Rationales: - Previous studies have shown a significantly positive association betwen BMD and mortality risk. Nevertheless, the occurance of incident fractures was not accounted for in the previous studies. Given a proven mortality risk following fragility fractures, it is critical to control for the occurence of incident fractures in any assessment of the association between BMD and mortality risk. - Evidence of “off-label” treatment of osteoporosis on mortality has been found, though there is no accepted biomechanisms. - Robust evidence of beneficial contribution of BMD (i.e., ~ possible benefits of osteoporosis treatments) would widen the treatment indications, ultimately reducing the risk of mortality. Analysis approach: - Multistate regression to differentiate the contribution of BMD to (i) incident fracture (which is well established), (ii) death without fractures, and (iii) post-fracture deaths.
bmd.0 = read.csv("C:\\Thach\\Research projects\\BMD and mortality\\Data\\SOF_MrOS_Nick_21mar24.csv")
bmd = subset(bmd.0, select = c("ID", "gender", "age", "race", "education", "weight", "height", "BMI", "smoke", "drink", "fall", "fx50", "physical", "hypertension", "copd", "parkinson", "cancer", "rheumatoid", "cvd", "renal", "depression", "diabetes", "fnbmd", "anyfx", "death", "Tscore", "event", "state", "time2event", "ageBase", "fnbmdBase", "TscoreBase", "time2end"))
dim(bmd)
## [1] 30538 33
head(bmd)
## ID gender age race education weight height BMI smoke drink fall fx50
## 1 1 F 69.00 1:WHITE 9 67.3 150.5 29.7127 1 1 2 1
## 2 1 F 86.01 1:WHITE 9 59.5 148.8 26.8727 1 1 2 1
## 3 2 F 84.00 1:WHITE 10 68.4 151.8 29.6833 0 0 1 1
## 4 2 F 90.53 1:WHITE 10 68.4 151.8 29.6833 0 0 1 1
## 5 3 F 75.00 1:WHITE 12 72.7 151.0 31.8846 1 1 3 0
## 6 3 F 93.46 1:WHITE 12 61.7 147.2 28.4754 1 1 3 0
## physical hypertension copd parkinson cancer rheumatoid cvd renal depression
## 1 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0
## 3 0 1 0 0 0 0 1 0 0
## 4 0 1 0 0 0 0 1 0 0
## 5 1 0 1 0 1 0 0 0 0
## 6 1 0 1 0 1 0 0 0 0
## diabetes fnbmd anyfx death Tscore event state time2event ageBase fnbmdBase
## 1 0 0.6560 0 0 -1.7000 Well 1 0.0000 69 0.656
## 2 0 0.6349 0 0 -1.8758 Well 1 17.2238 69 0.656
## 3 2 0.5850 0 1 -2.2917 Well 1 0.0000 84 0.585
## 4 2 0.5850 0 1 -2.2917 Death 3 6.5325 84 0.585
## 5 0 0.6540 0 0 -1.7167 Well 1 0.0000 75 0.654
## 6 0 0.5537 0 0 -2.5525 Well 1 18.6366 75 0.654
## TscoreBase time2end
## 1 -1.7000 17.2238
## 2 -1.7000 5.0103
## 3 -2.2917 6.5325
## 4 -2.2917 6.5325
## 5 -1.7167 18.6366
## 6 -1.7167 6.4586
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.3 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.3 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
bmd = bmd %>% mutate(fx_death = case_when(anyfx == 0 & death == 0 ~ "Event-free",
anyfx == 1 & death == 0 ~ "Fractured, Alive",
anyfx == 0 & death == 1 ~ "No Fractured, Dead",
anyfx == 1 & death == 1 ~ "Fractured, Dead"))
bmd = bmd %>% mutate(fall.no = case_when(fall == 0 ~ "0",
fall == 1 ~ "1",
fall == 2 ~ "2",
fall >= 3 ~ "3+"))
bmd = bmd %>% mutate(fall.yesno = case_when(fall == 0 ~ "No",
fall >= 1 ~ "Yes"))
bmd$Tscore.2 = bmd$Tscore*(-1)
bmd$TscoreBase.2 = bmd$TscoreBase*(-1)
bmd = bmd %>% mutate(cvd.n = case_when(cvd == 0 ~ "No",
cvd >= 1 ~ "Yes"))
bmd = bmd %>% mutate(diabetes.n = case_when(diabetes == 0 ~ "No",
diabetes >= 1 ~ "Yes"))
bmd = bmd %>% mutate(drink.n = case_when(drink == 0 ~ "No",
drink >= 1 ~ "Yes"))
men = subset(bmd, gender == "M" & race == "1:WHITE")
baseline.m = subset(men, state == 1 & time2event == 0)
library(table1)
##
## Attaching package: 'table1'
## The following objects are masked from 'package:base':
##
## units, units<-
table1(~ ageBase + fnbmdBase + TscoreBase + as.factor(fall.no) + fall.yesno + as.factor(fx50) + race + weight +
height + BMI + as.factor(smoke) + as.factor(drink.n) + as.factor(physical) + as.factor(cvd.n) +
as.factor(hypertension) + as.factor(copd) + as.factor(diabetes.n) + as.factor(cancer) + as.factor(parkinson) +
as.factor(rheumatoid) + as.factor(renal) + as.factor(depression) + as.factor(anyfx) + as.factor(death) |
fx_death, data = baseline.m)
Event-free (N=1722) |
Fractured, Alive (N=361) |
Fractured, Dead (N=655) |
No Fractured, Dead (N=2641) |
Overall (N=5379) |
|
---|---|---|---|---|---|
ageBase | |||||
Mean (SD) | 70.8 (4.66) | 71.7 (4.87) | 76.2 (5.83) | 75.6 (5.87) | 73.8 (5.92) |
Median [Min, Max] | 70.0 [64.0, 89.0] | 71.0 [65.0, 91.0] | 76.0 [65.0, 94.0] | 75.0 [65.0, 100] | 73.0 [64.0, 100] |
fnbmdBase | |||||
Mean (SD) | 0.803 (0.122) | 0.754 (0.115) | 0.727 (0.121) | 0.782 (0.122) | 0.780 (0.124) |
Median [Min, Max] | 0.794 [0.404, 1.32] | 0.744 [0.499, 1.27] | 0.719 [0.273, 1.15] | 0.773 [0.475, 1.33] | 0.772 [0.273, 1.33] |
TscoreBase | |||||
Mean (SD) | -0.929 (0.894) | -1.29 (0.843) | -1.48 (0.883) | -1.08 (0.893) | -1.09 (0.905) |
Median [Min, Max] | -0.992 [-3.84, 2.84] | -1.36 [-3.15, 2.49] | -1.54 [-4.80, 1.59] | -1.15 [-3.32, 2.89] | -1.16 [-4.80, 2.89] |
as.factor(fall.no) | |||||
0 | 1344 (78.0%) | 248 (68.7%) | 389 (59.4%) | 1966 (74.4%) | 3947 (73.4%) |
1 | 378 (22.0%) | 113 (31.3%) | 266 (40.6%) | 675 (25.6%) | 1432 (26.6%) |
fall.yesno | |||||
No | 1344 (78.0%) | 248 (68.7%) | 389 (59.4%) | 1966 (74.4%) | 3947 (73.4%) |
Yes | 378 (22.0%) | 113 (31.3%) | 266 (40.6%) | 675 (25.6%) | 1432 (26.6%) |
as.factor(fx50) | |||||
0 | 1475 (85.7%) | 280 (77.6%) | 492 (75.1%) | 2186 (82.8%) | 4433 (82.4%) |
1 | 247 (14.3%) | 81 (22.4%) | 163 (24.9%) | 455 (17.2%) | 946 (17.6%) |
race | |||||
1:WHITE | 1722 (100%) | 361 (100%) | 655 (100%) | 2641 (100%) | 5379 (100%) |
weight | |||||
Mean (SD) | 84.4 (12.2) | 83.9 (12.7) | 82.3 (13.3) | 83.2 (13.5) | 83.5 (13.0) |
Median [Min, Max] | 83.3 [52.7, 129] | 82.6 [58.0, 142] | 80.8 [52.6, 142] | 81.5 [50.8, 144] | 82.1 [50.8, 144] |
height | |||||
Mean (SD) | 175 (6.41) | 176 (6.90) | 174 (6.69) | 174 (6.66) | 174 (6.63) |
Median [Min, Max] | 175 [154, 198] | 175 [158, 199] | 174 [153, 193] | 174 [147, 198] | 174 [147, 199] |
Missing | 1 (0.1%) | 1 (0.3%) | 0 (0%) | 4 (0.2%) | 6 (0.1%) |
BMI | |||||
Mean (SD) | 27.5 (3.56) | 27.2 (3.56) | 27.1 (3.87) | 27.4 (3.96) | 27.4 (3.80) |
Median [Min, Max] | 27.1 [17.5, 50.7] | 26.6 [19.2, 41.9] | 26.6 [18.3, 41.5] | 26.8 [17.2, 48.5] | 26.9 [17.2, 50.7] |
Missing | 1 (0.1%) | 1 (0.3%) | 0 (0%) | 4 (0.2%) | 6 (0.1%) |
as.factor(smoke) | |||||
0 | 708 (41.1%) | 143 (39.6%) | 245 (37.4%) | 918 (34.8%) | 2014 (37.4%) |
1 | 1014 (58.9%) | 218 (60.4%) | 410 (62.6%) | 1723 (65.2%) | 3365 (62.6%) |
as.factor(drink.n) | |||||
No | 547 (31.8%) | 111 (30.7%) | 238 (36.3%) | 945 (35.8%) | 1841 (34.2%) |
Yes | 1175 (68.2%) | 250 (69.3%) | 417 (63.7%) | 1696 (64.2%) | 3538 (65.8%) |
as.factor(physical) | |||||
0 | 458 (26.6%) | 96 (26.6%) | 255 (38.9%) | 976 (37.0%) | 1785 (33.2%) |
1 | 1264 (73.4%) | 265 (73.4%) | 400 (61.1%) | 1665 (63.0%) | 3594 (66.8%) |
as.factor(cvd.n) | |||||
No | 1507 (87.5%) | 304 (84.2%) | 497 (75.9%) | 1946 (73.7%) | 4254 (79.1%) |
Yes | 215 (12.5%) | 57 (15.8%) | 158 (24.1%) | 695 (26.3%) | 1125 (20.9%) |
as.factor(hypertension) | |||||
0 | 1113 (64.6%) | 231 (64.0%) | 344 (52.5%) | 1436 (54.4%) | 3124 (58.1%) |
1 | 609 (35.4%) | 130 (36.0%) | 311 (47.5%) | 1205 (45.6%) | 2255 (41.9%) |
as.factor(copd) | |||||
0 | 1583 (91.9%) | 334 (92.5%) | 562 (85.8%) | 2321 (87.9%) | 4800 (89.2%) |
1 | 139 (8.1%) | 27 (7.5%) | 93 (14.2%) | 320 (12.1%) | 579 (10.8%) |
as.factor(diabetes.n) | |||||
No | 1611 (93.6%) | 338 (93.6%) | 582 (88.9%) | 2313 (87.6%) | 4844 (90.1%) |
Yes | 111 (6.4%) | 23 (6.4%) | 73 (11.1%) | 328 (12.4%) | 535 (9.9%) |
as.factor(cancer) | |||||
0 | 1481 (86.0%) | 305 (84.5%) | 529 (80.8%) | 2077 (78.6%) | 4392 (81.7%) |
1 | 241 (14.0%) | 56 (15.5%) | 126 (19.2%) | 564 (21.4%) | 987 (18.3%) |
as.factor(parkinson) | |||||
0 | 1505 (87.4%) | 311 (86.1%) | 579 (88.4%) | 2254 (85.3%) | 4649 (86.4%) |
1 | 217 (12.6%) | 50 (13.9%) | 76 (11.6%) | 387 (14.7%) | 730 (13.6%) |
as.factor(rheumatoid) | |||||
0 | 982 (57.0%) | 201 (55.7%) | 335 (51.1%) | 1314 (49.8%) | 2832 (52.6%) |
1 | 740 (43.0%) | 160 (44.3%) | 320 (48.9%) | 1327 (50.2%) | 2547 (47.4%) |
as.factor(renal) | |||||
0 | 1512 (87.8%) | 307 (85.0%) | 599 (91.5%) | 2446 (92.6%) | 4864 (90.4%) |
1 | 210 (12.2%) | 54 (15.0%) | 56 (8.5%) | 195 (7.4%) | 515 (9.6%) |
as.factor(depression) | |||||
0 | 1658 (96.3%) | 345 (95.6%) | 622 (95.0%) | 2551 (96.6%) | 5176 (96.2%) |
1 | 64 (3.7%) | 16 (4.4%) | 33 (5.0%) | 90 (3.4%) | 203 (3.8%) |
as.factor(anyfx) | |||||
0 | 1722 (100%) | 0 (0%) | 0 (0%) | 2641 (100%) | 4363 (81.1%) |
1 | 0 (0%) | 361 (100%) | 655 (100%) | 0 (0%) | 1016 (18.9%) |
as.factor(death) | |||||
0 | 1722 (100%) | 361 (100%) | 0 (0%) | 0 (0%) | 2083 (38.7%) |
1 | 0 (0%) | 0 (0%) | 655 (100%) | 2641 (100%) | 3296 (61.3%) |
#library(compareGroups)
#createTable(compareGroups(fx_death ~ ageBase + fnbmdBase + TscoreBase + fall.no + fall.yesno + fx50 + weight + height + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer + parkinson + rheumatoid + renal + depression + anyfx + death, data = baseline.m))
library(survival)
cox.m = coxph(Surv(time2end, death) ~ ageBase + TscoreBase.2, data = baseline.m)
summary(cox.m)
## Call:
## coxph(formula = Surv(time2end, death) ~ ageBase + TscoreBase.2,
## data = baseline.m)
##
## n= 5379, number of events= 3296
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.119424 1.126848 0.003122 38.252 <2e-16 ***
## TscoreBase.2 0.043428 1.044385 0.019810 2.192 0.0284 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.127 0.8874 1.120 1.134
## TscoreBase.2 1.044 0.9575 1.005 1.086
##
## Concordance= 0.683 (se = 0.005 )
## Likelihood ratio test= 1465 on 2 df, p=<2e-16
## Wald test = 1544 on 2 df, p=<2e-16
## Score (logrank) test = 1624 on 2 df, p=<2e-16
cox.m2 = coxph(Surv(time2end, death) ~ ageBase + TscoreBase.2 + fall.yesno + fx50 + cvd.n + copd + diabetes.n + cancer, data = baseline.m)
summary(cox.m2)
## Call:
## coxph(formula = Surv(time2end, death) ~ ageBase + TscoreBase.2 +
## fall.yesno + fx50 + cvd.n + copd + diabetes.n + cancer, data = baseline.m)
##
## n= 5379, number of events= 3296
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.116148 1.123162 0.003213 36.149 < 2e-16 ***
## TscoreBase.2 0.056079 1.057682 0.019974 2.808 0.004991 **
## fall.yesnoYes -0.051258 0.950034 0.039096 -1.311 0.189829
## fx50 0.061496 1.063426 0.045091 1.364 0.172620
## cvd.nYes 0.411689 1.509365 0.040635 10.131 < 2e-16 ***
## copd 0.344438 1.411196 0.052879 6.514 7.33e-11 ***
## diabetes.nYes 0.481182 1.617985 0.054185 8.880 < 2e-16 ***
## cancer 0.154837 1.167468 0.043331 3.573 0.000352 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.123 0.8903 1.1161 1.130
## TscoreBase.2 1.058 0.9455 1.0171 1.100
## fall.yesnoYes 0.950 1.0526 0.8800 1.026
## fx50 1.063 0.9404 0.9735 1.162
## cvd.nYes 1.509 0.6625 1.3938 1.634
## copd 1.411 0.7086 1.2723 1.565
## diabetes.nYes 1.618 0.6181 1.4550 1.799
## cancer 1.167 0.8566 1.0724 1.271
##
## Concordance= 0.7 (se = 0.005 )
## Likelihood ratio test= 1705 on 8 df, p=<2e-16
## Wald test = 1776 on 8 df, p=<2e-16
## Score (logrank) test = 1884 on 8 df, p=<2e-16
cox.m3 = coxph(Surv(time2end, death) ~ ageBase + TscoreBase.2 + fall.yesno + fx50 + BMI + smoke + drink.n +
physical + cvd.n + hypertension + copd + diabetes.n + cancer + renal + parkinson +
depression, data = baseline.m)
summary(cox.m3)
## Call:
## coxph(formula = Surv(time2end, death) ~ ageBase + TscoreBase.2 +
## fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n +
## hypertension + copd + diabetes.n + cancer + renal + parkinson +
## depression, data = baseline.m)
##
## n= 5373, number of events= 3292
## (6 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.114047 1.120805 0.003318 34.375 < 2e-16 ***
## TscoreBase.2 0.075446 1.078365 0.021064 3.582 0.000341 ***
## fall.yesnoYes -0.052975 0.948403 0.039254 -1.350 0.177154
## fx50 0.067608 1.069946 0.045136 1.498 0.134166
## BMI 0.013421 1.013512 0.005303 2.531 0.011375 *
## smoke 0.243538 1.275755 0.037240 6.540 6.16e-11 ***
## drink.nYes -0.097462 0.907137 0.037266 -2.615 0.008914 **
## physical -0.162434 0.850072 0.036899 -4.402 1.07e-05 ***
## cvd.nYes 0.385894 1.470928 0.040914 9.432 < 2e-16 ***
## hypertension 0.180788 1.198161 0.036079 5.011 5.42e-07 ***
## copd 0.276813 1.318919 0.053335 5.190 2.10e-07 ***
## diabetes.nYes 0.397446 1.488020 0.055429 7.170 7.48e-13 ***
## cancer 0.131224 1.140224 0.043562 3.012 0.002592 **
## renal -0.878005 0.415611 0.080458 -10.913 < 2e-16 ***
## parkinson 0.532339 1.702911 0.061545 8.650 < 2e-16 ***
## depression -0.112735 0.893387 0.092733 -1.216 0.224100
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.1208 0.8922 1.1135 1.1281
## TscoreBase.2 1.0784 0.9273 1.0348 1.1238
## fall.yesnoYes 0.9484 1.0544 0.8782 1.0242
## fx50 1.0699 0.9346 0.9794 1.1689
## BMI 1.0135 0.9867 1.0030 1.0241
## smoke 1.2758 0.7838 1.1860 1.3724
## drink.nYes 0.9071 1.1024 0.8432 0.9759
## physical 0.8501 1.1764 0.7908 0.9138
## cvd.nYes 1.4709 0.6798 1.3576 1.5937
## hypertension 1.1982 0.8346 1.1164 1.2860
## copd 1.3189 0.7582 1.1880 1.4643
## diabetes.nYes 1.4880 0.6720 1.3348 1.6588
## cancer 1.1402 0.8770 1.0469 1.2419
## renal 0.4156 2.4061 0.3550 0.4866
## parkinson 1.7029 0.5872 1.5094 1.9212
## depression 0.8934 1.1193 0.7449 1.0715
##
## Concordance= 0.718 (se = 0.004 )
## Likelihood ratio test= 1956 on 16 df, p=<2e-16
## Wald test = 2017 on 16 df, p=<2e-16
## Score (logrank) test = 2132 on 16 df, p=<2e-16
reorder_array <- function(Qx3) {
new_row_order <- c("Well", "Fracture", "Death")
new_col_order <- c("Well", "Fracture")
Qx3_reordered <- Qx3[new_col_order, new_row_order]
Death <- c(0, 0, 0)
Qx3_reordered <- rbind(Qx3_reordered, Death)
return(Qx3_reordered)
}
library(msm)
## Warning: package 'msm' was built under R version 4.3.3
Q.m = statetable.msm(event, subject = ID, data = bmd)
Q.m2 = reorder_array(Q.m)
qmatrix.n = crudeinits.msm(state ~ time2event, subject = ID, data = men, qmatrix = Q.m2)
qmatrix.n
## Well Fracture Death
## Well -0.05500799 0.0152825 0.03972549
## Fracture 0.00000000 -0.1033188 0.10331884
## Death 0.00000000 0.0000000 0.00000000
statetable.msm(state, ID, data = men)
## to
## from 1 2 3
## 1 1722 1016 2641
## 2 0 361 655
age.m1= msm(state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ ageBase + TscoreBase.2)
age.m1
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~ageBase + TscoreBase.2, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline ageBase
## Well - Well -0.04267 (-0.04452,-0.04089)
## Well - Fracture 0.01365 ( 0.01271, 0.01467) 1.061 (1.049,1.072)
## Well - Death 0.02901 ( 0.02753, 0.03058) 1.117 (1.109,1.124)
## Fracture - Fracture -0.07334 (-0.08547,-0.06294)
## Fracture - Death 0.07334 ( 0.06294, 0.08547) 1.103 (1.088,1.119)
## TscoreBase.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.6307 (1.5095,1.762) 1.541 (1.347,1.763)
## Well - Death 0.9809 (0.9399,1.024) 3.308 (2.997,3.651)
## Fracture - Fracture
## Fracture - Death 1.1391 (1.0396,1.248) 1.657 (1.258,2.182)
##
## -2 * log-likelihood: 35082.2
hazard.msm(age.m1)
## $ageBase
## HR L U
## Well - Fracture 1.060684 1.049403 1.072086
## Well - Death 1.116725 1.109467 1.124031
## Fracture - Death 1.103430 1.088470 1.118597
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.630696 1.5095166 1.761603
## Well - Death 0.980934 0.9398526 1.023811
## Fracture - Death 1.139145 1.0395698 1.248258
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.541144 1.347192 1.763018
## Well - Death 3.307866 2.996597 3.651467
## Fracture - Death 1.657043 1.258378 2.182008
age.m2= msm(state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ age + Tscore.2)
age.m2
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~age + Tscore.2, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline age
## Well - Well -0.04604 (-0.04799,-0.04417)
## Well - Fracture 0.01432 ( 0.01334, 0.01538) 1.061 (1.049,1.072)
## Well - Death 0.03172 ( 0.03014, 0.03338) 1.117 (1.109,1.124)
## Fracture - Fracture -0.05318 (-0.06310,-0.04481)
## Fracture - Death 0.05318 ( 0.04481, 0.06310) 1.094 (1.081,1.108)
## Tscore.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.6308 (1.5096,1.762) 1.5407 (1.3468,1.762)
## Well - Death 0.9809 (0.9399,1.024) 3.3078 (2.9965,3.651)
## Fracture - Fracture
## Fracture - Death 1.1555 (1.0536,1.267) 0.9588 (0.7299,1.259)
##
## -2 * log-likelihood: 35069.19
hazard.msm(age.m2)
## $age
## HR L U
## Well - Fracture 1.060684 1.049404 1.072086
## Well - Death 1.116699 1.109441 1.124005
## Fracture - Death 1.094149 1.080765 1.107698
##
## $Tscore.2
## HR L U
## Well - Fracture 1.630793 1.5096138 1.761699
## Well - Death 0.980941 0.9398584 1.023819
## Fracture - Death 1.155495 1.0535774 1.267271
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.5406553 1.3467891 1.762428
## Well - Death 3.3077907 2.9965212 3.651394
## Fracture - Death 0.9587954 0.7298911 1.259487
multi.me1= msm(state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ ageBase + TscoreBase.2 +
fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer)
multi.me1
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~ageBase + TscoreBase.2 + fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline ageBase
## Well - Well -0.04168 (-0.04352,-0.03992)
## Well - Fracture 0.01337 ( 0.01243, 0.01438) 1.055 (1.043,1.067)
## Well - Death 0.02831 ( 0.02684, 0.02986) 1.112 (1.104,1.119)
## Fracture - Fracture -0.07164 (-0.08373,-0.06129)
## Fracture - Death 0.07164 ( 0.06129, 0.08373) 1.102 (1.087,1.118)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.634 (1.5104,1.767) 1.6040 (1.4107,1.8237)
## Well - Death 1.001 (0.9587,1.045) 0.8754 (0.8014,0.9563)
## Fracture - Fracture
## Fracture - Death 1.153 (1.0513,1.265) 0.9155 (0.7799,1.0747)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.3744 (1.1882,1.590) 1.145 (0.9817,1.336)
## Well - Death 1.0308 (0.9308,1.141) 1.512 (1.3839,1.652)
## Fracture - Fracture
## Fracture - Death 0.9982 (0.8336,1.195) 1.173 (0.9758,1.409)
## hypertension copd
## Well - Well
## Well - Fracture 1.198 (1.056,1.358) 1.143 (0.9435,1.384)
## Well - Death 1.187 (1.098,1.283) 1.333 (1.1849,1.499)
## Fracture - Fracture
## Fracture - Death 1.319 (1.127,1.545) 1.478 (1.1844,1.845)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.272 (1.028,1.575) 0.9571 (0.8135,1.126)
## Well - Death 1.564 (1.390,1.760) 1.1817 (1.0753,1.299)
## Fracture - Fracture
## Fracture - Death 1.293 (1.003,1.668) 1.0148 (0.8333,1.236)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.594 (1.393,1.824)
## Well - Death 3.458 (3.132,3.819)
## Fracture - Fracture
## Fracture - Death 1.724 (1.307,2.274)
##
## -2 * log-likelihood: 34736.31
hazard.msm(multi.me1)
## $ageBase
## HR L U
## Well - Fracture 1.054914 1.043404 1.066552
## Well - Death 1.111779 1.104302 1.119306
## Fracture - Death 1.102462 1.087109 1.118031
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.633550 1.5103854 1.766758
## Well - Death 1.000990 0.9586538 1.045195
## Fracture - Death 1.153403 1.0513061 1.265414
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.6039588 1.4106632 1.8237406
## Well - Death 0.8754452 0.8014228 0.9563046
## Fracture - Death 0.9154675 0.7798582 1.0746579
##
## $fx50
## HR L U
## Well - Fracture 1.3743877 1.1882493 1.589684
## Well - Death 1.0307597 0.9308102 1.141442
## Fracture - Death 0.9982193 0.8336076 1.195337
##
## $cvd.nYes
## HR L U
## Well - Fracture 1.145045 0.9816527 1.335633
## Well - Death 1.512191 1.3838808 1.652399
## Fracture - Death 1.172537 0.9758125 1.408922
##
## $hypertension
## HR L U
## Well - Fracture 1.197531 1.055667 1.358458
## Well - Death 1.186891 1.098088 1.282876
## Fracture - Death 1.319439 1.126843 1.544953
##
## $copd
## HR L U
## Well - Fracture 1.142676 0.943541 1.383839
## Well - Death 1.332596 1.184945 1.498645
## Fracture - Death 1.478103 1.184388 1.844655
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.272375 1.028001 1.574842
## Well - Death 1.563967 1.389978 1.759736
## Fracture - Death 1.293216 1.002616 1.668045
##
## $cancer
## HR L U
## Well - Fracture 0.957080 0.8135196 1.125974
## Well - Death 1.181678 1.0752816 1.298603
## Fracture - Death 1.014791 0.8333236 1.235775
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.593833 1.392623 1.824114
## Well - Death 3.458342 3.132120 3.818541
## Fracture - Death 1.723676 1.306746 2.273632
multi.me2= msm(state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ age + Tscore.2 +
fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer)
multi.me2
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~age + Tscore.2 + fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline age
## Well - Well -0.04480 (-0.04674,-0.04295)
## Well - Fracture 0.01396 ( 0.01299, 0.01501) 1.055 (1.043,1.067)
## Well - Death 0.03084 ( 0.02928, 0.03249) 1.112 (1.104,1.119)
## Fracture - Fracture -0.04902 (-0.05858,-0.04102)
## Fracture - Death 0.04902 ( 0.04102, 0.05858) 1.097 (1.083,1.110)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.634 (1.5106,1.767) 1.6032 (1.4100,1.8229)
## Well - Death 1.001 (0.9586,1.045) 0.8754 (0.8014,0.9562)
## Fracture - Fracture
## Fracture - Death 1.172 (1.0671,1.286) 1.0560 (0.8995,1.2397)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.374 (1.1883,1.590) 1.145 (0.9818,1.336)
## Well - Death 1.031 (0.9308,1.141) 1.512 (1.3838,1.652)
## Fracture - Fracture
## Fracture - Death 1.097 (0.9148,1.315) 1.266 (1.0546,1.520)
## hypertension copd
## Well - Well
## Well - Fracture 1.197 (1.056,1.358) 1.143 (0.9438,1.384)
## Well - Death 1.187 (1.098,1.283) 1.333 (1.1852,1.499)
## Fracture - Fracture
## Fracture - Death 1.315 (1.122,1.541) 1.578 (1.2637,1.969)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.272 (1.028,1.575) 0.9569 (0.8133,1.126)
## Well - Death 1.564 (1.390,1.760) 1.1818 (1.0754,1.299)
## Fracture - Fracture
## Fracture - Death 1.361 (1.055,1.756) 1.0482 (0.8611,1.276)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.594 (1.3924,1.824)
## Well - Death 3.458 (3.1318,3.818)
## Fracture - Fracture
## Fracture - Death 1.035 (0.7859,1.362)
##
## -2 * log-likelihood: 34709.41
hazard.msm(multi.me2)
## $age
## HR L U
## Well - Fracture 1.054908 1.043398 1.066545
## Well - Death 1.111766 1.104289 1.119293
## Fracture - Death 1.096603 1.082895 1.110484
##
## $Tscore.2
## HR L U
## Well - Fracture 1.633751 1.5105733 1.766973
## Well - Death 1.000972 0.9586371 1.045177
## Fracture - Death 1.171577 1.0671066 1.286275
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.6032429 1.4100305 1.8229307
## Well - Death 0.8753802 0.8013617 0.9562354
## Fracture - Death 1.0560090 0.8995297 1.2397090
##
## $fx50
## HR L U
## Well - Fracture 1.374487 1.1883459 1.589786
## Well - Death 1.030766 0.9308155 1.141449
## Fracture - Death 1.096847 0.9148146 1.315100
##
## $cvd.nYes
## HR L U
## Well - Fracture 1.145187 0.9817847 1.335786
## Well - Death 1.512109 1.3838021 1.652313
## Fracture - Death 1.266245 1.0546011 1.520362
##
## $hypertension
## HR L U
## Well - Fracture 1.197473 1.055621 1.358386
## Well - Death 1.186594 1.097812 1.282556
## Fracture - Death 1.314628 1.121581 1.540903
##
## $copd
## HR L U
## Well - Fracture 1.142981 0.943816 1.384173
## Well - Death 1.332856 1.185185 1.498927
## Fracture - Death 1.577621 1.263716 1.969500
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.272274 1.027918 1.574718
## Well - Death 1.564041 1.390043 1.759819
## Fracture - Death 1.360782 1.054662 1.755753
##
## $cancer
## HR L U
## Well - Fracture 0.9568559 0.8133231 1.125719
## Well - Death 1.1817624 1.0753587 1.298694
## Fracture - Death 1.0482357 0.8610708 1.276083
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.593514 1.3923577 1.823732
## Well - Death 3.457999 3.1318135 3.818157
## Fracture - Death 1.034763 0.7858665 1.362488
multi.m1 = msm(state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ ageBase + TscoreBase.2 +
fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer +
renal + parkinson + depression)
multi.m1
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~ageBase + TscoreBase.2 + fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer + renal + parkinson + depression, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline ageBase
## Well - Well -0.04108 (-0.04291,-0.03933)
## Well - Fracture 0.01334 ( 0.01240, 0.01436) 1.057 (1.045,1.069)
## Well - Death 0.02774 ( 0.02628, 0.02928) 1.108 (1.100,1.116)
## Fracture - Fracture -0.06969 (-0.08165,-0.05949)
## Fracture - Death 0.06969 ( 0.05949, 0.08165) 1.105 (1.089,1.121)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.675 (1.5428,1.819) 1.5993 (1.4059,1.8193)
## Well - Death 1.010 (0.9653,1.057) 0.8769 (0.8025,0.9582)
## Fracture - Fracture
## Fracture - Death 1.183 (1.0726,1.304) 0.8717 (0.7407,1.0259)
## fx50 BMI
## Well - Well
## Well - Fracture 1.3650 (1.1797,1.579) 1.020 (1.002,1.039)
## Well - Death 1.0261 (0.9265,1.136) 1.013 (1.001,1.025)
## Fracture - Fracture
## Fracture - Death 0.9874 (0.8242,1.183) 1.007 (0.984,1.031)
## smoke drink.nYes
## Well - Well
## Well - Fracture 1.067 (0.9381,1.214) 0.9768 (0.8559,1.1148)
## Well - Death 1.275 (1.1749,1.383) 0.9084 (0.8373,0.9856)
## Fracture - Fracture
## Fracture - Death 1.183 (1.0034,1.394) 0.9248 (0.7826,1.0929)
## physical cvd.nYes
## Well - Well
## Well - Fracture 0.9272 (0.8124,1.0581) 1.133 (0.9703,1.323)
## Well - Death 0.8606 (0.7937,0.9331) 1.492 (1.3653,1.632)
## Fracture - Fracture
## Fracture - Death 0.9165 (0.7776,1.0803) 1.156 (0.9614,1.389)
## hypertension copd
## Well - Well
## Well - Fracture 1.166 (1.026,1.325) 1.123 (0.9258,1.361)
## Well - Death 1.142 (1.056,1.236) 1.254 (1.1140,1.412)
## Fracture - Fracture
## Fracture - Death 1.309 (1.115,1.538) 1.488 (1.1885,1.864)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.232 (0.9933,1.529) 0.9546 (0.8111,1.123)
## Well - Death 1.492 (1.3232,1.681) 1.1795 (1.0730,1.297)
## Fracture - Fracture
## Fracture - Death 1.281 (0.9880,1.661) 0.9774 (0.8004,1.194)
## renal parkinson
## Well - Well
## Well - Fracture 1.0167 (0.7851,1.3166) 0.8601 (0.6750,1.096)
## Well - Death 0.4328 (0.3624,0.5168) 1.7169 (1.5057,1.958)
## Fracture - Fracture
## Fracture - Death 0.4589 (0.3315,0.6354) 1.1814 (0.8887,1.570)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.0617 (0.7943,1.419) 1.606 (1.403,1.839)
## Well - Death 0.8303 (0.6718,1.026) 3.621 (3.277,3.999)
## Fracture - Fracture
## Fracture - Death 1.2174 (0.8500,1.743) 1.857 (1.404,2.457)
##
## -2 * log-likelihood: 34482.87
hazard.msm(multi.m1)
## $ageBase
## HR L U
## Well - Fracture 1.056546 1.044640 1.068587
## Well - Death 1.108130 1.100438 1.115877
## Fracture - Death 1.104521 1.088564 1.120712
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.675293 1.5428062 1.819157
## Well - Death 1.010163 0.9653202 1.057088
## Fracture - Death 1.182816 1.0726030 1.304353
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.5993353 1.4059333 1.8193420
## Well - Death 0.8769080 0.8024858 0.9582321
## Fracture - Death 0.8717051 0.7406923 1.0258913
##
## $fx50
## HR L U
## Well - Fracture 1.3650267 1.1797272 1.579431
## Well - Death 1.0260644 0.9265252 1.136297
## Fracture - Death 0.9873546 0.8241698 1.182850
##
## $BMI
## HR L U
## Well - Fracture 1.020471 1.0018024 1.039488
## Well - Death 1.012820 1.0012579 1.024515
## Fracture - Death 1.006990 0.9839527 1.030567
##
## $smoke
## HR L U
## Well - Fracture 1.067370 0.9381202 1.214427
## Well - Death 1.274774 1.1748640 1.383181
## Fracture - Death 1.182677 1.0034061 1.393977
##
## $drink.nYes
## HR L U
## Well - Fracture 0.9768408 0.8559284 1.1148338
## Well - Death 0.9084156 0.8372520 0.9856279
## Fracture - Death 0.9248342 0.7825822 1.0929436
##
## $physical
## HR L U
## Well - Fracture 0.9271842 0.8124486 1.0581231
## Well - Death 0.8605990 0.7937252 0.9331071
## Fracture - Death 0.9165490 0.7776290 1.0802866
##
## $cvd.nYes
## HR L U
## Well - Fracture 1.132837 0.9703376 1.322551
## Well - Death 1.492496 1.3653119 1.631527
## Fracture - Death 1.155582 0.9614215 1.388953
##
## $hypertension
## HR L U
## Well - Fracture 1.166079 1.026074 1.325187
## Well - Death 1.142402 1.055782 1.236128
## Fracture - Death 1.309404 1.115075 1.537599
##
## $copd
## HR L U
## Well - Fracture 1.122663 0.925805 1.361380
## Well - Death 1.254072 1.113987 1.411771
## Fracture - Death 1.488416 1.188492 1.864027
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.232288 0.9932675 1.528827
## Well - Death 1.491572 1.3231849 1.681387
## Fracture - Death 1.280897 0.9879516 1.660706
##
## $cancer
## HR L U
## Well - Fracture 0.9545850 0.8110881 1.123469
## Well - Death 1.1795137 1.0730453 1.296546
## Fracture - Death 0.9774277 0.8004478 1.193538
##
## $renal
## HR L U
## Well - Fracture 1.0167070 0.7851332 1.3165832
## Well - Death 0.4328100 0.3624450 0.5168356
## Fracture - Death 0.4589377 0.3314948 0.6353758
##
## $parkinson
## HR L U
## Well - Fracture 0.8601457 0.6750162 1.096049
## Well - Death 1.7169301 1.5056776 1.957822
## Fracture - Death 1.1813560 0.8886750 1.570430
##
## $depression
## HR L U
## Well - Fracture 1.061699 0.7943326 1.419058
## Well - Death 0.830307 0.6717878 1.026232
## Fracture - Death 1.217374 0.8500413 1.743444
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.606265 1.402872 1.839145
## Well - Death 3.620526 3.277497 3.999457
## Fracture - Death 1.857024 1.403578 2.456963
multi.m2= msm(state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ age + Tscore.2 + fall.yesno
+ fx50 + BMI + smoke + drink + physical + cvd + hypertension + copd + diabetes + cancer + renal + parkinson
+ depression)
multi.m2
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = men, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~age + Tscore.2 + fall.yesno + fx50 + BMI + smoke + drink + physical + cvd + hypertension + copd + diabetes + cancer + renal + parkinson + depression, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline age
## Well - Well -0.04410 (-0.04603,-0.04226)
## Well - Fracture 0.01395 ( 0.01297, 0.01500) 1.057 (1.045,1.069)
## Well - Death 0.03015 ( 0.02860, 0.03178) 1.108 (1.101,1.116)
## Fracture - Fracture -0.04795 (-0.05740,-0.04006)
## Fracture - Death 0.04795 ( 0.04006, 0.05740) 1.096 (1.082,1.110)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.675 (1.5421,1.819) 1.6002 (1.4065,1.8204)
## Well - Death 1.012 (0.9671,1.059) 0.8747 (0.8004,0.9558)
## Fracture - Fracture
## Fracture - Death 1.205 (1.0903,1.331) 1.0177 (0.8653,1.1969)
## fx50 BMI
## Well - Well
## Well - Fracture 1.365 (1.1796,1.579) 1.020 (1.0017,1.039)
## Well - Death 1.027 (0.9271,1.137) 1.013 (1.0018,1.025)
## Fracture - Fracture
## Fracture - Death 1.085 (0.9047,1.302) 1.010 (0.9861,1.034)
## smoke drink
## Well - Well
## Well - Fracture 1.069 (0.9383,1.217) 0.9930 (0.9509,1.037)
## Well - Death 1.268 (1.1677,1.376) 0.9889 (0.9626,1.016)
## Fracture - Fracture
## Fracture - Death 1.135 (0.9626,1.339) 0.9953 (0.9406,1.053)
## physical cvd
## Well - Well
## Well - Fracture 0.9271 (0.8124,1.0581) 1.133 (0.9706,1.323)
## Well - Death 0.8594 (0.7926,0.9318) 1.500 (1.3720,1.639)
## Fracture - Fracture
## Fracture - Death 0.8557 (0.7277,1.0063) 1.247 (1.0370,1.499)
## hypertension copd
## Well - Well
## Well - Fracture 1.166 (1.026,1.326) 1.123 (0.9262,1.362)
## Well - Death 1.143 (1.056,1.237) 1.260 (1.1192,1.418)
## Fracture - Fracture
## Fracture - Death 1.302 (1.109,1.530) 1.552 (1.2396,1.943)
## diabetes cancer
## Well - Well
## Well - Fracture 1.233 (0.9937,1.529) 0.9542 (0.8108,1.123)
## Well - Death 1.505 (1.3351,1.696) 1.1770 (1.0708,1.294)
## Fracture - Fracture
## Fracture - Death 1.341 (1.0342,1.739) 1.0073 (0.8252,1.230)
## renal parkinson
## Well - Well
## Well - Fracture 1.0173 (0.7856,1.3173) 0.8598 (0.6747,1.096)
## Well - Death 0.4316 (0.3614,0.5154) 1.7245 (1.5122,1.967)
## Fracture - Fracture
## Fracture - Death 0.4689 (0.3351,0.6560) 1.2100 (0.9017,1.624)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.0600 (0.7932,1.417) 1.606 (1.4026,1.839)
## Well - Death 0.8277 (0.6697,1.023) 3.615 (3.2727,3.994)
## Fracture - Fracture
## Fracture - Death 1.2079 (0.8453,1.726) 1.112 (0.8412,1.469)
##
## -2 * log-likelihood: 34462.53
hazard.msm(multi.m2)
## $age
## HR L U
## Well - Fracture 1.056570 1.044664 1.068611
## Well - Death 1.108328 1.100629 1.116082
## Fracture - Death 1.096260 1.082355 1.110344
##
## $Tscore.2
## HR L U
## Well - Fracture 1.674721 1.5420523 1.818803
## Well - Death 1.012175 0.9671222 1.059327
## Fracture - Death 1.204762 1.0902598 1.331290
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.6001564 1.4065287 1.8204396
## Well - Death 0.8746621 0.8004058 0.9558075
## Fracture - Death 1.0176745 0.8652604 1.1969360
##
## $fx50
## HR L U
## Well - Fracture 1.364864 1.1795886 1.579240
## Well - Death 1.026662 0.9270577 1.136967
## Fracture - Death 1.085207 0.9047267 1.301691
##
## $BMI
## HR L U
## Well - Fracture 1.020409 1.0017204 1.039447
## Well - Death 1.013402 1.0018080 1.025130
## Fracture - Death 1.009760 0.9860529 1.034036
##
## $smoke
## HR L U
## Well - Fracture 1.068511 0.9382613 1.216841
## Well - Death 1.267724 1.1677324 1.376278
## Fracture - Death 1.135320 0.9626011 1.339030
##
## $drink
## HR L U
## Well - Fracture 0.9930048 0.9508621 1.037015
## Well - Death 0.9888865 0.9626160 1.015874
## Fracture - Death 0.9952812 0.9405593 1.053187
##
## $physical
## HR L U
## Well - Fracture 0.9271293 0.8124043 1.058055
## Well - Death 0.8594246 0.7926377 0.931839
## Fracture - Death 0.8557376 0.7277214 1.006274
##
## $cvd
## HR L U
## Well - Fracture 1.133114 0.9706489 1.322771
## Well - Death 1.499757 1.3719823 1.639432
## Fracture - Death 1.246841 1.0370190 1.499116
##
## $hypertension
## HR L U
## Well - Fracture 1.166422 1.026394 1.325555
## Well - Death 1.142921 1.056257 1.236694
## Fracture - Death 1.302444 1.108841 1.529849
##
## $copd
## HR L U
## Well - Fracture 1.123038 0.9261638 1.361760
## Well - Death 1.259936 1.1192194 1.418344
## Fracture - Death 1.551957 1.2396025 1.943019
##
## $diabetes
## HR L U
## Well - Fracture 1.232738 0.993742 1.529214
## Well - Death 1.504881 1.335069 1.696291
## Fracture - Death 1.341176 1.034180 1.739304
##
## $cancer
## HR L U
## Well - Fracture 0.9541689 0.8107589 1.122946
## Well - Death 1.1770365 1.0707994 1.293814
## Fracture - Death 1.0072977 0.8251633 1.229634
##
## $renal
## HR L U
## Well - Fracture 1.0172769 0.7855852 1.3173012
## Well - Death 0.4315937 0.3614036 0.5154156
## Fracture - Death 0.4688591 0.3351264 0.6559582
##
## $parkinson
## HR L U
## Well - Fracture 0.859820 0.6747487 1.095653
## Well - Death 1.724504 1.5121765 1.966645
## Fracture - Death 1.210036 0.9017124 1.623785
##
## $depression
## HR L U
## Well - Fracture 1.0599914 0.7931759 1.416561
## Well - Death 0.8277142 0.6696892 1.023028
## Fracture - Death 1.2078658 0.8453157 1.725911
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.605877 1.4025580 1.838669
## Well - Death 3.615157 3.2726543 3.993504
## Fracture - Death 1.111629 0.8411597 1.469066
# Osteopenia:
options(digits = 5)
pmatrix.msm(multi.m2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)
## Well Fracture Death
## Well 0.99744 0.00056862 0.0019935
## Fracture 0.00000 0.99524036 0.0047596
## Death 0.00000 0.00000000 1.0000000
pmatrix.msm(multi.m2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)
## Well Fracture Death
## Well 0.97633 0.0034702 0.020197
## Fracture 0.00000 0.9753878 0.024612
## Death 0.00000 0.0000000 1.000000
pmatrix.msm(multi.m2, t = 10, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)
## Well Fracture Death
## Well 0.93745 0.0077057 0.054843
## Fracture 0.00000 0.9498625 0.050138
## Death 0.00000 0.0000000 1.000000
# Osteoporosis:
pmatrix.msm(multi.m2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)
## Well Fracture Death
## Well 0.99769 0.00033971 0.0019691
## Fracture 0.00000 0.99604771 0.0039523
## Death 0.00000 0.00000000 1.0000000
pmatrix.msm(multi.m2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)
## Well Fracture Death
## Well 0.97797 0.0020778 0.019954
## Fracture 0.00000 0.9795277 0.020472
## Death 0.00000 0.0000000 1.000000
pmatrix.msm(multi.m2, t = 10, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)
## Well Fracture Death
## Well 0.94117 0.004629 0.054206
## Fracture 0.00000 0.958203 0.041797
## Death 0.00000 0.000000 1.000000
# Osteoporosis + comorbidities:
pmatrix.msm(multi.m2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5, cvd = 1, diabetes = 1, cancer = 1), 2)
## Well Fracture Death
## Well 0.99433 0.0004514 0.0052219
## Fracture 0.00000 0.9933516 0.0066484
## Death 0.00000 0.0000000 1.0000000
pmatrix.msm(multi.m2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5, cvd = 1, diabetes = 1, cancer = 1), 2)
## Well Fracture Death
## Well 0.94518 0.0027137 0.052106
## Fracture 0.00000 0.9657579 0.034242
## Death 0.00000 0.0000000 1.000000
pmatrix.msm(multi.m2, t = 10, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5, cvd = 1, diabetes = 1, cancer = 1), 2)
## Well Fracture Death
## Well 0.85671 0.0058369 0.137455
## Fracture 0.00000 0.9306071 0.069393
## Death 0.00000 0.0000000 1.000000
prevalence.msm(multi.m2, times = seq(0,20,1), covariates = "mean", ci = "normal")
## $Observed
## State 1 State 2 State 3 Total
## 0 5373 0 0 5373
## 1 5268 49 53 5370
## 2 5118 101 148 5367
## 3 4921 159 262 5342
## 4 4731 198 394 5323
## 5 4475 257 559 5291
## 6 4250 290 726 5266
## 7 4020 323 905 5248
## 8 3753 371 1102 5226
## 9 3495 392 1322 5209
## 10 3242 413 1533 5188
## 11 2984 419 1764 5167
## 12 2748 418 1978 5144
## 13 2480 414 2226 5120
## 14 2220 413 2455 5088
## 15 1961 399 2673 5033
## 16 1744 365 2871 4980
## 17 1528 346 3066 4940
## 18 1337 310 3230 4877
## 19 1181 265 3291 4737
## 20 1018 212 3292 4522
##
## $Expected
## $Expected$estimates
## Well Fracture Death Total
## 0 5373.0 0.000 0.000 5373
## 1 5226.0 57.334 86.653 5370
## 2 5083.0 110.516 173.438 5367
## 3 4923.7 159.121 259.168 5342
## 4 4774.6 203.879 344.474 5323
## 5 4618.7 244.302 428.008 5291
## 6 4260.4 307.865 697.730 5266
## 7 3935.1 362.528 950.398 5248
## 8 3631.8 408.587 1185.651 5226
## 9 3355.0 447.570 1406.440 5209
## 10 3096.9 479.528 1611.581 5188
## 11 2858.6 505.488 1802.912 5167
## 12 2637.6 525.892 1980.533 5144
## 13 2433.1 541.414 2145.470 5120
## 14 2240.9 551.825 2295.242 5088
## 15 2054.5 555.909 2422.630 5033
## 16 1884.0 556.829 2539.135 4980
## 17 1732.1 556.281 2651.608 4940
## 18 1584.9 550.616 2741.525 4877
## 19 1426.7 534.101 2776.207 4737
## 20 1262.3 507.421 2752.327 4522
##
## $Expected$ci
## , , 2.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 5373.0 0.000 0.000 5373
## [2,] 5215.1 51.702 79.083 5370
## [3,] 5061.9 99.710 158.530 5367
## [4,] 4893.0 143.204 237.206 5342
## [5,] 4734.9 183.219 315.927 5323
## [6,] 4570.7 219.115 393.160 5291
## [7,] 4213.3 284.004 663.601 5266
## [8,] 3886.0 337.887 913.131 5248
## [9,] 3581.9 382.569 1141.878 5226
## [10,] 3303.1 419.262 1357.583 5209
## [11,] 3041.1 448.918 1559.167 5188
## [12,] 2799.4 472.290 1745.416 5167
## [13,] 2576.1 490.427 1919.332 5144
## [14,] 2369.1 503.275 2081.167 5120
## [15,] 2175.8 512.157 2227.955 5088
## [16,] 1989.8 512.658 2352.849 5033
## [17,] 1820.6 511.819 2467.717 4980
## [18,] 1669.3 511.200 2578.596 4940
## [19,] 1523.3 505.227 2667.492 4877
## [20,] 1367.6 488.389 2702.586 4737
## [21,] 1206.8 462.175 2681.197 4522
##
## , , 97.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 5373.0 0.000 0.000 5373
## [2,] 5235.6 64.339 94.413 5370
## [3,] 5101.6 124.042 188.778 5367
## [4,] 4950.7 178.851 281.361 5342
## [5,] 4809.6 229.484 373.338 5323
## [6,] 4661.0 275.400 463.926 5291
## [7,] 4302.7 337.960 734.380 5266
## [8,] 3979.7 392.016 989.372 5248
## [9,] 3679.8 438.461 1227.584 5226
## [10,] 3406.9 478.566 1452.528 5209
## [11,] 3152.8 512.715 1662.620 5188
## [12,] 2918.6 541.474 1857.465 5167
## [13,] 2701.1 564.304 2039.443 5144
## [14,] 2498.9 581.998 2208.432 5120
## [15,] 2306.7 595.035 2361.060 5088
## [16,] 2121.4 601.044 2491.266 5033
## [17,] 1951.5 603.343 2610.034 4980
## [18,] 1798.5 604.609 2724.109 4940
## [19,] 1650.0 599.487 2814.206 4877
## [20,] 1489.6 582.714 2848.005 4737
## [21,] 1321.8 555.839 2821.030 4522
##
##
##
## $`Observed percentages`
## State 1 State 2 State 3
## 0 100.000 0.00000 0.00000
## 1 98.101 0.91248 0.98696
## 2 95.361 1.88187 2.75759
## 3 92.119 2.97641 4.90453
## 4 88.878 3.71971 7.40184
## 5 84.578 4.85730 10.56511
## 6 80.706 5.50703 13.78656
## 7 76.601 6.15473 17.24466
## 8 71.814 7.09912 21.08687
## 9 67.095 7.52544 25.37915
## 10 62.490 7.96068 29.54896
## 11 57.751 8.10915 34.13973
## 12 53.421 8.12597 38.45257
## 13 48.438 8.08594 43.47656
## 14 43.632 8.11714 48.25079
## 15 38.963 7.92768 53.10948
## 16 35.020 7.32932 57.65060
## 17 30.931 7.00405 62.06478
## 18 27.414 6.35637 66.22924
## 19 24.931 5.59426 69.47435
## 20 22.512 4.68819 72.79965
##
## $`Expected percentages`
## $`Expected percentages`$estimates
## Well Fracture Death
## 0 100.000 0.0000 0.0000
## 1 97.319 1.0677 1.6137
## 2 94.709 2.0592 3.2316
## 3 92.170 2.9787 4.8515
## 4 89.698 3.8301 6.4714
## 5 87.293 4.6173 8.0894
## 6 80.904 5.8463 13.2497
## 7 74.982 6.9079 18.1097
## 8 69.494 7.8184 22.6875
## 9 64.408 8.5922 27.0002
## 10 59.693 9.2430 31.0636
## 11 55.324 9.7830 34.8928
## 12 51.275 10.2234 38.5018
## 13 47.522 10.5745 41.9037
## 14 44.044 10.8456 45.1109
## 15 40.820 11.0453 48.1349
## 16 37.832 11.1813 50.9866
## 17 35.063 11.2608 53.6763
## 18 32.497 11.2901 56.2134
## 19 30.118 11.2751 58.6069
## 20 27.914 11.2212 60.8653
##
## $`Expected percentages`$ci
## , , 2.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.00000 0.0000
## [2,] 97.116 0.96279 1.4727
## [3,] 94.315 1.85784 2.9538
## [4,] 91.594 2.68071 4.4404
## [5,] 88.953 3.44203 5.9351
## [6,] 86.387 4.14127 7.4307
## [7,] 80.010 5.39317 12.6016
## [8,] 74.048 6.43840 17.3996
## [9,] 68.540 7.32048 21.8499
## [10,] 63.412 8.04880 26.0623
## [11,] 58.619 8.65301 30.0533
## [12,] 54.179 9.14050 33.7801
## [13,] 50.080 9.53396 37.3121
## [14,] 46.272 9.82959 40.6478
## [15,] 42.763 10.06598 43.7884
## [16,] 39.536 10.18594 46.7484
## [17,] 36.558 10.27749 49.5526
## [18,] 33.792 10.34817 52.1983
## [19,] 31.235 10.35938 54.6953
## [20,] 28.872 10.31010 57.0527
## [21,] 26.687 10.22060 59.2923
##
## , , 97.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.0000 0.0000
## [2,] 97.496 1.1981 1.7581
## [3,] 95.055 2.3112 3.5174
## [4,] 92.675 3.3480 5.2670
## [5,] 90.355 4.3112 7.0137
## [6,] 88.093 5.2051 8.7682
## [7,] 81.706 6.4178 13.9457
## [8,] 75.833 7.4698 18.8524
## [9,] 70.414 8.3900 23.4899
## [10,] 65.403 9.1873 27.8850
## [11,] 60.771 9.8827 32.0474
## [12,] 56.485 10.4795 35.9486
## [13,] 52.509 10.9701 39.6470
## [14,] 48.807 11.3672 43.1334
## [15,] 45.337 11.6949 46.4045
## [16,] 42.150 11.9421 49.4986
## [17,] 39.187 12.1153 52.4103
## [18,] 36.407 12.2391 55.1439
## [19,] 33.832 12.2921 57.7036
## [20,] 31.447 12.3013 60.1226
## [21,] 29.230 12.2919 62.3846
plot.prevalence.msm(multi.m2, mintime = 0, maxtime = 20, legend.pos = c(10, 80), col.obs = "gray",
col.exp = "black")
par(mfrow= c(1,2))
plot.survfit.msm(multi.m2, from = 1, main = "No fracture", range = c(0,20),
ci = "normal", col = "black", col.ci = "black", lty = 2, lwd = 2,
col.surv ="grey", lty.surv = 2, lwd.surv = 1, xlab = "Time (years)")
legend(0.4,0.35, legend = c("Expected", "Expected (95% CI)", "Observed", "Observed (95% CI)"),
col = c("black", "black", "grey", "gray"), lty = c(2, 2, 1, 2), lwd = c(2, 1, 2, 1))
plot.survfit.msm(multi.m2, from = 2, main = "Initial fracture", range = c(0,20),
ci = "normal", col = "black", col.ci = "black", lty = 2, lwd = 2,
col.surv ="grey", lty.surv = 2, lwd.surv = 1, xlab = "Time (years)")
women = subset(bmd, gender == "F" & race == "1:WHITE")
baseline.w = subset(women, state == 1 & time2event == 0)
table1(~ ageBase + fnbmdBase + TscoreBase + as.factor(fall.no) + fall.yesno + as.factor(fx50) + race + weight + height + BMI + as.factor(smoke) + as.factor(drink.n) + as.factor(physical) + as.factor(cvd.n) + as.factor(hypertension) + as.factor(copd) + as.factor(diabetes.n) + as.factor(cancer) + as.factor(parkinson) + as.factor(rheumatoid) + as.factor(renal) + as.factor(depression) + as.factor(anyfx) + as.factor(death) | fx_death, data = baseline.w)
Event-free (N=1888) |
Fractured, Alive (N=1210) |
Fractured, Dead (N=1486) |
No Fractured, Dead (N=2779) |
Overall (N=7363) |
|
---|---|---|---|---|---|
ageBase | |||||
Mean (SD) | 71.7 (4.00) | 72.0 (4.20) | 75.4 (5.29) | 74.7 (5.33) | 73.6 (5.08) |
Median [Min, Max] | 71.0 [67.0, 88.0] | 71.0 [67.0, 90.0] | 75.0 [67.0, 91.0] | 74.0 [67.0, 90.0] | 73.0 [67.0, 91.0] |
fnbmdBase | |||||
Mean (SD) | 0.676 (0.107) | 0.638 (0.104) | 0.604 (0.101) | 0.658 (0.114) | 0.648 (0.111) |
Median [Min, Max] | 0.666 [0.387, 1.15] | 0.630 [0.302, 1.11] | 0.597 [0.297, 1.13] | 0.648 [0.277, 1.19] | 0.639 [0.277, 1.19] |
TscoreBase | |||||
Mean (SD) | -1.54 (0.893) | -1.85 (0.869) | -2.13 (0.843) | -1.69 (0.947) | -1.76 (0.924) |
Median [Min, Max] | -1.62 [-3.94, 2.39] | -1.92 [-4.65, 2.12] | -2.20 [-4.69, 2.22] | -1.77 [-4.86, 2.73] | -1.84 [-4.86, 2.73] |
as.factor(fall.no) | |||||
0 | 1418 (75.1%) | 854 (70.6%) | 1034 (69.6%) | 2038 (73.3%) | 5344 (72.6%) |
1 | 333 (17.6%) | 257 (21.2%) | 286 (19.2%) | 473 (17.0%) | 1349 (18.3%) |
2 | 97 (5.1%) | 71 (5.9%) | 107 (7.2%) | 176 (6.3%) | 451 (6.1%) |
3+ | 40 (2.1%) | 28 (2.3%) | 59 (4.0%) | 92 (3.3%) | 219 (3.0%) |
fall.yesno | |||||
No | 1418 (75.1%) | 854 (70.6%) | 1034 (69.6%) | 2038 (73.3%) | 5344 (72.6%) |
Yes | 470 (24.9%) | 356 (29.4%) | 452 (30.4%) | 741 (26.7%) | 2019 (27.4%) |
as.factor(fx50) | |||||
0 | 1297 (68.7%) | 654 (54.0%) | 708 (47.6%) | 1700 (61.2%) | 4359 (59.2%) |
1 | 591 (31.3%) | 556 (46.0%) | 778 (52.4%) | 1079 (38.8%) | 3004 (40.8%) |
race | |||||
1:WHITE | 1888 (100%) | 1210 (100%) | 1486 (100%) | 2779 (100%) | 7363 (100%) |
weight | |||||
Mean (SD) | 67.3 (11.8) | 66.3 (11.7) | 64.7 (11.6) | 66.7 (12.8) | 66.4 (12.1) |
Median [Min, Max] | 65.8 [41.7, 112] | 65.0 [40.8, 112] | 63.3 [40.2, 110] | 65.3 [40.0, 112] | 65.0 [40.0, 112] |
Missing | 11 (0.6%) | 11 (0.9%) | 20 (1.3%) | 24 (0.9%) | 66 (0.9%) |
height | |||||
Mean (SD) | 160 (5.66) | 160 (5.65) | 159 (6.01) | 159 (5.94) | 159 (5.85) |
Median [Min, Max] | 160 [142, 175] | 160 [143, 176] | 159 [142, 175] | 159 [141, 175] | 159 [141, 176] |
Missing | 8 (0.4%) | 7 (0.6%) | 16 (1.1%) | 13 (0.5%) | 44 (0.6%) |
BMI | |||||
Mean (SD) | 26.4 (4.36) | 26.0 (4.37) | 25.7 (4.35) | 26.5 (4.69) | 26.2 (4.50) |
Median [Min, Max] | 25.8 [16.0, 44.1] | 25.4 [16.2, 48.8] | 25.3 [16.9, 48.3] | 25.9 [15.3, 44.7] | 25.7 [15.3, 48.8] |
Missing | 11 (0.6%) | 11 (0.9%) | 20 (1.3%) | 25 (0.9%) | 67 (0.9%) |
as.factor(smoke) | |||||
0 | 1182 (62.6%) | 771 (63.7%) | 915 (61.6%) | 1614 (58.1%) | 4482 (60.9%) |
1 | 706 (37.4%) | 439 (36.3%) | 571 (38.4%) | 1165 (41.9%) | 2881 (39.1%) |
as.factor(drink.n) | |||||
No | 723 (38.3%) | 480 (39.7%) | 724 (48.7%) | 1336 (48.1%) | 3263 (44.3%) |
Yes | 1165 (61.7%) | 730 (60.3%) | 762 (51.3%) | 1443 (51.9%) | 4100 (55.7%) |
as.factor(physical) | |||||
0 | 567 (30.0%) | 355 (29.3%) | 734 (49.4%) | 1400 (50.4%) | 3056 (41.5%) |
1 | 1321 (70.0%) | 855 (70.7%) | 752 (50.6%) | 1379 (49.6%) | 4307 (58.5%) |
as.factor(cvd.n) | |||||
No | 1554 (82.3%) | 1002 (82.8%) | 1079 (72.6%) | 1956 (70.4%) | 5591 (75.9%) |
Yes | 334 (17.7%) | 208 (17.2%) | 407 (27.4%) | 823 (29.6%) | 1772 (24.1%) |
as.factor(hypertension) | |||||
0 | 1326 (70.2%) | 864 (71.4%) | 846 (56.9%) | 1555 (56.0%) | 4591 (62.4%) |
1 | 562 (29.8%) | 346 (28.6%) | 640 (43.1%) | 1224 (44.0%) | 2772 (37.6%) |
as.factor(copd) | |||||
0 | 1628 (86.2%) | 1007 (83.2%) | 1190 (80.1%) | 2289 (82.4%) | 6114 (83.0%) |
1 | 260 (13.8%) | 203 (16.8%) | 296 (19.9%) | 490 (17.6%) | 1249 (17.0%) |
as.factor(diabetes.n) | |||||
No | 1821 (96.5%) | 1153 (95.3%) | 1357 (91.3%) | 2543 (91.5%) | 6874 (93.4%) |
Yes | 67 (3.5%) | 57 (4.7%) | 129 (8.7%) | 236 (8.5%) | 489 (6.6%) |
as.factor(cancer) | |||||
0 | 1546 (81.9%) | 977 (80.7%) | 1181 (79.5%) | 2232 (80.3%) | 5936 (80.6%) |
1 | 342 (18.1%) | 233 (19.3%) | 305 (20.5%) | 547 (19.7%) | 1427 (19.4%) |
as.factor(parkinson) | |||||
0 | 1882 (99.7%) | 1204 (99.5%) | 1470 (98.9%) | 2764 (99.5%) | 7320 (99.4%) |
1 | 6 (0.3%) | 6 (0.5%) | 16 (1.1%) | 15 (0.5%) | 43 (0.6%) |
as.factor(rheumatoid) | |||||
0 | 1804 (95.6%) | 1146 (94.7%) | 1393 (93.7%) | 2629 (94.6%) | 6972 (94.7%) |
1 | 84 (4.4%) | 64 (5.3%) | 93 (6.3%) | 150 (5.4%) | 391 (5.3%) |
as.factor(renal) | |||||
0 | 1867 (98.9%) | 1203 (99.4%) | 1463 (98.5%) | 2741 (98.6%) | 7274 (98.8%) |
1 | 21 (1.1%) | 7 (0.6%) | 23 (1.5%) | 38 (1.4%) | 89 (1.2%) |
as.factor(depression) | |||||
0 | 1765 (93.5%) | 1117 (92.3%) | 1352 (91.0%) | 2562 (92.2%) | 6796 (92.3%) |
1 | 123 (6.5%) | 93 (7.7%) | 134 (9.0%) | 217 (7.8%) | 567 (7.7%) |
as.factor(anyfx) | |||||
0 | 1888 (100%) | 0 (0%) | 0 (0%) | 2779 (100%) | 4667 (63.4%) |
1 | 0 (0%) | 1210 (100%) | 1486 (100%) | 0 (0%) | 2696 (36.6%) |
as.factor(death) | |||||
0 | 1888 (100%) | 1210 (100%) | 0 (0%) | 0 (0%) | 3098 (42.1%) |
1 | 0 (0%) | 0 (0%) | 1486 (100%) | 2779 (100%) | 4265 (57.9%) |
#createTable(compareGroups(fx_death ~ ageBase + fnbmdBase + TscoreBase + fall.no + fall.yesno + fx50 + race + weight + height + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer + parkinson + rheumatoid + renal + depression + anyfx + death, data = baseline.w))
cox.w1 = coxph(Surv(time2end, death) ~ ageBase + TscoreBase.2, data = baseline.w)
summary(cox.w1)
## Call:
## coxph(formula = Surv(time2end, death) ~ ageBase + TscoreBase.2,
## data = baseline.w)
##
## n= 7363, number of events= 4265
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.11955 1.12699 0.00308 38.83 < 2e-16 ***
## TscoreBase.2 0.07487 1.07774 0.01788 4.19 2.8e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.13 0.887 1.12 1.13
## TscoreBase.2 1.08 0.928 1.04 1.12
##
## Concordance= 0.664 (se = 0.004 )
## Likelihood ratio test= 1545 on 2 df, p=<2e-16
## Wald test = 1718 on 2 df, p=<2e-16
## Score (logrank) test = 1810 on 2 df, p=<2e-16
cox.w2 = coxph(Surv(time2end, death) ~ ageBase + TscoreBase.2 + fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer, data = baseline.w)
summary(cox.w2)
## Call:
## coxph(formula = Surv(time2end, death) ~ ageBase + TscoreBase.2 +
## fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n +
## cancer, data = baseline.w)
##
## n= 7363, number of events= 4265
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.11275 1.11935 0.00316 35.72 < 2e-16 ***
## TscoreBase.2 0.09486 1.09951 0.01830 5.18 2.2e-07 ***
## fall.yesnoYes -0.02686 0.97349 0.03426 -0.78 0.4329
## fx50 0.09454 1.09916 0.03184 2.97 0.0030 **
## cvd.nYes 0.32071 1.37811 0.03433 9.34 < 2e-16 ***
## hypertension 0.31682 1.37275 0.03137 10.10 < 2e-16 ***
## copd 0.12413 1.13216 0.03965 3.13 0.0017 **
## diabetes.nYes 0.58169 1.78905 0.05539 10.50 < 2e-16 ***
## cancer 0.02435 1.02465 0.03837 0.63 0.5257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.119 0.893 1.11 1.13
## TscoreBase.2 1.100 0.909 1.06 1.14
## fall.yesnoYes 0.973 1.027 0.91 1.04
## fx50 1.099 0.910 1.03 1.17
## cvd.nYes 1.378 0.726 1.29 1.47
## hypertension 1.373 0.728 1.29 1.46
## copd 1.132 0.883 1.05 1.22
## diabetes.nYes 1.789 0.559 1.60 1.99
## cancer 1.025 0.976 0.95 1.10
##
## Concordance= 0.687 (se = 0.004 )
## Likelihood ratio test= 1877 on 9 df, p=<2e-16
## Wald test = 2065 on 9 df, p=<2e-16
## Score (logrank) test = 2168 on 9 df, p=<2e-16
cox.w3 = coxph(Surv(time2end, death) ~ ageBase + TscoreBase.2 + fall.yesno + fx50 + BMI + smoke + drink.n +
physical + cvd.n + hypertension + copd + diabetes.n + cancer + renal + parkinson +
depression, data = baseline.w)
summary(cox.w3)
## Call:
## coxph(formula = Surv(time2end, death) ~ ageBase + TscoreBase.2 +
## fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n +
## hypertension + copd + diabetes.n + cancer + renal + parkinson +
## depression, data = baseline.w)
##
## n= 7296, number of events= 4220
## (67 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.10628 1.11214 0.00327 32.51 < 2e-16 ***
## TscoreBase.2 0.06549 1.06768 0.01954 3.35 0.00080 ***
## fall.yesnoYes -0.00126 0.99874 0.03448 -0.04 0.97076
## fx50 0.08041 1.08373 0.03218 2.50 0.01247 *
## BMI -0.01361 0.98648 0.00396 -3.44 0.00059 ***
## smoke 0.30303 1.35395 0.03264 9.28 < 2e-16 ***
## drink.nYes -0.16704 0.84617 0.03238 -5.16 2.5e-07 ***
## physical -0.59912 0.54930 0.03288 -18.22 < 2e-16 ***
## cvd.nYes 0.28535 1.33022 0.03462 8.24 < 2e-16 ***
## hypertension 0.29332 1.34088 0.03173 9.24 < 2e-16 ***
## copd 0.02906 1.02948 0.04045 0.72 0.47259
## diabetes.nYes 0.47070 1.60112 0.05673 8.30 < 2e-16 ***
## cancer 0.06810 1.07047 0.03869 1.76 0.07842 .
## renal 0.36107 1.43486 0.13048 2.77 0.00565 **
## parkinson 0.20283 1.22487 0.18680 1.09 0.27755
## depression 0.08250 1.08600 0.05664 1.46 0.14519
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.112 0.899 1.105 1.119
## TscoreBase.2 1.068 0.937 1.028 1.109
## fall.yesnoYes 0.999 1.001 0.933 1.069
## fx50 1.084 0.923 1.017 1.154
## BMI 0.986 1.014 0.979 0.994
## smoke 1.354 0.739 1.270 1.443
## drink.nYes 0.846 1.182 0.794 0.902
## physical 0.549 1.821 0.515 0.586
## cvd.nYes 1.330 0.752 1.243 1.424
## hypertension 1.341 0.746 1.260 1.427
## copd 1.029 0.971 0.951 1.114
## diabetes.nYes 1.601 0.625 1.433 1.789
## cancer 1.070 0.934 0.992 1.155
## renal 1.435 0.697 1.111 1.853
## parkinson 1.225 0.816 0.849 1.766
## depression 1.086 0.921 0.972 1.213
##
## Concordance= 0.716 (se = 0.004 )
## Likelihood ratio test= 2329 on 16 df, p=<2e-16
## Wald test = 2502 on 16 df, p=<2e-16
## Score (logrank) test = 2653 on 16 df, p=<2e-16
qmatrix.n = crudeinits.msm(state ~ time2event, subject = ID, data = women, qmatrix = Q.m2)
qmatrix.n
## Well Fracture Death
## Well -0.069616 0.034280 0.035335
## Fracture 0.000000 -0.081983 0.081983
## Death 0.000000 0.000000 0.000000
statetable.msm(state, ID, data = women)
## to
## from 1 2 3
## 1 1888 2696 2779
## 2 0 1210 1486
age.w1= msm(state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ ageBase + TscoreBase.2)
age.w1
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~ageBase + TscoreBase.2, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline ageBase
## Well - Well -0.06128 (-0.06320,-0.05942)
## Well - Fracture 0.03321 ( 0.03189, 0.03458) 1.040 (1.032,1.048)
## Well - Death 0.02807 ( 0.02677, 0.02944) 1.105 (1.097,1.113)
## Fracture - Fracture -0.05900 (-0.06485,-0.05369)
## Fracture - Death 0.05900 ( 0.05369, 0.06485) 1.096 (1.085,1.107)
## TscoreBase.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.5795 (1.5067,1.656) 1.308 (1.209,1.416)
## Well - Death 0.9858 (0.9452,1.028) 3.093 (2.821,3.390)
## Fracture - Fracture
## Fracture - Death 1.0820 (1.0134,1.155) 1.899 (1.592,2.264)
##
## -2 * log-likelihood: 55919
hazard.msm(age.w1)
## $ageBase
## HR L U
## Well - Fracture 1.0402 1.0323 1.0483
## Well - Death 1.1051 1.0972 1.1131
## Fracture - Death 1.0961 1.0855 1.1069
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.57949 1.50667 1.6558
## Well - Death 0.98579 0.94516 1.0282
## Fracture - Death 1.08203 1.01342 1.1553
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3084 1.2091 1.4159
## Well - Death 3.0926 2.8209 3.3904
## Fracture - Death 1.8986 1.5920 2.2641
age.w2= msm(state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ age + Tscore.2)
age.w2
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~age + Tscore.2, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline age
## Well - Well -0.06683 (-0.06892,-0.06480)
## Well - Fracture 0.03494 ( 0.03353, 0.03642) 1.041 (1.033,1.049)
## Well - Death 0.03189 ( 0.03045, 0.03339) 1.106 (1.098,1.114)
## Fracture - Fracture -0.04280 (-0.04751,-0.03855)
## Fracture - Death 0.04280 ( 0.03855, 0.04751) 1.105 (1.096,1.114)
## Tscore.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.5757 (1.5030,1.652) 1.312 (1.212,1.420)
## Well - Death 0.9811 (0.9406,1.023) 3.132 (2.855,3.435)
## Fracture - Fracture
## Fracture - Death 1.1221 (1.0527,1.196) 1.196 (1.000,1.429)
##
## -2 * log-likelihood: 55414
hazard.msm(age.w2)
## $age
## HR L U
## Well - Fracture 1.0405 1.0325 1.0486
## Well - Death 1.1061 1.0981 1.1141
## Fracture - Death 1.1047 1.0956 1.1139
##
## $Tscore.2
## HR L U
## Well - Fracture 1.57570 1.50295 1.6520
## Well - Death 0.98111 0.94061 1.0234
## Fracture - Death 1.12210 1.05275 1.1960
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3118 1.2119 1.4199
## Well - Death 3.1317 2.8548 3.4354
## Fracture - Death 1.1955 1.0003 1.4288
multi.we1= msm(state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ ageBase + TscoreBase.2 +
fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer)
multi.we1
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~ageBase + TscoreBase.2 + fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline ageBase
## Well - Well -0.06070 (-0.06262,-0.05883)
## Well - Fracture 0.03306 ( 0.03174, 0.03444) 1.036 (1.028,1.044)
## Well - Death 0.02763 ( 0.02634, 0.02900) 1.097 (1.089,1.105)
## Fracture - Fracture -0.05819 (-0.06402,-0.05289)
## Fracture - Death 0.05819 ( 0.05289, 0.06402) 1.090 (1.079,1.101)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.540 (1.4678,1.616) 1.1510 (1.0596,1.250)
## Well - Death 1.009 (0.9661,1.053) 0.9697 (0.8912,1.055)
## Fracture - Fracture
## Fracture - Death 1.107 (1.0361,1.183) 0.9416 (0.8425,1.052)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.4806 (1.3703,1.600) 0.9945 (0.9079,1.089)
## Well - Death 1.0771 (0.9960,1.165) 1.3773 (1.2682,1.496)
## Fracture - Fracture
## Fracture - Death 0.9459 (0.8518,1.050) 1.2497 (1.1121,1.404)
## hypertension copd
## Well - Well
## Well - Fracture 1.072 (0.9896,1.160) 1.133 (1.0277,1.249)
## Well - Death 1.330 (1.2329,1.435) 1.132 (1.0265,1.248)
## Fracture - Fracture
## Fracture - Death 1.310 (1.1787,1.456) 1.096 (0.9638,1.247)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.473 (1.267,1.712) 1.0472 (0.9527,1.151)
## Well - Death 1.601 (1.399,1.832) 1.0076 (0.9175,1.107)
## Fracture - Fracture
## Fracture - Death 1.702 (1.417,2.044) 0.9854 (0.8685,1.118)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.343 (1.241,1.454)
## Well - Death 3.197 (2.916,3.506)
## Fracture - Fracture
## Fracture - Death 1.952 (1.636,2.328)
##
## -2 * log-likelihood: 55507
hazard.msm(multi.we1)
## $ageBase
## HR L U
## Well - Fracture 1.0362 1.0280 1.0444
## Well - Death 1.0973 1.0892 1.1055
## Fracture - Death 1.0900 1.0790 1.1012
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.5401 1.4678 1.6159
## Well - Death 1.0086 0.9661 1.0530
## Fracture - Death 1.1072 1.0361 1.1832
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.15105 1.05957 1.2504
## Well - Death 0.96975 0.89121 1.0552
## Fracture - Death 0.94160 0.84247 1.0524
##
## $fx50
## HR L U
## Well - Fracture 1.48061 1.37026 1.5998
## Well - Death 1.07711 0.99604 1.1648
## Fracture - Death 0.94592 0.85177 1.0505
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.99449 0.90795 1.0893
## Well - Death 1.37731 1.26818 1.4958
## Fracture - Death 1.24974 1.11207 1.4045
##
## $hypertension
## HR L U
## Well - Fracture 1.0715 0.98961 1.1602
## Well - Death 1.3301 1.23293 1.4350
## Fracture - Death 1.3101 1.17870 1.4562
##
## $copd
## HR L U
## Well - Fracture 1.1331 1.02772 1.2492
## Well - Death 1.1321 1.02654 1.2485
## Fracture - Death 1.0963 0.96376 1.2470
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4730 1.2674 1.7119
## Well - Death 1.6013 1.3993 1.8324
## Fracture - Death 1.7019 1.4173 2.0438
##
## $cancer
## HR L U
## Well - Fracture 1.04719 0.95266 1.1511
## Well - Death 1.00762 0.91750 1.1066
## Fracture - Death 0.98537 0.86852 1.1179
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3435 1.2412 1.4542
## Well - Death 3.1975 2.9159 3.5062
## Fracture - Death 1.9517 1.6360 2.3284
multi.we2= msm(state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ age + Tscore.2 +
fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer)
multi.we2
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~age + Tscore.2 + fall.yesno + fx50 + cvd.n + hypertension + copd + diabetes.n + cancer, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline age
## Well - Well -0.06570 (-0.06779,-0.06368)
## Well - Fracture 0.03461 ( 0.03319, 0.03609) 1.036 (1.028,1.045)
## Well - Death 0.03109 ( 0.02967, 0.03259) 1.098 (1.090,1.107)
## Fracture - Fracture -0.04158 (-0.04624,-0.03739)
## Fracture - Death 0.04158 ( 0.03739, 0.04624) 1.103 (1.093,1.112)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.537 (1.4643,1.612) 1.1442 (1.0529,1.243)
## Well - Death 1.004 (0.9616,1.048) 0.9707 (0.8919,1.057)
## Fracture - Fracture
## Fracture - Death 1.129 (1.0582,1.204) 0.9511 (0.8504,1.064)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.481 (1.3708,1.601) 0.9931 (0.9064,1.088)
## Well - Death 1.074 (0.9931,1.162) 1.3763 (1.2669,1.495)
## Fracture - Fracture
## Fracture - Death 1.038 (0.9350,1.153) 1.2836 (1.1430,1.442)
## hypertension copd
## Well - Well
## Well - Fracture 1.072 (0.9895,1.161) 1.131 (1.0260,1.248)
## Well - Death 1.320 (1.2230,1.424) 1.140 (1.0335,1.257)
## Fracture - Fracture
## Fracture - Death 1.331 (1.1986,1.479) 1.103 (0.9696,1.255)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.467 (1.262,1.706) 1.048 (0.9536,1.153)
## Well - Death 1.611 (1.407,1.843) 1.014 (0.9227,1.113)
## Fracture - Fracture
## Fracture - Death 1.773 (1.476,2.131) 1.052 (0.9266,1.194)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.347 (1.244,1.458)
## Well - Death 3.237 (2.950,3.552)
## Fracture - Fracture
## Fracture - Death 1.277 (1.067,1.527)
##
## -2 * log-likelihood: 54994
hazard.msm(multi.we2)
## $age
## HR L U
## Well - Fracture 1.0364 1.0283 1.0447
## Well - Death 1.0985 1.0903 1.1066
## Fracture - Death 1.1025 1.0933 1.1119
##
## $Tscore.2
## HR L U
## Well - Fracture 1.5366 1.46433 1.6124
## Well - Death 1.0040 0.96164 1.0483
## Fracture - Death 1.1290 1.05821 1.2044
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.14419 1.05295 1.2433
## Well - Death 0.97071 0.89188 1.0565
## Fracture - Death 0.95107 0.85039 1.0637
##
## $fx50
## HR L U
## Well - Fracture 1.4814 1.37080 1.6010
## Well - Death 1.0743 0.99313 1.1620
## Fracture - Death 1.0385 0.93496 1.1534
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.99311 0.90644 1.0881
## Well - Death 1.37632 1.26693 1.4952
## Fracture - Death 1.28364 1.14296 1.4416
##
## $hypertension
## HR L U
## Well - Fracture 1.0716 0.98952 1.1605
## Well - Death 1.3198 1.22301 1.4243
## Fracture - Death 1.3315 1.19859 1.4791
##
## $copd
## HR L U
## Well - Fracture 1.1314 1.02598 1.2476
## Well - Death 1.1399 1.03355 1.2572
## Fracture - Death 1.1030 0.96959 1.2547
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4672 1.2619 1.7060
## Well - Death 1.6106 1.4074 1.8431
## Fracture - Death 1.7731 1.4756 2.1307
##
## $cancer
## HR L U
## Well - Fracture 1.0484 0.95360 1.1526
## Well - Death 1.0135 0.92274 1.1132
## Fracture - Death 1.0519 0.92656 1.1943
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3467 1.2439 1.4580
## Well - Death 3.2372 2.9502 3.5520
## Fracture - Death 1.2766 1.0671 1.5272
multi.w1= msm(state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ ageBase + TscoreBase.2 +
fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer +
renal + parkinson + depression)
multi.w1
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~ageBase + TscoreBase.2 + fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer + renal + parkinson + depression, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline ageBase
## Well - Well -0.05973 (-0.06165,-0.05787)
## Well - Fracture 0.03295 ( 0.03163, 0.03433) 1.032 (1.024,1.041)
## Well - Death 0.02678 ( 0.02549, 0.02813) 1.088 (1.080,1.096)
## Fracture - Fracture -0.05636 (-0.06212,-0.05113)
## Fracture - Death 0.05636 ( 0.05113, 0.06212) 1.087 (1.076,1.099)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.5290 (1.4519,1.610) 1.146 (1.0537,1.245)
## Well - Death 0.9881 (0.9437,1.035) 0.999 (0.9177,1.087)
## Fracture - Fracture
## Fracture - Death 1.0547 (0.9815,1.133) 0.953 (0.8517,1.066)
## fx50 BMI
## Well - Well
## Well - Fracture 1.4770 (1.3658,1.597) 0.9957 (0.9861,1.0055)
## Well - Death 1.0615 (0.9809,1.149) 0.9876 (0.9784,0.9969)
## Fracture - Fracture
## Fracture - Death 0.9282 (0.8344,1.032) 0.9898 (0.9765,1.0034)
## smoke drink.nYes
## Well - Well
## Well - Fracture 0.9911 (0.9136,1.075) 0.9731 (0.8984,1.0540)
## Well - Death 1.3373 (1.2361,1.447) 0.8724 (0.8067,0.9434)
## Fracture - Fracture
## Fracture - Death 1.2351 (1.1056,1.380) 0.8260 (0.7404,0.9216)
## physical cvd.nYes
## Well - Well
## Well - Fracture 0.8309 (0.7654,0.9019) 0.9826 (0.8964,1.077)
## Well - Death 0.5633 (0.5203,0.6098) 1.3234 (1.2178,1.438)
## Fracture - Fracture
## Fracture - Death 0.6508 (0.5834,0.7260) 1.2125 (1.0773,1.365)
## hypertension copd
## Well - Well
## Well - Fracture 1.057 (0.975,1.146) 1.108 (1.0030,1.224)
## Well - Death 1.316 (1.219,1.421) 1.043 (0.9438,1.152)
## Fracture - Fracture
## Fracture - Death 1.251 (1.124,1.392) 1.028 (0.9015,1.173)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.430 (1.227,1.667) 1.063 (0.9666,1.170)
## Well - Death 1.427 (1.243,1.639) 1.057 (0.9621,1.162)
## Fracture - Fracture
## Fracture - Death 1.538 (1.274,1.856) 1.008 (0.8871,1.145)
## renal parkinson
## Well - Well
## Well - Fracture 1.048 (0.7304,1.504) 2.0886 (1.3579,3.213)
## Well - Death 1.222 (0.8820,1.693) 1.2961 (0.7630,2.202)
## Fracture - Fracture
## Fracture - Death 1.556 (1.0275,2.357) 0.9516 (0.5705,1.587)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.115 (0.9707,1.280) 1.371 (1.266,1.485)
## Well - Death 1.030 (0.8949,1.185) 3.368 (3.069,3.696)
## Fracture - Fracture
## Fracture - Death 1.026 (0.8553,1.231) 2.109 (1.762,2.523)
##
## -2 * log-likelihood: 54539
hazard.msm(multi.w1)
## $ageBase
## HR L U
## Well - Fracture 1.0322 1.0238 1.0406
## Well - Death 1.0880 1.0796 1.0964
## Fracture - Death 1.0874 1.0761 1.0988
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.52904 1.45190 1.6103
## Well - Death 0.98813 0.94366 1.0347
## Fracture - Death 1.05467 0.98146 1.1333
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.14555 1.05372 1.2454
## Well - Death 0.99897 0.91770 1.0874
## Fracture - Death 0.95299 0.85169 1.0663
##
## $fx50
## HR L U
## Well - Fracture 1.47704 1.36578 1.5974
## Well - Death 1.06153 0.98089 1.1488
## Fracture - Death 0.92818 0.83445 1.0324
##
## $BMI
## HR L U
## Well - Fracture 0.99574 0.98608 1.00548
## Well - Death 0.98761 0.97838 0.99692
## Fracture - Death 0.98985 0.97645 1.00342
##
## $smoke
## HR L U
## Well - Fracture 0.99114 0.91364 1.0752
## Well - Death 1.33728 1.23610 1.4467
## Fracture - Death 1.23508 1.10562 1.3797
##
## $drink.nYes
## HR L U
## Well - Fracture 0.97312 0.89841 1.05404
## Well - Death 0.87238 0.80669 0.94342
## Fracture - Death 0.82604 0.74037 0.92163
##
## $physical
## HR L U
## Well - Fracture 0.83087 0.76541 0.90193
## Well - Death 0.56327 0.52031 0.60977
## Fracture - Death 0.65081 0.58341 0.72600
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.98259 0.89639 1.0771
## Well - Death 1.32340 1.21780 1.4382
## Fracture - Death 1.21250 1.07733 1.3646
##
## $hypertension
## HR L U
## Well - Fracture 1.0568 0.97503 1.1455
## Well - Death 1.3159 1.21869 1.4210
## Fracture - Death 1.2508 1.12379 1.3923
##
## $copd
## HR L U
## Well - Fracture 1.1081 1.00300 1.2242
## Well - Death 1.0427 0.94384 1.1519
## Fracture - Death 1.0283 0.90147 1.1730
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4301 1.2267 1.6671
## Well - Death 1.4271 1.2429 1.6386
## Fracture - Death 1.5378 1.2739 1.8565
##
## $cancer
## HR L U
## Well - Fracture 1.0635 0.96663 1.1700
## Well - Death 1.0574 0.96213 1.1621
## Fracture - Death 1.0078 0.88709 1.1450
##
## $renal
## HR L U
## Well - Fracture 1.0480 0.73036 1.5037
## Well - Death 1.2220 0.88195 1.6931
## Fracture - Death 1.5562 1.02753 2.3569
##
## $parkinson
## HR L U
## Well - Fracture 2.08862 1.35787 3.2126
## Well - Death 1.29614 0.76302 2.2018
## Fracture - Death 0.95156 0.57052 1.5871
##
## $depression
## HR L U
## Well - Fracture 1.1149 0.97070 1.2805
## Well - Death 1.0299 0.89494 1.1853
## Fracture - Death 1.0260 0.85532 1.2308
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3710 1.2656 1.4852
## Well - Death 3.3683 3.0693 3.6963
## Fracture - Death 2.1086 1.7624 2.5227
multi.w2= msm(state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, exacttimes = TRUE,
method = "BFGS", control = list(fnscale = 4000, maxit = 10000), pci = 5, covariates =~ age + Tscore.2 + fall.yesno
+ fx50 + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer + renal + parkinson
+ depression)
multi.w2
##
## Call:
## msm(formula = state ~ time2event, subject = ID, data = women, qmatrix = qmatrix.n, gen.inits = TRUE, covariates = ~age + Tscore.2 + fall.yesno + fx50 + BMI + smoke + drink.n + physical + cvd.n + hypertension + copd + diabetes.n + cancer + renal + parkinson + depression, exacttimes = TRUE, pci = 5, method = "BFGS", control = list(fnscale = 4000, maxit = 10000))
##
## Maximum likelihood estimates
## Baselines are with covariates set to their means
##
## Transition intensities with hazard ratios for each covariate
## Baseline age
## Well - Well -0.06416 (-0.06624,-0.06215)
## Well - Fracture 0.03431 ( 0.03289, 0.03579) 1.032 (1.024,1.041)
## Well - Death 0.02986 ( 0.02845, 0.03134) 1.089 (1.081,1.098)
## Fracture - Fracture -0.03959 (-0.04414,-0.03551)
## Fracture - Death 0.03959 ( 0.03551, 0.04414) 1.104 (1.094,1.113)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.5240 (1.4470,1.605) 1.1391 (1.0475,1.239)
## Well - Death 0.9864 (0.9419,1.033) 0.9992 (0.9177,1.088)
## Fracture - Fracture
## Fracture - Death 1.0633 (0.9911,1.141) 0.9593 (0.8566,1.074)
## fx50 BMI
## Well - Well
## Well - Fracture 1.478 (1.3669,1.599) 0.9954 (0.9857,1.0051)
## Well - Death 1.058 (0.9773,1.145) 0.9883 (0.9791,0.9976)
## Fracture - Fracture
## Fracture - Death 1.021 (0.9178,1.136) 0.9862 (0.9728,0.9997)
## smoke drink.nYes
## Well - Well
## Well - Fracture 0.995 (0.9171,1.080) 0.9724 (0.8976,1.0534)
## Well - Death 1.347 (1.2447,1.457) 0.8737 (0.8077,0.9451)
## Fracture - Fracture
## Fracture - Death 1.289 (1.1538,1.441) 0.8055 (0.7216,0.8992)
## physical cvd.nYes
## Well - Well
## Well - Fracture 0.8320 (0.7663,0.9033) 0.9813 (0.895,1.076)
## Well - Death 0.5685 (0.5251,0.6156) 1.3217 (1.216,1.437)
## Fracture - Fracture
## Fracture - Death 0.6352 (0.5697,0.7081) 1.2404 (1.103,1.395)
## hypertension copd
## Well - Well
## Well - Fracture 1.058 (0.9757,1.147) 1.106 (1.0008,1.222)
## Well - Death 1.307 (1.2105,1.412) 1.048 (0.9485,1.158)
## Fracture - Fracture
## Fracture - Death 1.268 (1.1396,1.411) 1.031 (0.9036,1.176)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.426 (1.223,1.663) 1.065 (0.9675,1.171)
## Well - Death 1.435 (1.250,1.648) 1.062 (0.9664,1.168)
## Fracture - Fracture
## Fracture - Death 1.572 (1.300,1.900) 1.079 (0.9494,1.227)
## renal parkinson
## Well - Well
## Well - Fracture 1.051 (0.7323,1.508) 2.095 (1.3621,3.222)
## Well - Death 1.229 (0.8874,1.703) 1.306 (0.7696,2.216)
## Fracture - Fracture
## Fracture - Death 1.763 (1.1628,2.673) 1.098 (0.6580,1.833)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.112 (0.9682,1.278) 1.374 (1.268,1.489)
## Well - Death 1.035 (0.8989,1.191) 3.395 (3.092,3.728)
## Fracture - Fracture
## Fracture - Death 1.072 (0.8925,1.287) 1.400 (1.167,1.681)
##
## -2 * log-likelihood: 54034
hazard.msm(multi.w2)
## $age
## HR L U
## Well - Fracture 1.0324 1.0240 1.0409
## Well - Death 1.0892 1.0808 1.0977
## Fracture - Death 1.1037 1.0942 1.1132
##
## $Tscore.2
## HR L U
## Well - Fracture 1.52397 1.4470 1.6051
## Well - Death 0.98638 0.9419 1.0330
## Fracture - Death 1.06326 0.9911 1.1407
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.13912 1.04751 1.2388
## Well - Death 0.99918 0.91768 1.0879
## Fracture - Death 0.95927 0.85661 1.0742
##
## $fx50
## HR L U
## Well - Fracture 1.4785 1.36687 1.5992
## Well - Death 1.0579 0.97728 1.1451
## Fracture - Death 1.0212 0.91781 1.1362
##
## $BMI
## HR L U
## Well - Fracture 0.99538 0.98571 1.00514
## Well - Death 0.98831 0.97906 0.99764
## Fracture - Death 0.98618 0.97283 0.99972
##
## $smoke
## HR L U
## Well - Fracture 0.99497 0.91707 1.0795
## Well - Death 1.34685 1.24472 1.4574
## Fracture - Death 1.28944 1.15382 1.4410
##
## $drink.nYes
## HR L U
## Well - Fracture 0.97239 0.89758 1.05343
## Well - Death 0.87372 0.80775 0.94507
## Fracture - Death 0.80553 0.72161 0.89922
##
## $physical
## HR L U
## Well - Fracture 0.83195 0.76625 0.90329
## Well - Death 0.56852 0.52505 0.61558
## Fracture - Death 0.63516 0.56972 0.70811
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.98135 0.89501 1.0760
## Well - Death 1.32169 1.21591 1.4367
## Fracture - Death 1.24037 1.10258 1.3954
##
## $hypertension
## HR L U
## Well - Fracture 1.0578 0.97571 1.1468
## Well - Death 1.3074 1.21046 1.4120
## Fracture - Death 1.2680 1.13959 1.4108
##
## $copd
## HR L U
## Well - Fracture 1.1059 1.00079 1.2221
## Well - Death 1.0479 0.94847 1.1577
## Fracture - Death 1.0307 0.90359 1.1758
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4258 1.2225 1.6628
## Well - Death 1.4349 1.2496 1.6477
## Fracture - Death 1.5717 1.3003 1.8996
##
## $cancer
## HR L U
## Well - Fracture 1.0646 0.96748 1.1715
## Well - Death 1.0622 0.96639 1.1675
## Fracture - Death 1.0795 0.94940 1.2273
##
## $renal
## HR L U
## Well - Fracture 1.0509 0.73233 1.5080
## Well - Death 1.2291 0.88735 1.7026
## Fracture - Death 1.7631 1.16279 2.6732
##
## $parkinson
## HR L U
## Well - Fracture 2.0950 1.36205 3.2224
## Well - Death 1.3059 0.76958 2.2158
## Fracture - Death 1.0982 0.65795 1.8330
##
## $depression
## HR L U
## Well - Fracture 1.1124 0.96821 1.2780
## Well - Death 1.0345 0.89889 1.1906
## Fracture - Death 1.0717 0.89250 1.2868
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3742 1.2683 1.4890
## Well - Death 3.3952 3.0923 3.7278
## Fracture - Death 1.4004 1.1666 1.6810
# Osteopenia:
options(digits = 5)
pmatrix.msm(multi.w2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)
## Well Fracture Death
## Well 0.98867 0.004378 0.006953
## Fracture 0.00000 0.989975 0.010025
## Death 0.00000 0.000000 1.000000
pmatrix.msm(multi.w2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)
## Well Fracture Death
## Well 0.91057 0.023747 0.065680
## Fracture 0.00000 0.943229 0.056771
## Death 0.00000 0.000000 1.000000
pmatrix.msm(multi.w2, t = 10, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)
## Well Fracture Death
## Well 0.78473 0.046948 0.16832
## Fracture 0.00000 0.878979 0.12102
## Death 0.00000 0.000000 1.00000
# Osteoporosis:
pmatrix.msm(multi.w2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)
## Well Fracture Death
## Well 0.99008 0.0028756 0.0070452
## Fracture 0.00000 0.9905687 0.0094313
## Death 0.00000 0.0000000 1.0000000
pmatrix.msm(multi.w2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)
## Well Fracture Death
## Well 0.91771 0.015672 0.066621
## Fracture 0.00000 0.946515 0.053485
## Death 0.00000 0.000000 1.000000
pmatrix.msm(multi.w2, t = 10, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)
## Well Fracture Death
## Well 0.79788 0.031186 0.17093
## Fracture 0.00000 0.885750 0.11425
## Death 0.00000 0.000000 1.00000
# Osteoporosis + comorbidities:
pmatrix.msm(multi.w2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5, cvd = 1, diabetes = 1, cancer = 1), 2)
## Warning in factorcov2numeric.msm(covariates, x, mod): Covariates "cvd,
## diabetes" unknown, ignoring
## Warning in msm.fill.pci.covs(x, covariates): Covariate cvd unknown
## Warning in msm.fill.pci.covs(x, covariates): Covariate diabetes unknown
## Well Fracture Death
## Well 0.98946 0.0030593 0.0074823
## Fracture 0.00000 0.9898231 0.0101769
## Death 0.00000 0.0000000 1.0000000
pmatrix.msm(multi.w2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5, cvd = 1, diabetes = 1, cancer = 1), 2)
## Warning in factorcov2numeric.msm(covariates, x, mod): Covariates "cvd,
## diabetes" unknown, ignoring
## Warning in msm.fill.pci.covs(x, covariates): Covariate cvd unknown
## Warning in msm.fill.pci.covs(x, covariates): Covariate diabetes unknown
## Well Fracture Death
## Well 0.91278 0.016611 0.070608
## Fracture 0.00000 0.942390 0.057610
## Death 0.00000 0.000000 1.000000
pmatrix.msm(multi.w2, t = 10, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5, cvd = 1, diabetes = 1, cancer = 1), 2)
## Warning in factorcov2numeric.msm(covariates, x, mod): Covariates "cvd,
## diabetes" unknown, ignoring
## Warning in msm.fill.pci.covs(x, covariates): Covariate cvd unknown
## Warning in msm.fill.pci.covs(x, covariates): Covariate diabetes unknown
## Well Fracture Death
## Well 0.78669 0.032833 0.18048
## Fracture 0.00000 0.877253 0.12275
## Death 0.00000 0.000000 1.00000
prevalence.msm(multi.w2, times = seq(0,20,1), covariates = "mean", ci = "normal")
## $Observed
## State 1 State 2 State 3 Total
## 0 7269 0 0 7269
## 1 6946 246 74 7266
## 2 6619 428 205 7252
## 3 6345 558 342 7245
## 4 5966 728 529 7223
## 5 5613 866 713 7192
## 6 5242 982 934 7158
## 7 4911 1078 1134 7123
## 8 4573 1154 1359 7086
## 9 4214 1214 1591 7019
## 10 3865 1203 1862 6930
## 11 3499 1226 2108 6833
## 12 3136 1201 2420 6757
## 13 2823 1175 2661 6659
## 14 2468 1122 2953 6543
## 15 2171 1085 3203 6459
## 16 1901 1029 3456 6386
## 17 1603 916 3658 6177
## 18 1163 737 3837 5737
## 19 909 625 4031 5565
## 20 381 299 4153 4833
##
## $Expected
## $Expected$estimates
## Well Fracture Death Total
## 0 7269.00 0.00 0.00 7269
## 1 6942.06 204.70 119.24 7266
## 2 6619.78 392.78 239.44 7252
## 3 6318.54 565.79 360.67 7245
## 4 6018.51 722.95 481.54 7223
## 5 5725.51 864.96 601.54 7192
## 6 5178.83 1035.16 944.01 7158
## 7 4683.58 1176.19 1263.23 7123
## 8 4234.40 1291.21 1560.38 7086
## 9 3811.90 1377.71 1829.39 7019
## 10 3420.39 1439.06 2070.55 6930
## 11 3064.99 1480.38 2287.63 6833
## 12 2754.53 1510.49 2491.98 6757
## 13 2467.05 1522.17 2669.78 6659
## 14 2203.03 1518.02 2821.95 6543
## 15 1976.45 1511.41 2971.14 6459
## 16 1775.92 1499.13 3110.95 6386
## 17 1561.16 1448.03 3167.81 6177
## 18 1317.74 1337.62 3081.64 5737
## 19 1161.68 1285.98 3117.34 5565
## 20 916.88 1103.47 2812.64 4833
##
## $Expected$ci
## , , 2.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 7269.00 0.00 0.00 7269
## [2,] 6926.03 193.21 110.06 7266
## [3,] 6589.25 370.66 221.74 7252
## [4,] 6274.89 534.41 334.19 7245
## [5,] 5963.13 682.97 446.66 7223
## [6,] 5659.73 817.27 558.89 7192
## [7,] 5118.32 991.34 901.15 7158
## [8,] 4619.61 1129.12 1218.06 7123
## [9,] 4167.95 1241.66 1511.05 7086
## [10,] 3742.30 1324.17 1775.79 7019
## [11,] 3348.61 1381.66 2011.97 6930
## [12,] 2991.05 1419.01 2224.89 6833
## [13,] 2681.03 1446.22 2423.67 6757
## [14,] 2394.05 1455.94 2597.48 6659
## [15,] 2132.16 1450.19 2746.16 6543
## [16,] 1906.44 1442.54 2891.75 6459
## [17,] 1707.54 1428.61 3028.79 6386
## [18,] 1496.73 1376.51 3087.06 6177
## [19,] 1259.25 1270.36 3005.11 5737
## [20,] 1106.71 1218.98 3040.02 5565
## [21,] 870.76 1043.21 2744.01 4833
##
## , , 97.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 7269.00 0.00 0.00 7269
## [2,] 6957.27 217.69 128.75 7266
## [3,] 6648.82 418.45 258.53 7252
## [4,] 6360.17 602.26 388.80 7245
## [5,] 6071.44 768.12 518.78 7223
## [6,] 5788.52 918.39 648.43 7192
## [7,] 5237.47 1086.11 991.50 7158
## [8,] 4745.74 1227.08 1313.45 7123
## [9,] 4299.07 1344.40 1614.12 7086
## [10,] 3876.10 1431.82 1888.27 7019
## [11,] 3487.53 1496.56 2135.14 6930
## [12,] 3132.39 1540.58 2356.79 6833
## [13,] 2825.16 1573.11 2565.09 6757
## [14,] 2537.75 1587.71 2746.06 6659
## [15,] 2272.85 1585.98 2900.24 6543
## [16,] 2045.07 1582.16 3050.91 6459
## [17,] 1843.15 1571.50 3192.64 6386
## [18,] 1624.92 1520.97 3248.50 6177
## [19,] 1375.61 1407.81 3158.33 5737
## [20,] 1216.66 1355.73 3192.70 5565
## [21,] 963.61 1165.26 2878.85 4833
##
##
##
## $`Observed percentages`
## State 1 State 2 State 3
## 0 100.0000 0.0000 0.0000
## 1 95.5959 3.3856 1.0184
## 2 91.2714 5.9018 2.8268
## 3 87.5776 7.7019 4.7205
## 4 82.5973 10.0789 7.3238
## 5 78.0451 12.0412 9.9138
## 6 73.2327 13.7189 13.0483
## 7 68.9457 15.1341 15.9203
## 8 64.5357 16.2856 19.1787
## 9 60.0370 17.2959 22.6670
## 10 55.7720 17.3593 26.8687
## 11 51.2074 17.9423 30.8503
## 12 46.4111 17.7742 35.8147
## 13 42.3938 17.6453 39.9610
## 14 37.7197 17.1481 45.1322
## 15 33.6120 16.7983 49.5897
## 16 29.7682 16.1134 54.1184
## 17 25.9511 14.8292 59.2197
## 18 20.2719 12.8464 66.8816
## 19 16.3342 11.2309 72.4349
## 20 7.8833 6.1866 85.9301
##
## $`Expected percentages`
## $`Expected percentages`$estimates
## Well Fracture Death
## 0 100.000 0.0000 0.0000
## 1 95.542 2.8173 1.6410
## 2 91.282 5.4161 3.3018
## 3 87.212 7.8093 4.9782
## 4 83.324 10.0090 6.6668
## 5 79.609 12.0266 8.3640
## 6 72.350 14.4616 13.1882
## 7 65.753 16.5126 17.7345
## 8 59.757 18.2220 22.0206
## 9 54.308 19.6283 26.0634
## 10 49.356 20.7656 29.8781
## 11 44.856 21.6651 33.4792
## 12 40.766 22.3545 36.8800
## 13 37.048 22.8589 40.0928
## 14 33.670 23.2007 43.1292
## 15 30.600 23.4001 46.0000
## 16 27.810 23.4752 48.7151
## 17 25.274 23.4422 51.2840
## 18 22.969 23.3156 53.7152
## 19 20.875 23.1084 56.0169
## 20 18.971 22.8320 58.1966
##
## $`Expected percentages`$ci
## , , 2.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.0000 0.0000
## [2,] 95.321 2.6592 1.5147
## [3,] 90.861 5.1111 3.0576
## [4,] 86.610 7.3762 4.6126
## [5,] 82.558 9.4555 6.1838
## [6,] 78.695 11.3636 7.7710
## [7,] 71.505 13.8494 12.5894
## [8,] 64.855 15.8517 17.1004
## [9,] 58.820 17.5227 21.3244
## [10,] 53.317 18.8655 25.2997
## [11,] 48.320 19.9374 29.0328
## [12,] 43.774 20.7671 32.5610
## [13,] 39.678 21.4033 35.8690
## [14,] 35.952 21.8643 39.0071
## [15,] 32.587 22.1640 41.9709
## [16,] 29.516 22.3338 44.7709
## [17,] 26.739 22.3710 47.4286
## [18,] 24.231 22.2844 49.9767
## [19,] 21.950 22.1433 52.3812
## [20,] 19.887 21.9044 54.6275
## [21,] 18.017 21.5850 56.7764
##
## , , 97.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.0000 0.0000
## [2,] 95.751 2.9960 1.7720
## [3,] 91.683 5.7702 3.5650
## [4,] 87.787 8.3128 5.3664
## [5,] 84.057 10.6343 7.1823
## [6,] 80.486 12.7696 9.0160
## [7,] 73.170 15.1734 13.8516
## [8,] 66.626 17.2271 18.4396
## [9,] 60.670 18.9726 22.7790
## [10,] 55.223 20.3993 26.9023
## [11,] 50.325 21.5953 30.8100
## [12,] 45.842 22.5461 34.4913
## [13,] 41.811 23.2812 37.9620
## [14,] 38.110 23.8431 41.2383
## [15,] 34.737 24.2394 44.3259
## [16,] 31.662 24.4954 47.2349
## [17,] 28.862 24.6085 49.9944
## [18,] 26.306 24.6231 52.5903
## [19,] 23.978 24.5392 55.0520
## [20,] 21.863 24.3617 57.3711
## [21,] 19.938 24.1105 59.5666
plot.prevalence.msm(multi.w2, mintime = 0, maxtime = 20, legend.pos = c(10, 80), col.obs = "gray",
col.exp = "black")
par(mfrow= c(1,2))
plot.survfit.msm(multi.w2, from = 1, main = "No fracture", range = c(0,20),
ci = "normal", col = "black", col.ci = "black", lty = 2, lwd = 2,
col.surv ="grey", lty.surv = 2, lwd.surv = 1, xlab = "Time (years)")
legend(0.4,0.35, legend = c("Expected", "Expected (95% CI)", "Observed", "Observed (95% CI)"),
col = c("black", "black", "grey", "gray"), lty = c(2, 2, 1, 2), lwd = c(2, 1, 2, 1))
plot.survfit.msm(multi.w2, from = 2, main = "Initial fracture", range = c(0,20),
ci = "normal", col = "black", col.ci = "black", lty = 2, lwd = 2,
col.surv ="grey", lty.surv = 2, lwd.surv = 1, xlab = "Time (years)")