 (35.3)
Median [Q1, Q3]	36.0 [23.5, 42.5]	16.0 [15.5, 16.5]	11.0 [10.5, 11.5]	15.0 [15.0, 15.0]	13.0 [13.0, 13.0]	65.5 [42.8, 88.3]	26.0 [17.0, 42.0]
Median [min, max]	36.0 [17.0, 171]	16.0 [15.0, 17.0]	11.0 [9.00, 13.0]	15.0 [15.0, 15.0]	13.0 [13.0, 13.0]	65.5 [20.0, 111]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.0127 (0.00949)	0.0153 (0.00135)	0.00809 (0.000924)	NA	NA	0.0667 (0.0423)	0.0155 (0.0167)
Median [Q1, Q3]	0.00754 [0.00562, 0.0177]	0.0153 [0.0148, 0.0157]	0.00799 [0.00755, 0.00853]	0.00768 [0.00768, 0.00768]	0.0288 [0.0288, 0.0288]	0.0667 [0.0517, 0.0816]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.00754 [0.00230, 0.0361]	0.0153 [0.0143, 0.0162]	0.00799 [0.00711, 0.00928]	0.00768 [0.00768, 0.00768]	0.0288 [0.0288, 0.0288]	0.0667 [0.0368, 0.0966]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	2 (7.4%)	2 (100%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)	4 (10.8%)
1	16 (59.3%)	0 (0%)	4 (100%)	0 (0%)	0 (0%)	1 (50.0%)	21 (56.8%)
Missing	9 (33.3%)	0 (0%)	0 (0%)	1 (100%)	1 (100%)	1 (50.0%)	12 (32.4%)

kruskal.test(FI_final ~ journal, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by journal
## Kruskal-Wallis chi-squared = 18.362, df = 5, p-value = 0.002526

kruskal.test(FQ_final ~ journal, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by journal
## Kruskal-Wallis chi-squared = 8.3947, df = 5, p-value = 0.1358

Box plots

p1 = ggplot(data = p_sig2, aes(y = FI_final, x = as.factor(timing), fill = as.factor(journal_code2))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by timing of fracture assessment", x = "Timing of fracture assessment", y = "Fragility index") 
p1

(2.3.6) By sex

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | sex, data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Both (N=1)	Women (N=36)	Overall (N=37)
no_rand
Mean (SD)	NA	4340 (2860)	4240 (2890)
Median [Q1, Q3]	578 [578, 578]	4090 [1640, 7180]	4090 [1640, 7180]
Median [min, max]	578 [578, 578]	4090 [704, 7870]	4090 [578, 7870]
active_sample
Mean (SD)	NA	3850 (2610)	3750 (2630)
Median [Q1, Q3]	451 [451, 451]	3660 [1310, 6640]	3660 [1270, 6640]
Median [min, max]	451 [451, 451]	3660 [544, 7810]	3660 [451, 7810]
n_event
Mean (SD)	NA	215 (205)	211 (204)
Median [Q1, Q3]	48.0 [48.0, 48.0]	108 [80.5, 315]	106 [76.0, 312]
Median [min, max]	48.0 [48.0, 48.0]	108 [34.0, 764]	106 [34.0, 764]
FI_final
Mean (SD)	NA	39.2 (35.5)	38.5 (35.3)
Median [Q1, Q3]	13.0 [13.0, 13.0]	26.5 [18.5, 42.0]	26.0 [17.0, 42.0]
Median [min, max]	13.0 [13.0, 13.0]	26.5 [9.00, 171]	26.0 [9.00, 171]
FQ_final
Mean (SD)	NA	0.0152 (0.0168)	0.0155 (0.0167)
Median [Q1, Q3]	0.0288 [0.0288, 0.0288]	0.00878 [0.00640, 0.0173]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.0288 [0.0288, 0.0288]	0.00878 [0.00230, 0.0966]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	0 (0%)	4 (11.1%)	4 (10.8%)
1	0 (0%)	21 (58.3%)	21 (56.8%)
Missing	1 (100%)	11 (30.6%)	12 (32.4%)

kruskal.test(FI_final ~ sex, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by sex
## Kruskal-Wallis chi-squared = 1.8465, df = 1, p-value = 0.1742

kruskal.test(FQ_final ~ sex, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by sex
## Kruskal-Wallis chi-squared = 1.7193, df = 1, p-value = 0.1898

Box plots

p1 = ggplot(data = p_sig2, aes(y = FI_final, x = as.factor(sex), fill = as.factor(sex))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by sex", x = "Sex", y = "Fragility index") 
p1

(2.3.7) By placebo

table1(~ no_rand + active_sample + n_event + FI_final + FQ_final + as.factor(missing_fi) | placebo, data = p_sig2, render.continuous = c(. = "Mean (SD)", . = "Median [Q1, Q3]", . = "Median [min, max]" ))

	Active (N=10)	Placebo (N=27)	Overall (N=37)
no_rand
Mean (SD)	2810 (1350)	4770 (3140)	4240 (2890)
Median [Q1, Q3]	2870 [1640, 4090]	7180 [1640, 7740]	4090 [1640, 7180]
Median [min, max]	2870 [1360, 4090]	7180 [578, 7870]	4090 [578, 7870]
active_sample
Mean (SD)	2490 (1330)	4220 (2850)	3750 (2630)
Median [Q1, Q3]	2480 [1300, 3660]	5680 [1240, 6650]	3660 [1270, 6640]
Median [min, max]	2480 [1050, 3980]	5680 [451, 7810]	3660 [451, 7810]
n_event
Mean (SD)	212 (198)	210 (209)	211 (204)
Median [Q1, Q3]	161 [56.0, 306]	106 [79.0, 279]	106 [76.0, 312]
Median [min, max]	161 [34.0, 658]	106 [46.0, 764]	106 [34.0, 764]
FI_final
Mean (SD)	27.6 (18.7)	42.5 (39.3)	38.5 (35.3)
Median [Q1, Q3]	21.5 [13.5, 39.0]	27.0 [20.5, 41.0]	26.0 [17.0, 42.0]
Median [min, max]	21.5 [9.00, 65.0]	27.0 [11.0, 171]	26.0 [9.00, 171]
FQ_final
Mean (SD)	0.0111 (0.00383)	0.0172 (0.0193)	0.0155 (0.0167)
Median [Q1, Q3]	0.0104 [0.00758, 0.0140]	0.00828 [0.00562, 0.0252]	0.00928 [0.00653, 0.0185]
Median [min, max]	0.0104 [0.00711, 0.0169]	0.00828 [0.00230, 0.0966]	0.00928 [0.00230, 0.0966]
as.factor(missing_fi)
0	3 (30.0%)	1 (3.7%)	4 (10.8%)
1	7 (70.0%)	14 (51.9%)	21 (56.8%)
Missing	0 (0%)	12 (44.4%)	12 (32.4%)

kruskal.test(FI_final ~ placebo, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FI_final by placebo
## Kruskal-Wallis chi-squared = 1.3537, df = 1, p-value = 0.2446

kruskal.test(FQ_final ~ placebo, data = p_sig2)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  FQ_final by placebo
## Kruskal-Wallis chi-squared = 0.018713, df = 1, p-value = 0.8912

Box plots

p1 = ggplot(data = p_sig2, aes(y = FI_final, x = as.factor(control), fill = as.factor(control))) + geom_boxplot() + 
  geom_jitter(alpha=0.2) + theme_bw() + theme(legend.position="none") + 
  labs(title = "Fragility index by types of control", x = "Types of control", y = "Fragility index") 
p1

Fragility of evidence for anti-fracture efficacy

Nick Tran

2022-10-07

Fragility of evidence for anti-fracture efficacy: A systematic review

Data management

Calculate Fragility index (FI)

(1) All analyses with statistically significant results from logistic regression

(1.1) Overall

(1.1.1) Overall

(1.1.2) By fracture sites

(1.1.3) By pharmacological interventions

(1.1.4) Timing of fracture assessment

(1.1.5) By journal

(1.1.6) By sex

(1.1.7) By placebo

(1.2) Fracture as the predefined primary endpoint

(1.2.1) Overall

(1.2.2) By fracture sites

(1.2.3) By pharmacological interventions

(1.2.4) Timing of fracture assessment

(1.2.5) By journal

(1.2.6) By sex

(1.2.7) By placebo

(1.3) Analyses with P< 0.001

(1.3.1) Overall

(1.3.2) By fracture sites

(1.3.3) By pharmacological interventions

(1.3.4) Timing of fracture assessment

(1.3.5) By journal

(1.3.6) By sex

(1.3.7) By placebo

(2) Only analyses from the primary analyses (i.e., those from the extended studies or sensitivity/subgroup analyses will be excluded)

(2.1) Overall

(2.1.1) Overall

(2.1.2) By fracture sites

(2.1.3) By pharmacological interventions

(2.1.5) By journal

(2.1.6) By sex

(2.1.7) By placebo

(2.2) Fracture as the predefined primary endpoint

(2.2.1) Overall

(2.2.2) By fracture sites

(2.2.3) By pharmacological interventions

(2.2.4) Timing of fracture assessment

(2.2.5) By journal

(2.2.6) By sex

(2.2.7) By placebo

(2.3) Analyses with P< 0.001

(2.3.1) Overall

(2.3.2) By fracture sites

(2.3.3) By pharmacological interventions

(2.3.4) Timing of fracture assessment

(2.3.5) By journal

(2.3.6) By sex

(2.3.7) By placebo

R Markdown file saved at https://rpubs.com/ThachTran/1153595