Association between BMD and mortality risk: A multistate approach
Nick Tran
2024-03-24
Association between BMD and mortality risk: A multistate approach
Analysis plan
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.
Data management
bmd.0 = read.csv("C:\\Thach\\Research projects\\BMD and mortality\\Data\\SOF_MrOS_Dubbo_CaMos_Nick_28mar24.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"), data == "MrOS" | data == "SOF")
dim(bmd)## [1] 30553 33head(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 -2.1077 Well 1 0.0000 69 0.656
## 2 0 0.6349 0 0 -2.2700 Well 1 17.2238 69 0.656
## 3 2 0.5850 0 1 -2.6538 Well 1 0.0000 84 0.585
## 4 2 0.5850 0 1 -2.6538 Death 3 6.5325 84 0.585
## 5 0 0.6540 0 0 -2.1231 Well 1 0.0000 75 0.654
## 6 0 0.5537 0 0 -2.8946 Well 1 18.6366 75 0.654
## TscoreBase time2end
## 1 -2.1077 17.2238
## 2 -2.1077 5.0103
## 3 -2.6538 6.5325
## 4 -2.6538 6.5325
## 5 -2.1231 18.6366
## 6 -2.1231 6.4586library(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 errorsbmd = 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"))1. MEN
1.1 Description of study sample
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=1723) |
Fractured, Alive (N=361) |
Fractured, Dead (N=655) |
No Fractured, Dead (N=2642) |
Overall (N=5381) |
|
|---|---|---|---|---|---|
| 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 (0.123) | 0.754 (0.115) | 0.727 (0.121) | 0.783 (0.123) | 0.780 (0.124) |
| Median [Min, Max] | 0.794 [0.404, 1.38] | 0.744 [0.499, 1.27] | 0.719 [0.273, 1.15] | 0.773 [0.475, 1.35] | 0.772 [0.273, 1.38] |
| TscoreBase | |||||
| Mean (SD) | -1.51 (0.856) | -1.85 (0.802) | -2.04 (0.840) | -1.65 (0.853) | -1.66 (0.865) |
| Median [Min, Max] | -1.57 [-4.28, 2.51] | -1.92 [-3.62, 1.75] | -2.09 [-5.19, 0.892] | -1.72 [-3.78, 2.28] | -1.72 [-5.19, 2.51] |
| as.factor(fall.no) | |||||
| 0 | 1344 (78.0%) | 248 (68.7%) | 389 (59.4%) | 1966 (74.4%) | 3947 (73.4%) |
| 1 | 379 (22.0%) | 113 (31.3%) | 266 (40.6%) | 676 (25.6%) | 1434 (26.6%) |
| fall.yesno | |||||
| No | 1344 (78.0%) | 248 (68.7%) | 389 (59.4%) | 1966 (74.4%) | 3947 (73.4%) |
| Yes | 379 (22.0%) | 113 (31.3%) | 266 (40.6%) | 676 (25.6%) | 1434 (26.6%) |
| as.factor(fx50) | |||||
| 0 | 1476 (85.7%) | 280 (77.6%) | 492 (75.1%) | 2187 (82.8%) | 4435 (82.4%) |
| 1 | 247 (14.3%) | 81 (22.4%) | 163 (24.9%) | 455 (17.2%) | 946 (17.6%) |
| race | |||||
| 1:WHITE | 1723 (100%) | 361 (100%) | 655 (100%) | 2642 (100%) | 5381 (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 (6.67) | 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 | 709 (41.1%) | 143 (39.6%) | 245 (37.4%) | 919 (34.8%) | 2016 (37.5%) |
| 1 | 1014 (58.9%) | 218 (60.4%) | 410 (62.6%) | 1723 (65.2%) | 3365 (62.5%) |
| as.factor(drink.n) | |||||
| No | 547 (31.7%) | 111 (30.7%) | 238 (36.3%) | 945 (35.8%) | 1841 (34.2%) |
| Yes | 1176 (68.3%) | 250 (69.3%) | 417 (63.7%) | 1697 (64.2%) | 3540 (65.8%) |
| as.factor(physical) | |||||
| 0 | 458 (26.6%) | 96 (26.6%) | 255 (38.9%) | 976 (36.9%) | 1785 (33.2%) |
| 1 | 1265 (73.4%) | 265 (73.4%) | 400 (61.1%) | 1666 (63.1%) | 3596 (66.8%) |
| as.factor(cvd.n) | |||||
| No | 1508 (87.5%) | 304 (84.2%) | 497 (75.9%) | 1946 (73.7%) | 4255 (79.1%) |
| Yes | 215 (12.5%) | 57 (15.8%) | 158 (24.1%) | 696 (26.3%) | 1126 (20.9%) |
| as.factor(hypertension) | |||||
| 0 | 1114 (64.7%) | 231 (64.0%) | 344 (52.5%) | 1436 (54.4%) | 3125 (58.1%) |
| 1 | 609 (35.3%) | 130 (36.0%) | 311 (47.5%) | 1206 (45.6%) | 2256 (41.9%) |
| as.factor(copd) | |||||
| 0 | 1584 (91.9%) | 334 (92.5%) | 562 (85.8%) | 2322 (87.9%) | 4802 (89.2%) |
| 1 | 139 (8.1%) | 27 (7.5%) | 93 (14.2%) | 320 (12.1%) | 579 (10.8%) |
| as.factor(diabetes.n) | |||||
| No | 1612 (93.6%) | 338 (93.6%) | 582 (88.9%) | 2314 (87.6%) | 4846 (90.1%) |
| Yes | 111 (6.4%) | 23 (6.4%) | 73 (11.1%) | 328 (12.4%) | 535 (9.9%) |
| as.factor(cancer) | |||||
| 0 | 1482 (86.0%) | 305 (84.5%) | 529 (80.8%) | 2077 (78.6%) | 4393 (81.6%) |
| 1 | 241 (14.0%) | 56 (15.5%) | 126 (19.2%) | 565 (21.4%) | 988 (18.4%) |
| as.factor(parkinson) | |||||
| 0 | 1506 (87.4%) | 311 (86.1%) | 579 (88.4%) | 2255 (85.4%) | 4651 (86.4%) |
| 1 | 217 (12.6%) | 50 (13.9%) | 76 (11.6%) | 387 (14.6%) | 730 (13.6%) |
| as.factor(rheumatoid) | |||||
| 0 | 983 (57.1%) | 201 (55.7%) | 335 (51.1%) | 1314 (49.7%) | 2833 (52.6%) |
| 1 | 740 (42.9%) | 160 (44.3%) | 320 (48.9%) | 1328 (50.3%) | 2548 (47.4%) |
| as.factor(renal) | |||||
| 0 | 1513 (87.8%) | 307 (85.0%) | 599 (91.5%) | 2447 (92.6%) | 4866 (90.4%) |
| 1 | 210 (12.2%) | 54 (15.0%) | 56 (8.5%) | 195 (7.4%) | 515 (9.6%) |
| as.factor(depression) | |||||
| 0 | 1659 (96.3%) | 345 (95.6%) | 622 (95.0%) | 2552 (96.6%) | 5178 (96.2%) |
| 1 | 64 (3.7%) | 16 (4.4%) | 33 (5.0%) | 90 (3.4%) | 203 (3.8%) |
| as.factor(anyfx) | |||||
| 0 | 1723 (100%) | 0 (0%) | 0 (0%) | 2642 (100%) | 4365 (81.1%) |
| 1 | 0 (0%) | 361 (100%) | 655 (100%) | 0 (0%) | 1016 (18.9%) |
| as.factor(death) | |||||
| 0 | 1723 (100%) | 361 (100%) | 0 (0%) | 0 (0%) | 2084 (38.7%) |
| 1 | 0 (0%) | 0 (0%) | 655 (100%) | 2642 (100%) | 3297 (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))1.2 Conventional Cox’s PH model
1.2.1 Age-adjusted model
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= 5381, number of events= 3297
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.119424 1.126848 0.003121 38.261 <2e-16 ***
## TscoreBase.2 0.047200 1.048331 0.020694 2.281 0.0226 *
## ---
## 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 1.048 0.9539 1.007 1.092
##
## Concordance= 0.684 (se = 0.005 )
## Likelihood ratio test= 1467 on 2 df, p=<2e-16
## Wald test = 1546 on 2 df, p=<2e-16
## Score (logrank) test = 1626 on 2 df, p=<2e-161.2.3 Adjusted for essential covariates (~ JBMR paper)
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= 5381, number of events= 3297
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.116141 1.123154 0.003213 36.146 < 2e-16 ***
## TscoreBase.2 0.060915 1.062808 0.020854 2.921 0.003489 **
## fall.yesnoYes -0.052394 0.948955 0.039084 -1.341 0.180071
## fx50 0.061556 1.063490 0.045092 1.365 0.172216
## cvd.nYes 0.411120 1.508506 0.040618 10.122 < 2e-16 ***
## copd 0.344799 1.411706 0.052878 6.521 7e-11 ***
## diabetes.nYes 0.482317 1.619823 0.054167 8.904 < 2e-16 ***
## cancer 0.154026 1.166522 0.043308 3.557 0.000376 ***
## ---
## 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 1.063 0.9409 1.0202 1.107
## fall.yesnoYes 0.949 1.0538 0.8790 1.025
## fx50 1.063 0.9403 0.9735 1.162
## cvd.nYes 1.509 0.6629 1.3931 1.634
## copd 1.412 0.7084 1.2727 1.566
## diabetes.nYes 1.620 0.6174 1.4567 1.801
## cancer 1.167 0.8572 1.0716 1.270
##
## Concordance= 0.7 (se = 0.005 )
## Likelihood ratio test= 1707 on 8 df, p=<2e-16
## Wald test = 1777 on 8 df, p=<2e-16
## Score (logrank) test = 1885 on 8 df, p=<2e-161.2.3 Multivariable-adjusted model
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= 5375, number of events= 3293
## (6 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.114056 1.120815 0.003318 34.378 < 2e-16 ***
## TscoreBase.2 0.080642 1.083983 0.022022 3.662 0.00025 ***
## fall.yesnoYes -0.053736 0.947682 0.039240 -1.369 0.17087
## fx50 0.067626 1.069965 0.045137 1.498 0.13407
## BMI 0.013457 1.013548 0.005303 2.538 0.01116 *
## smoke 0.244277 1.276698 0.037225 6.562 5.31e-11 ***
## drink.nYes -0.097682 0.906937 0.037265 -2.621 0.00876 **
## physical -0.162773 0.849784 0.036896 -4.412 1.03e-05 ***
## cvd.nYes 0.385533 1.470398 0.040894 9.428 < 2e-16 ***
## hypertension 0.180792 1.198165 0.036076 5.011 5.40e-07 ***
## copd 0.276893 1.319025 0.053336 5.191 2.09e-07 ***
## diabetes.nYes 0.398043 1.488908 0.055419 7.182 6.85e-13 ***
## cancer 0.130736 1.139667 0.043538 3.003 0.00267 **
## renal -0.877874 0.415666 0.080457 -10.911 < 2e-16 ***
## parkinson 0.532403 1.703019 0.061545 8.651 < 2e-16 ***
## depression -0.112416 0.893673 0.092731 -1.212 0.22541
## ---
## 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 1.1136 1.1281
## TscoreBase.2 1.0840 0.9225 1.0382 1.1318
## fall.yesnoYes 0.9477 1.0552 0.8775 1.0234
## fx50 1.0700 0.9346 0.9794 1.1689
## BMI 1.0135 0.9866 1.0031 1.0241
## smoke 1.2767 0.7833 1.1869 1.3733
## drink.nYes 0.9069 1.1026 0.8431 0.9757
## physical 0.8498 1.1768 0.7905 0.9135
## cvd.nYes 1.4704 0.6801 1.3571 1.5931
## hypertension 1.1982 0.8346 1.1164 1.2860
## copd 1.3190 0.7581 1.1881 1.4644
## diabetes.nYes 1.4889 0.6716 1.3357 1.6597
## cancer 1.1397 0.8774 1.0465 1.2412
## renal 0.4157 2.4058 0.3550 0.4867
## parkinson 1.7030 0.5872 1.5095 1.9214
## depression 0.8937 1.1190 0.7452 1.0718
##
## Concordance= 0.718 (se = 0.004 )
## Likelihood ratio test= 1958 on 16 df, p=<2e-16
## Wald test = 2018 on 16 df, p=<2e-16
## Score (logrank) test = 2133 on 16 df, p=<2e-161.3 Multistate regression
1.3.1 Data preparation
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 4.3.3Q.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 -0.05499161 0.01527378 0.03971784
## Fracture 0.00000000 -0.10331884 0.10331884
## Death 0.00000000 0.00000000 0.00000000statetable.msm(state, ID, data = men)## to
## from 1 2 3
## 1 1723 1016 2642
## 2 0 361 6551.3.2 Age-adjusted model:
Age and FNBMD at baseline:
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 -0.04264 (-0.04450,-0.04087)
## Well - Fracture 0.01364 ( 0.01270, 0.01465) 1.061 (1.049,1.072)
## Well - Death 0.02900 ( 0.02752, 0.03057) 1.117 (1.109,1.124)
## Fracture - Fracture -0.07333 (-0.08546,-0.06292)
## Fracture - Death 0.07333 ( 0.06292, 0.08546) 1.103 (1.088,1.119)
## TscoreBase.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.6729 (1.543,1.814) 1.541 (1.347,1.763)
## Well - Death 0.9819 (0.939,1.027) 3.309 (2.998,3.653)
## Fracture - Fracture
## Fracture - Death 1.1461 (1.041,1.262) 1.658 (1.259,2.183)
##
## -2 * log-likelihood: 35090.96hazard.msm(age.m1)## $ageBase
## HR L U
## Well - Fracture 1.060677 1.049396 1.072079
## Well - Death 1.116706 1.109450 1.124010
## Fracture - Death 1.103441 1.088480 1.118608
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.6728647 1.5425823 1.814151
## Well - Death 0.9818919 0.9390253 1.026715
## Fracture - Death 1.1461358 1.0410791 1.261794
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.541029 1.347086 1.762894
## Well - Death 3.309001 2.997627 3.652720
## Fracture - Death 1.657590 1.258728 2.182841Age and FNBMD at fracture time:
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 -0.04602 (-0.04797,-0.04415)
## Well - Fracture 0.01431 ( 0.01333, 0.01536) 1.061 (1.049,1.072)
## Well - Death 0.03171 ( 0.03013, 0.03337) 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 1.6731 (1.543,1.814) 1.5407 (1.3469,1.763)
## Well - Death 0.9819 (0.939,1.027) 3.3084 (2.9971,3.652)
## Fracture - Fracture
## Fracture - Death 1.1641 (1.056,1.283) 0.9587 (0.7298,1.259)
##
## -2 * log-likelihood: 35077.96hazard.msm(age.m2)## $age
## HR L U
## Well - Fracture 1.060668 1.049389 1.072068
## Well - Death 1.116670 1.109414 1.123974
## Fracture - Death 1.094131 1.080748 1.107680
##
## $Tscore.2
## HR L U
## Well - Fracture 1.6730828 1.5428031 1.814364
## Well - Death 0.9819034 0.9390353 1.026729
## Fracture - Death 1.1641039 1.0564348 1.282746
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.5407403 1.3468723 1.762514
## Well - Death 3.3084328 2.9971142 3.652089
## Fracture - Death 0.9586784 0.7298231 1.2592971.3.3 Adjusted for essential covariates:
Age and FNBMD at baseline:
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 -0.04166 (-0.04350,-0.03990)
## Well - Fracture 0.01336 ( 0.01242, 0.01437) 1.055 (1.043,1.067)
## Well - Death 0.02830 ( 0.02683, 0.02986) 1.112 (1.104,1.119)
## Fracture - Fracture -0.07161 (-0.08370,-0.06127)
## Fracture - Death 0.07161 ( 0.06127, 0.08370) 1.102 (1.087,1.118)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.676 (1.5440,1.820) 1.6032 (1.4100,1.8229)
## Well - Death 1.003 (0.9591,1.050) 0.8740 (0.8001,0.9547)
## Fracture - Fracture
## Fracture - Death 1.162 (1.0541,1.281) 0.9154 (0.7798,1.0746)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.3744 (1.1883,1.590) 1.145 (0.9815,1.335)
## Well - Death 1.0309 (0.9309,1.142) 1.511 (1.3828,1.651)
## Fracture - Fracture
## Fracture - Death 0.9981 (0.8335,1.195) 1.173 (0.9758,1.409)
## hypertension copd
## Well - Well
## Well - Fracture 1.198 (1.056,1.358) 1.143 (0.9438,1.384)
## Well - Death 1.187 (1.098,1.283) 1.333 (1.1857,1.500)
## Fracture - Fracture
## Fracture - Death 1.320 (1.127,1.545) 1.478 (1.1839,1.844)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.273 (1.028,1.575) 0.9567 (0.8132,1.125)
## Well - Death 1.566 (1.392,1.762) 1.1804 (1.0742,1.297)
## Fracture - Fracture
## Fracture - Death 1.293 (1.002,1.668) 1.0146 (0.8332,1.236)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.593 (1.392,1.824)
## Well - Death 3.458 (3.132,3.819)
## Fracture - Fracture
## Fracture - Death 1.724 (1.307,2.274)
##
## -2 * log-likelihood: 34744.9hazard.msm(multi.me1)## $ageBase
## HR L U
## Well - Fracture 1.054893 1.043383 1.066529
## Well - Death 1.111739 1.104262 1.119266
## Fracture - Death 1.102465 1.087112 1.118035
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.676388 1.5439838 1.820147
## Well - Death 1.003356 0.9591305 1.049620
## Fracture - Death 1.161975 1.0541115 1.280875
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.6031880 1.4099895 1.8228589
## Well - Death 0.8740106 0.8001366 0.9547051
## Fracture - Death 0.9154343 0.7798266 1.0746235
##
## $fx50
## HR L U
## Well - Fracture 1.3743945 1.1882655 1.589679
## Well - Death 1.0308641 0.9309001 1.141563
## Fracture - Death 0.9980506 0.8334572 1.195148
##
## $cvd.nYes
## HR L U
## Well - Fracture 1.144834 0.9814826 1.335372
## Well - Death 1.510965 1.3828041 1.651004
## Fracture - Death 1.172581 0.9758481 1.408975
##
## $hypertension
## HR L U
## Well - Fracture 1.197515 1.055659 1.358432
## Well - Death 1.186812 1.098014 1.282791
## Fracture - Death 1.319750 1.127106 1.545320
##
## $copd
## HR L U
## Well - Fracture 1.142991 0.9438275 1.384182
## Well - Death 1.333414 1.1856837 1.499550
## Fracture - Death 1.477535 1.1838938 1.844007
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.272761 1.028335 1.575284
## Well - Death 1.566059 1.391904 1.762004
## Fracture - Death 1.292961 1.002401 1.667743
##
## $cancer
## HR L U
## Well - Fracture 0.9566555 0.8131619 1.125471
## Well - Death 1.1803967 1.0741758 1.297121
## Fracture - Death 1.0146369 0.8331869 1.235603
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.593472 1.392327 1.823675
## Well - Death 3.458493 3.132276 3.818685
## Fracture - Death 1.723856 1.306865 2.273901Age and FNBMD at fracture time:
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 -0.04478 (-0.04671,-0.04293)
## Well - Fracture 0.01395 ( 0.01297, 0.01500) 1.055 (1.043,1.067)
## Well - Death 0.03083 ( 0.02927, 0.03247) 1.112 (1.104,1.119)
## Fracture - Fracture -0.04901 (-0.05857,-0.04101)
## Fracture - Death 0.04901 ( 0.04101, 0.05857) 1.097 (1.083,1.110)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.676 (1.5440,1.820) 1.603 (1.4097,1.8225)
## Well - Death 1.003 (0.9591,1.050) 0.874 (0.8001,0.9547)
## Fracture - Fracture
## Fracture - Death 1.181 (1.0707,1.303) 1.056 (0.8995,1.2397)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.374 (1.1883,1.590) 1.145 (0.9815,1.335)
## Well - Death 1.031 (0.9309,1.142) 1.511 (1.3828,1.651)
## Fracture - Fracture
## Fracture - Death 1.097 (0.9149,1.315) 1.266 (1.0546,1.520)
## hypertension copd
## Well - Well
## Well - Fracture 1.197 (1.056,1.358) 1.143 (0.9439,1.384)
## Well - Death 1.187 (1.098,1.283) 1.334 (1.1858,1.500)
## Fracture - Fracture
## Fracture - Death 1.315 (1.122,1.541) 1.578 (1.2637,1.970)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.273 (1.028,1.575) 0.9565 (0.813,1.125)
## Well - Death 1.566 (1.392,1.762) 1.1805 (1.074,1.297)
## Fracture - Fracture
## Fracture - Death 1.361 (1.055,1.756) 1.0482 (0.861,1.276)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.593 (1.3922,1.824)
## Well - Death 3.459 (3.1323,3.819)
## Fracture - Fracture
## Fracture - Death 1.035 (0.7858,1.362)
##
## -2 * log-likelihood: 34718hazard.msm(multi.me2)## $age
## HR L U
## Well - Fracture 1.054893 1.043382 1.066530
## Well - Death 1.111736 1.104259 1.119264
## Fracture - Death 1.096603 1.082896 1.110485
##
## $Tscore.2
## HR L U
## Well - Fracture 1.676407 1.5439937 1.820177
## Well - Death 1.003344 0.9591196 1.049608
## Fracture - Death 1.181165 1.0707167 1.303007
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.6028547 1.4096812 1.8224994
## Well - Death 0.8739604 0.8000898 0.9546513
## Fracture - Death 1.0560219 0.8995404 1.2397244
##
## $fx50
## HR L U
## Well - Fracture 1.374483 1.1883343 1.589790
## Well - Death 1.030870 0.9309054 1.141569
## Fracture - Death 1.096912 0.9148719 1.315175
##
## $cvd.nYes
## HR L U
## Well - Fracture 1.144918 0.9815492 1.335479
## Well - Death 1.510998 1.3828338 1.651040
## Fracture - Death 1.266295 1.0546447 1.520420
##
## $hypertension
## HR L U
## Well - Fracture 1.197487 1.055627 1.358411
## Well - Death 1.186690 1.097900 1.282660
## Fracture - Death 1.314632 1.121583 1.540907
##
## $copd
## HR L U
## Well - Fracture 1.143115 0.943925 1.384338
## Well - Death 1.333526 1.185788 1.499672
## Fracture - Death 1.577629 1.263723 1.969510
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.272735 1.028300 1.575275
## Well - Death 1.566080 1.391923 1.762028
## Fracture - Death 1.360714 1.054603 1.755677
##
## $cancer
## HR L U
## Well - Fracture 0.956539 0.8130495 1.125352
## Well - Death 1.180495 1.0742670 1.297227
## Fracture - Death 1.048199 0.8610391 1.276042
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.593385 1.392242 1.823587
## Well - Death 3.458543 3.132319 3.818742
## Fracture - Death 1.034724 0.785842 1.3624291.3.4 Multivariable-adjusted model:
All covariates at baseline:
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 -0.04106 (-0.04289,-0.03931)
## Well - Fracture 0.01333 ( 0.01239, 0.01435) 1.057 (1.045,1.069)
## Well - Death 0.02773 ( 0.02627, 0.02927) 1.108 (1.100,1.116)
## Fracture - Fracture -0.06968 (-0.08163,-0.05948)
## Fracture - Death 0.06968 ( 0.05948, 0.08163) 1.105 (1.089,1.121)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.721 (1.5785,1.877) 1.5985 (1.4052,1.818)
## Well - Death 1.012 (0.9652,1.061) 0.8758 (0.8015,0.957)
## Fracture - Fracture
## Fracture - Death 1.193 (1.0765,1.322) 0.8715 (0.7405,1.026)
## fx50 BMI
## Well - Well
## Well - Fracture 1.3651 (1.1798,1.580) 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 1.068 (0.9385,1.215) 0.9768 (0.8559,1.1148)
## Well - Death 1.276 (1.1761,1.384) 0.9081 (0.8370,0.9853)
## Fracture - Fracture
## Fracture - Death 1.183 (1.0034,1.394) 0.9249 (0.7826,1.0930)
## physical cvd.nYes
## Well - Well
## Well - Fracture 0.9271 (0.8123,1.0580) 1.133 (0.9702,1.322)
## Well - Death 0.8604 (0.7935,0.9328) 1.492 (1.3649,1.631)
## Fracture - Fracture
## Fracture - Death 0.9167 (0.7778,1.0805) 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 (1.1143,1.412)
## Fracture - Fracture
## Fracture - Death 1.309 (1.115,1.538) 1.489 (1.1893,1.865)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.233 (0.9938,1.529) 0.9543 (0.8108,1.123)
## Well - Death 1.492 (1.3240,1.682) 1.1789 (1.0725,1.296)
## Fracture - Fracture
## Fracture - Death 1.281 (0.9880,1.661) 0.9775 (0.8005,1.194)
## renal parkinson
## Well - Well
## Well - Fracture 1.0165 (0.7850,1.3163) 0.8601 (0.6750,1.096)
## Well - Death 0.4330 (0.3626,0.5171) 1.7169 (1.5057,1.958)
## Fracture - Fracture
## Fracture - Death 0.4588 (0.3314,0.6353) 1.1816 (0.8889,1.571)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.0618 (0.7944,1.419) 1.606 (1.403,1.839)
## Well - Death 0.8306 (0.6721,1.027) 3.621 (3.278,4.000)
## Fracture - Fracture
## Fracture - Death 1.2171 (0.8498,1.743) 1.856 (1.403,2.456)
##
## -2 * log-likelihood: 34491.05hazard.msm(multi.m1)## $ageBase
## HR L U
## Well - Fracture 1.056532 1.044627 1.068573
## Well - Death 1.108127 1.100434 1.115874
## Fracture - Death 1.104515 1.088557 1.120706
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.721052 1.5784643 1.876519
## Well - Death 1.012130 0.9652314 1.061308
## Fracture - Death 1.193110 1.0765397 1.322303
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.5985235 1.4052214 1.8184162
## Well - Death 0.8758376 0.8015349 0.9570282
## Fracture - Death 0.8715066 0.7405168 1.0256671
##
## $fx50
## HR L U
## Well - Fracture 1.3651281 1.1798251 1.579535
## Well - Death 1.0260681 0.9265258 1.136305
## Fracture - Death 0.9873639 0.8241734 1.182867
##
## $BMI
## HR L U
## Well - Fracture 1.020475 1.0018068 1.039491
## Well - Death 1.012850 1.0012874 1.024547
## Fracture - Death 1.006997 0.9839584 1.030574
##
## $smoke
## HR L U
## Well - Fracture 1.067754 0.9384658 1.214854
## Well - Death 1.276023 1.1760566 1.384487
## Fracture - Death 1.182703 1.0034209 1.394017
##
## $drink.nYes
## HR L U
## Well - Fracture 0.9767765 0.8558774 1.114753
## Well - Death 0.9080883 0.8369526 0.985270
## Fracture - Death 0.9248804 0.7826158 1.093006
##
## $physical
## HR L U
## Well - Fracture 0.9270604 0.8123462 1.0579738
## Well - Death 0.8603537 0.7935042 0.9328351
## Fracture - Death 0.9167199 0.7777671 1.0804975
##
## $cvd.nYes
## HR L U
## Well - Fracture 1.132618 0.9701617 1.322277
## Well - Death 1.492011 1.3649366 1.630917
## Fracture - Death 1.155622 0.9614487 1.389011
##
## $hypertension
## HR L U
## Well - Fracture 1.166131 1.026127 1.325238
## Well - Death 1.142403 1.055792 1.236119
## Fracture - Death 1.309470 1.115126 1.537684
##
## $copd
## HR L U
## Well - Fracture 1.122635 0.9257888 1.361335
## Well - Death 1.254417 1.1143020 1.412150
## Fracture - Death 1.489421 1.1893413 1.865213
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.232859 0.9937647 1.529478
## Well - Death 1.492432 1.3239788 1.682317
## Fracture - Death 1.280957 0.9879886 1.660800
##
## $cancer
## HR L U
## Well - Fracture 0.954256 0.8108125 1.123077
## Well - Death 1.178874 1.0725265 1.295767
## Fracture - Death 0.977499 0.8005035 1.193629
##
## $renal
## HR L U
## Well - Fracture 1.0165166 0.7849800 1.3163471
## Well - Death 0.4330191 0.3626234 0.5170807
## Fracture - Death 0.4588461 0.3314259 0.6352544
##
## $parkinson
## HR L U
## Well - Fracture 0.8600922 0.6749731 1.095982
## Well - Death 1.7169247 1.5056692 1.957821
## Fracture - Death 1.1816255 0.8888873 1.570771
##
## $depression
## HR L U
## Well - Fracture 1.0617969 0.7944134 1.419176
## Well - Death 0.8306316 0.6720585 1.026620
## Fracture - Death 1.2171307 0.8498407 1.743159
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.606226 1.402850 1.839085
## Well - Death 3.620799 3.277774 3.999722
## Fracture - Death 1.856101 1.402940 2.455636Age and FNBMD at fracture time (other covariates at baseline):
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 -0.04408 (-0.04600,-0.04224)
## Well - Fracture 0.01394 ( 0.01296, 0.01499) 1.057 (1.045,1.069)
## Well - Death 0.03014 ( 0.02859, 0.03177) 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 1.721 (1.5777,1.876) 1.5989 (1.4054,1.8190)
## Well - Death 1.014 (0.9672,1.064) 0.8736 (0.7995,0.9547)
## Fracture - Fracture
## Fracture - Death 1.216 (1.0951,1.351) 1.0174 (0.8650,1.1966)
## fx50 BMI
## Well - Well
## Well - Fracture 1.365 (1.1799,1.580) 1.020 (1.0017,1.039)
## Well - Death 1.027 (0.9270,1.137) 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 (0.9385,1.217) 0.9930 (0.9509,1.037)
## Well - Death 1.268 (1.1683,1.377) 0.9888 (0.9625,1.016)
## Fracture - Fracture
## Fracture - Death 1.135 (0.9626,1.339) 0.9953 (0.9406,1.053)
## physical cvd
## Well - Well
## Well - Fracture 0.927 (0.8123,1.0578) 1.133 (0.9706,1.323)
## Well - Death 0.859 (0.7922,0.9313) 1.499 (1.3714,1.639)
## Fracture - Fracture
## Fracture - Death 0.856 (0.7280,1.0066) 1.247 (1.0371,1.499)
## hypertension copd
## Well - Well
## Well - Fracture 1.167 (1.027,1.326) 1.123 (0.9261,1.362)
## Well - Death 1.143 (1.056,1.237) 1.260 (1.1196,1.419)
## Fracture - Fracture
## Fracture - Death 1.302 (1.109,1.530) 1.554 (1.2414,1.945)
## diabetes cancer
## Well - Well
## Well - Fracture 1.234 (0.9945,1.530) 0.9537 (0.8104,1.122)
## Well - Death 1.506 (1.3359,1.697) 1.1763 (1.0702,1.293)
## Fracture - Fracture
## Fracture - Death 1.341 (1.0343,1.739) 1.0075 (0.8254,1.230)
## renal parkinson
## Well - Well
## Well - Fracture 1.0167 (0.7851,1.3166) 0.8598 (0.6747,1.096)
## Well - Death 0.4318 (0.3616,0.5156) 1.7243 (1.5120,1.966)
## Fracture - Fracture
## Fracture - Death 0.4687 (0.3350,0.6557) 1.2108 (0.9024,1.625)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.0600 (0.7932,1.417) 1.606 (1.4027,1.839)
## Well - Death 0.8281 (0.6700,1.023) 3.616 (3.2731,3.994)
## Fracture - Fracture
## Fracture - Death 1.2069 (0.8445,1.725) 1.110 (0.8403,1.467)
##
## -2 * log-likelihood: 34470.73hazard.msm(multi.m2)## $age
## HR L U
## Well - Fracture 1.056557 1.044652 1.068598
## Well - Death 1.108332 1.100632 1.116086
## Fracture - Death 1.096287 1.082381 1.110371
##
## $Tscore.2
## HR L U
## Well - Fracture 1.720524 1.5777383 1.876232
## Well - Death 1.014341 0.9672201 1.063757
## Fracture - Death 1.216304 1.0951054 1.350916
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.5989006 1.4054221 1.8190145
## Well - Death 0.8736494 0.7995108 0.9546629
## Fracture - Death 1.0174197 0.8650423 1.1966383
##
## $fx50
## HR L U
## Well - Fracture 1.365187 1.1798854 1.579590
## Well - Death 1.026617 0.9270134 1.136923
## Fracture - Death 1.085141 0.9046731 1.301610
##
## $BMI
## HR L U
## Well - Fracture 1.020414 1.0017261 1.039451
## Well - Death 1.013435 1.0018398 1.025164
## Fracture - Death 1.009768 0.9860617 1.034044
##
## $smoke
## HR L U
## Well - Fracture 1.068799 0.9385241 1.217157
## Well - Death 1.268305 1.1683139 1.376853
## Fracture - Death 1.135351 0.9626285 1.339065
##
## $drink
## HR L U
## Well - Fracture 0.9930187 0.9508768 1.037028
## Well - Death 0.9888032 0.9625315 1.015792
## Fracture - Death 0.9952847 0.9405634 1.053190
##
## $physical
## HR L U
## Well - Fracture 0.9269554 0.8122600 1.0578464
## Well - Death 0.8589759 0.7922314 0.9313435
## Fracture - Death 0.8560163 0.7279584 1.0066013
##
## $cvd
## HR L U
## Well - Fracture 1.133023 0.9705892 1.322642
## Well - Death 1.499006 1.3713565 1.638538
## Fracture - Death 1.246936 1.0371028 1.499224
##
## $hypertension
## HR L U
## Well - Fracture 1.166554 1.026518 1.325694
## Well - Death 1.143080 1.056413 1.236856
## Fracture - Death 1.302362 1.108775 1.529748
##
## $copd
## HR L U
## Well - Fracture 1.122966 0.9261099 1.361667
## Well - Death 1.260384 1.1196275 1.418836
## Fracture - Death 1.554060 1.2414050 1.945460
##
## $diabetes
## HR L U
## Well - Fracture 1.233613 0.9945055 1.530209
## Well - Death 1.505779 1.3358999 1.697262
## Fracture - Death 1.341307 1.0342839 1.739469
##
## $cancer
## HR L U
## Well - Fracture 0.9537327 0.8103887 1.122432
## Well - Death 1.1762833 1.0701796 1.292907
## Fracture - Death 1.0075191 0.8253600 1.229881
##
## $renal
## HR L U
## Well - Fracture 1.0166769 0.7850960 1.3165676
## Well - Death 0.4317897 0.3615690 0.5156481
## Fracture - Death 0.4687098 0.3350274 0.6557341
##
## $parkinson
## HR L U
## Well - Fracture 0.8597611 0.6746954 1.095589
## Well - Death 1.7243383 1.5120242 1.966465
## Fracture - Death 1.2108287 0.9023629 1.624741
##
## $depression
## HR L U
## Well - Fracture 1.0600160 0.7931910 1.416599
## Well - Death 0.8280899 0.6700044 1.023475
## Fracture - Death 1.2068968 0.8445388 1.724728
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.605983 1.4026624 1.838777
## Well - Death 3.615570 3.2730570 3.993925
## Fracture - Death 1.110399 0.8403278 1.4672691.3.4 Transition risks
# 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 0.99765 0.00038895 0.0019646
## Fracture 0.00000 0.99584765 0.0041524
## 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 0.97771 0.0023779 0.019910
## Fracture 0.00000 0.9785105 0.021489
## 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 0.94062 0.005294 0.054087
## Fracture 0.00000 0.956164 0.043836
## Death 0.00000 0.000000 1.000000# Osteoporosis:
pmatrix.msm(multi.m2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)## Well Fracture Death
## Well 0.99784 0.00022617 0.0019366
## Fracture 0.00000 0.99658483 0.0034152
## 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 0.97898 0.0013853 0.019631
## Fracture 0.00000 0.9822981 0.017702
## 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 0.94355 0.0030931 0.053354
## Fracture 0.00000 0.9638169 0.036183
## Death 0.00000 0.0000000 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 0.99457 0.00030065 0.0051333
## Fracture 0.00000 0.99425183 0.0057482
## Death 0.00000 0.00000000 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 0.94693 0.0018119 0.051260
## Fracture 0.00000 0.9703517 0.029648
## 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 0.86071 0.0039121 0.135377
## Fracture 0.00000 0.9397865 0.060214
## Death 0.00000 0.0000000 1.0000001.3.5 Check the model goodness-of-fit
Model validation
prevalence.msm(multi.m2, times = seq(0,20,1), covariates = "mean", ci = "normal")## $Observed
## State 1 State 2 State 3 Total
## 0 5375 0 0 5375
## 1 5270 49 53 5372
## 2 5120 101 148 5369
## 3 4923 159 262 5344
## 4 4733 198 394 5325
## 5 4477 257 559 5293
## 6 4252 290 726 5268
## 7 4022 323 905 5250
## 8 3755 371 1102 5228
## 9 3497 392 1322 5211
## 10 3244 413 1533 5190
## 11 2986 419 1764 5169
## 12 2750 418 1978 5146
## 13 2482 414 2226 5122
## 14 2222 413 2455 5090
## 15 1963 399 2673 5035
## 16 1746 365 2871 4982
## 17 1530 346 3066 4942
## 18 1338 310 3231 4879
## 19 1182 265 3292 4739
## 20 1019 212 3293 4524
##
## $Expected
## $Expected$estimates
## Well Fracture Death Total
## 0 5375.0 0.000 0.00 5375
## 1 5228.0 57.308 86.65 5372
## 2 5085.1 110.466 173.43 5369
## 3 4925.8 159.049 259.16 5344
## 4 4776.7 203.785 344.47 5325
## 5 4620.8 244.190 428.01 5293
## 6 4262.5 307.745 697.76 5268
## 7 3937.1 362.408 950.46 5250
## 8 3633.8 408.471 1185.75 5228
## 9 3357.0 447.461 1406.58 5211
## 10 3098.8 479.431 1611.76 5190
## 11 2860.5 505.405 1803.13 5169
## 12 2639.4 525.826 1980.79 5146
## 13 2434.9 541.365 2145.77 5122
## 14 2242.6 551.795 2295.59 5090
## 15 2056.1 555.900 2423.02 5035
## 16 1885.6 556.841 2539.57 4982
## 17 1733.6 556.312 2652.09 4942
## 18 1586.3 550.668 2742.06 4879
## 19 1428.0 534.174 2776.80 4739
## 20 1263.5 507.517 2752.98 4524
##
## $Expected$ci
## , , 2.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 5375.0 0.000 0.000 5375
## [2,] 5217.3 51.314 79.152 5372
## [3,] 5064.2 98.982 158.422 5369
## [4,] 4895.4 142.408 237.155 5344
## [5,] 4737.6 182.398 316.426 5325
## [6,] 4573.5 218.024 393.777 5293
## [7,] 4215.3 282.478 662.813 5268
## [8,] 3889.1 336.418 912.472 5250
## [9,] 3584.3 380.843 1144.791 5228
## [10,] 3304.7 416.011 1360.904 5211
## [11,] 3043.4 447.141 1560.867 5190
## [12,] 2802.4 471.783 1747.564 5169
## [13,] 2579.1 490.337 1921.759 5146
## [14,] 2372.6 503.378 2084.077 5122
## [15,] 2179.3 512.004 2231.992 5090
## [16,] 1993.6 514.227 2358.605 5035
## [17,] 1824.3 513.772 2472.185 4982
## [18,] 1672.2 511.668 2580.438 4942
## [19,] 1525.5 505.216 2670.427 4879
## [20,] 1369.1 488.196 2707.607 4739
## [21,] 1207.7 461.874 2686.791 4524
##
## , , 97.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 5375.0 0.000 0.000 5375
## [2,] 5237.8 64.119 94.832 5372
## [3,] 5104.1 123.731 189.528 5369
## [4,] 4953.5 178.281 283.000 5344
## [5,] 4812.6 228.360 375.720 5325
## [6,] 4664.2 274.452 467.100 5293
## [7,] 4303.9 337.180 735.765 5268
## [8,] 3981.4 392.110 990.494 5250
## [9,] 3681.6 438.563 1230.042 5228
## [10,] 3407.1 479.720 1455.976 5211
## [11,] 3153.0 513.262 1664.678 5190
## [12,] 2917.3 541.107 1857.979 5169
## [13,] 2698.1 562.924 2039.696 5146
## [14,] 2496.6 580.507 2206.831 5122
## [15,] 2304.9 593.344 2360.294 5090
## [16,] 2118.6 600.434 2489.107 5035
## [17,] 1947.9 602.994 2605.932 4982
## [18,] 1795.4 603.624 2718.921 4942
## [19,] 1647.0 599.477 2807.753 4879
## [20,] 1486.2 583.247 2842.825 4739
## [21,] 1318.0 556.208 2816.547 4524
##
##
##
## $`Observed percentages`
## State 1 State 2 State 3
## 0 100.000 0.00000 0.0000
## 1 98.101 0.91214 0.9866
## 2 95.362 1.88117 2.7566
## 3 92.122 2.97530 4.9027
## 4 88.883 3.71831 7.3991
## 5 84.583 4.85547 10.5611
## 6 80.714 5.50494 13.7813
## 7 76.610 6.15238 17.2381
## 8 71.825 7.09640 21.0788
## 9 67.108 7.52255 25.3694
## 10 62.505 7.95761 29.5376
## 11 57.767 8.10602 34.1265
## 12 53.440 8.12281 38.4376
## 13 48.458 8.08278 43.4596
## 14 43.654 8.11395 48.2318
## 15 38.987 7.92453 53.0884
## 16 35.046 7.32637 57.6275
## 17 30.959 7.00121 62.0397
## 18 27.424 6.35376 66.2226
## 19 24.942 5.59190 69.4661
## 20 22.524 4.68612 72.7896
##
## $`Expected percentages`
## $`Expected percentages`$estimates
## Well Fracture Death
## 0 100.000 0.0000 0.0000
## 1 97.320 1.0668 1.6130
## 2 94.712 2.0575 3.2303
## 3 92.174 2.9762 4.8496
## 4 89.704 3.8269 6.4690
## 5 87.300 4.6134 8.0863
## 6 80.913 5.8418 13.2453
## 7 74.993 6.9030 18.1041
## 8 69.506 7.8131 22.6808
## 9 64.421 8.5869 26.9925
## 10 59.707 9.2376 31.0551
## 11 55.339 9.7776 34.8835
## 12 51.290 10.2181 38.4919
## 13 47.537 10.5694 41.8932
## 14 44.059 10.8408 45.1000
## 15 40.836 11.0407 48.1236
## 16 37.848 11.1770 50.9750
## 17 35.079 11.2568 53.6644
## 18 32.512 11.2865 56.2012
## 19 30.134 11.2719 58.5946
## 20 27.929 11.2183 60.8529
##
## $`Expected percentages`$ci
## , , 2.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.00000 0.0000
## [2,] 97.120 0.95521 1.4734
## [3,] 94.323 1.84358 2.9507
## [4,] 91.606 2.66481 4.4378
## [5,] 88.968 3.42532 5.9423
## [6,] 86.406 4.11910 7.4396
## [7,] 80.017 5.36215 12.5819
## [8,] 74.078 6.40796 17.3804
## [9,] 68.560 7.28467 21.8973
## [10,] 63.418 7.98332 26.1160
## [11,] 58.640 8.61543 30.0745
## [12,] 54.215 9.12717 33.8085
## [13,] 50.119 9.52850 37.3447
## [14,] 46.322 9.82776 40.6887
## [15,] 42.816 10.05902 43.8505
## [16,] 39.595 10.21305 46.8442
## [17,] 36.617 10.31256 49.6223
## [18,] 33.836 10.35346 52.2144
## [19,] 31.266 10.35490 54.7331
## [20,] 28.891 10.30167 57.1346
## [21,] 26.695 10.20942 59.3897
##
## , , 97.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.0000 0.0000
## [2,] 97.502 1.1936 1.7653
## [3,] 95.067 2.3045 3.5300
## [4,] 92.692 3.3361 5.2957
## [5,] 90.377 4.2885 7.0558
## [6,] 88.119 5.1852 8.8249
## [7,] 81.699 6.4005 13.9667
## [8,] 75.836 7.4688 18.8665
## [9,] 70.421 8.3887 23.5280
## [10,] 65.382 9.2059 27.9404
## [11,] 60.751 9.8894 32.0747
## [12,] 56.438 10.4683 35.9447
## [13,] 52.430 10.9391 39.6365
## [14,] 48.743 11.3336 43.0853
## [15,] 45.284 11.6571 46.3712
## [16,] 42.078 11.9252 49.4361
## [17,] 39.099 12.1035 52.3069
## [18,] 36.330 12.2142 55.0166
## [19,] 33.757 12.2869 57.5477
## [20,] 31.361 12.3074 59.9879
## [21,] 29.133 12.2946 62.2579plot.prevalence.msm(multi.m2, mintime = 0, maxtime = 20, legend.pos = c(10, 80), col.obs = "gray",
col.exp = "black")
Diagnostic plots for survival
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)")
2. WOMEN
2.1 Description of study sample
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=1211) |
Fractured, Dead (N=1487) |
No Fractured, Dead (N=2781) |
Overall (N=7367) |
|
|---|---|---|---|---|---|
| ageBase | |||||
| Mean (SD) | 71.6 (3.99) | 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) | 0.639 (0.106) | 0.605 (0.102) | 0.658 (0.115) | 0.649 (0.112) |
| Median [Min, Max] | 0.666 [0.387, 1.15] | 0.630 [0.302, 1.21] | 0.597 [0.297, 1.21] | 0.648 [0.277, 1.30] | 0.639 [0.277, 1.30] |
| TscoreBase | |||||
| Mean (SD) | -1.96 (0.824) | -2.24 (0.812) | -2.50 (0.788) | -2.09 (0.883) | -2.16 (0.860) |
| Median [Min, Max] | -2.03 [-4.18, 1.67] | -2.31 [-4.83, 2.18] | -2.56 [-4.87, 2.18] | -2.17 [-5.02, 2.83] | -2.24 [-5.02, 2.83] |
| as.factor(fall.no) | |||||
| 0 | 1418 (75.1%) | 854 (70.5%) | 1034 (69.5%) | 2038 (73.3%) | 5344 (72.5%) |
| 1 | 333 (17.6%) | 257 (21.2%) | 287 (19.3%) | 474 (17.0%) | 1351 (18.3%) |
| 2 | 97 (5.1%) | 71 (5.9%) | 107 (7.2%) | 176 (6.3%) | 451 (6.1%) |
| 3+ | 40 (2.1%) | 29 (2.4%) | 59 (4.0%) | 93 (3.3%) | 221 (3.0%) |
| fall.yesno | |||||
| No | 1418 (75.1%) | 854 (70.5%) | 1034 (69.5%) | 2038 (73.3%) | 5344 (72.5%) |
| Yes | 470 (24.9%) | 357 (29.5%) | 453 (30.5%) | 743 (26.7%) | 2023 (27.5%) |
| as.factor(fx50) | |||||
| 0 | 1297 (68.7%) | 655 (54.1%) | 709 (47.7%) | 1702 (61.2%) | 4363 (59.2%) |
| 1 | 591 (31.3%) | 556 (45.9%) | 778 (52.3%) | 1079 (38.8%) | 3004 (40.8%) |
| race | |||||
| 1:WHITE | 1888 (100%) | 1211 (100%) | 1487 (100%) | 2781 (100%) | 7367 (100%) |
| weight | |||||
| Mean (SD) | 67.3 (11.8) | 66.3 (11.7) | 64.7 (11.6) | 66.7 (12.8) | 66.4 (12.2) |
| Median [Min, Max] | 65.8 [41.7, 112] | 65.0 [40.8, 112] | 63.3 [40.2, 112] | 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 (4.37) | 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%) | 916 (61.6%) | 1615 (58.1%) | 4484 (60.9%) |
| 1 | 706 (37.4%) | 440 (36.3%) | 571 (38.4%) | 1166 (41.9%) | 2883 (39.1%) |
| as.factor(drink.n) | |||||
| No | 723 (38.3%) | 481 (39.7%) | 724 (48.7%) | 1337 (48.1%) | 3265 (44.3%) |
| Yes | 1165 (61.7%) | 730 (60.3%) | 763 (51.3%) | 1444 (51.9%) | 4102 (55.7%) |
| as.factor(physical) | |||||
| 0 | 567 (30.0%) | 355 (29.3%) | 734 (49.4%) | 1400 (50.3%) | 3056 (41.5%) |
| 1 | 1321 (70.0%) | 856 (70.7%) | 753 (50.6%) | 1381 (49.7%) | 4311 (58.5%) |
| as.factor(cvd.n) | |||||
| No | 1554 (82.3%) | 1003 (82.8%) | 1080 (72.6%) | 1958 (70.4%) | 5595 (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%) | 865 (71.4%) | 847 (57.0%) | 1557 (56.0%) | 4595 (62.4%) |
| 1 | 562 (29.8%) | 346 (28.6%) | 640 (43.0%) | 1224 (44.0%) | 2772 (37.6%) |
| as.factor(copd) | |||||
| 0 | 1628 (86.2%) | 1008 (83.2%) | 1191 (80.1%) | 2291 (82.4%) | 6118 (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%) | 1154 (95.3%) | 1358 (91.3%) | 2545 (91.5%) | 6878 (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%) | 978 (80.8%) | 1182 (79.5%) | 2234 (80.3%) | 5940 (80.6%) |
| 1 | 342 (18.1%) | 233 (19.2%) | 305 (20.5%) | 547 (19.7%) | 1427 (19.4%) |
| as.factor(parkinson) | |||||
| 0 | 1882 (99.7%) | 1205 (99.5%) | 1471 (98.9%) | 2766 (99.5%) | 7324 (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%) | 1147 (94.7%) | 1393 (93.7%) | 2630 (94.6%) | 6974 (94.7%) |
| 1 | 84 (4.4%) | 64 (5.3%) | 94 (6.3%) | 151 (5.4%) | 393 (5.3%) |
| as.factor(renal) | |||||
| 0 | 1867 (98.9%) | 1204 (99.4%) | 1464 (98.5%) | 2743 (98.6%) | 7278 (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 (92.2%) | 1352 (90.9%) | 2564 (92.2%) | 6798 (92.3%) |
| 1 | 123 (6.5%) | 94 (7.8%) | 135 (9.1%) | 217 (7.8%) | 569 (7.7%) |
| as.factor(anyfx) | |||||
| 0 | 1888 (100%) | 0 (0%) | 0 (0%) | 2781 (100%) | 4669 (63.4%) |
| 1 | 0 (0%) | 1211 (100%) | 1487 (100%) | 0 (0%) | 2698 (36.6%) |
| as.factor(death) | |||||
| 0 | 1888 (100%) | 1211 (100%) | 0 (0%) | 0 (0%) | 3099 (42.1%) |
| 1 | 0 (0%) | 0 (0%) | 1487 (100%) | 2781 (100%) | 4268 (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))2.2 Conventional Cox’s PH model
2.2.1 Age-adjusted model:
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= 7367, number of events= 4268
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.11971 1.12717 0.00308 38.90 < 2e-16 ***
## TscoreBase.2 0.07819 1.08132 0.01925 4.06 4.9e-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 0.925 1.04 1.12
##
## Concordance= 0.664 (se = 0.004 )
## Likelihood ratio test= 1546 on 2 df, p=<2e-16
## Wald test = 1720 on 2 df, p=<2e-16
## Score (logrank) test = 1812 on 2 df, p=<2e-162.2.2 Essential covariates
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= 7367, number of events= 4268
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.11294 1.11956 0.00315 35.80 < 2e-16 ***
## TscoreBase.2 0.09890 1.10395 0.01973 5.01 5.4e-07 ***
## fall.yesnoYes -0.02540 0.97492 0.03423 -0.74 0.4580
## fx50 0.09498 1.09964 0.03183 2.98 0.0028 **
## cvd.nYes 0.31972 1.37674 0.03433 9.31 < 2e-16 ***
## hypertension 0.31536 1.37075 0.03136 10.06 < 2e-16 ***
## copd 0.12368 1.13166 0.03964 3.12 0.0018 **
## diabetes.nYes 0.58033 1.78662 0.05539 10.48 < 2e-16 ***
## cancer 0.02340 1.02368 0.03837 0.61 0.5419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ageBase 1.120 0.893 1.113 1.13
## TscoreBase.2 1.104 0.906 1.062 1.15
## fall.yesnoYes 0.975 1.026 0.912 1.04
## fx50 1.100 0.909 1.033 1.17
## cvd.nYes 1.377 0.726 1.287 1.47
## hypertension 1.371 0.730 1.289 1.46
## copd 1.132 0.884 1.047 1.22
## diabetes.nYes 1.787 0.560 1.603 1.99
## cancer 1.024 0.977 0.950 1.10
##
## Concordance= 0.686 (se = 0.004 )
## Likelihood ratio test= 1876 on 9 df, p=<2e-16
## Wald test = 2064 on 9 df, p=<2e-16
## Score (logrank) test = 2167 on 9 df, p=<2e-162.2.3 Multivariable-adjusted model
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= 7300, number of events= 4223
## (67 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ageBase 0.106438 1.112309 0.003268 32.57 < 2e-16 ***
## TscoreBase.2 0.067567 1.069902 0.021052 3.21 0.00133 **
## fall.yesnoYes 0.000279 1.000279 0.034449 0.01 0.99355
## fx50 0.080579 1.083914 0.032173 2.50 0.01226 *
## BMI -0.013499 0.986592 0.003955 -3.41 0.00064 ***
## smoke 0.302597 1.353368 0.032631 9.27 < 2e-16 ***
## drink.nYes -0.166401 0.846707 0.032366 -5.14 2.7e-07 ***
## physical -0.598213 0.549793 0.032871 -18.20 < 2e-16 ***
## cvd.nYes 0.284623 1.329261 0.034618 8.22 < 2e-16 ***
## hypertension 0.292155 1.339310 0.031722 9.21 < 2e-16 ***
## copd 0.028812 1.029231 0.040449 0.71 0.47628
## diabetes.nYes 0.469461 1.599133 0.056721 8.28 < 2e-16 ***
## cancer 0.067294 1.069610 0.038688 1.74 0.08197 .
## renal 0.360623 1.434222 0.130476 2.76 0.00571 **
## parkinson 0.203365 1.225520 0.186795 1.09 0.27628
## depression 0.083361 1.086934 0.056561 1.47 0.14053
## ---
## 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 1.070 0.935 1.027 1.115
## fall.yesnoYes 1.000 1.000 0.935 1.070
## fx50 1.084 0.923 1.018 1.154
## BMI 0.987 1.014 0.979 0.994
## smoke 1.353 0.739 1.270 1.443
## drink.nYes 0.847 1.181 0.795 0.902
## physical 0.550 1.819 0.515 0.586
## cvd.nYes 1.329 0.752 1.242 1.423
## hypertension 1.339 0.747 1.259 1.425
## copd 1.029 0.972 0.951 1.114
## diabetes.nYes 1.599 0.625 1.431 1.787
## cancer 1.070 0.935 0.992 1.154
## renal 1.434 0.697 1.111 1.852
## parkinson 1.226 0.816 0.850 1.767
## depression 1.087 0.920 0.973 1.214
##
## Concordance= 0.716 (se = 0.004 )
## Likelihood ratio test= 2326 on 16 df, p=<2e-16
## Wald test = 2499 on 16 df, p=<2e-16
## Score (logrank) test = 2650 on 16 df, p=<2e-162.3 Multistate regression
2.3.1 Data preparation
qmatrix.n = crudeinits.msm(state ~ time2event, subject = ID, data = women, qmatrix = Q.m2)
qmatrix.n## Well Fracture Death
## Well -0.069633 0.034289 0.035344
## Fracture 0.000000 -0.081958 0.081958
## Death 0.000000 0.000000 0.000000statetable.msm(state, ID, data = women)## to
## from 1 2 3
## 1 1889 2698 2781
## 2 0 1211 14872.3.2 Age-adjusted model:
Age and FNBMD at baseline:
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 -0.06129 (-0.06321,-0.05942)
## Well - Fracture 0.03322 ( 0.03191, 0.03459) 1.040 (1.032,1.048)
## Well - Death 0.02806 ( 0.02676, 0.02943) 1.105 (1.097,1.113)
## Fracture - Fracture -0.05903 (-0.06487,-0.05371)
## Fracture - Death 0.05903 ( 0.05371, 0.06487) 1.096 (1.086,1.107)
## TscoreBase.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.632 (1.5504,1.717) 1.307 (1.208,1.415)
## Well - Death 0.983 (0.9396,1.028) 3.095 (2.824,3.394)
## Fracture - Fracture
## Fracture - Death 1.087 (1.0131,1.166) 1.899 (1.592,2.264)
##
## -2 * log-likelihood: 55963hazard.msm(age.w1)## $ageBase
## HR L U
## Well - Fracture 1.0404 1.0324 1.0484
## Well - Death 1.1053 1.0973 1.1132
## Fracture - Death 1.0962 1.0855 1.1070
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.63155 1.55040 1.7169
## Well - Death 0.98304 0.93961 1.0285
## Fracture - Death 1.08691 1.01308 1.1661
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3072 1.2079 1.4146
## Well - Death 3.0955 2.8236 3.3935
## Fracture - Death 1.8985 1.5920 2.2641Age and FNBMD at baseline and at fracture time:
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 -0.06685 (-0.06894,-0.06482)
## Well - Fracture 0.03497 ( 0.03355, 0.03645) 1.041 (1.033,1.049)
## Well - Death 0.03188 ( 0.03044, 0.03338) 1.106 (1.098,1.114)
## Fracture - Fracture -0.04282 (-0.04753,-0.03858)
## Fracture - Death 0.04282 ( 0.03858, 0.04753) 1.105 (1.096,1.114)
## Tscore.2 timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.6272 (1.5461,1.712) 1.310 (1.2104,1.418)
## Well - Death 0.9781 (0.9348,1.023) 3.134 (2.8573,3.438)
## Fracture - Fracture
## Fracture - Death 1.1294 (1.0544,1.210) 1.195 (0.9996,1.428)
##
## -2 * log-likelihood: 55458hazard.msm(age.w2)## $age
## HR L U
## Well - Fracture 1.0406 1.0326 1.0486
## Well - Death 1.1062 1.0983 1.1142
## Fracture - Death 1.1048 1.0957 1.1140
##
## $Tscore.2
## HR L U
## Well - Fracture 1.62719 1.54614 1.7125
## Well - Death 0.97808 0.93479 1.0234
## Fracture - Death 1.12936 1.05439 1.2097
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3101 1.21038 1.4180
## Well - Death 3.1345 2.85734 3.4385
## Fracture - Death 1.1947 0.99965 1.42782.3.3 Essential covariates:
Age and FNBMD at baseline:
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 (-0.06263,-0.05884)
## Well - Fracture 0.03308 ( 0.03176, 0.03445) 1.036 (1.028,1.045)
## Well - Death 0.02762 ( 0.02633, 0.02899) 1.098 (1.089,1.106)
## Fracture - Fracture -0.05823 (-0.06406,-0.05293)
## Fracture - Death 0.05823 ( 0.05293, 0.06406) 1.090 (1.079,1.101)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.587 (1.5069,1.672) 1.1534 (1.0618,1.253)
## Well - Death 1.006 (0.9608,1.054) 0.9709 (0.8923,1.056)
## Fracture - Fracture
## Fracture - Death 1.113 (1.0366,1.196) 0.9426 (0.8434,1.053)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.4807 (1.3703,1.600) 0.9934 (0.9069,1.088)
## Well - Death 1.0776 (0.9965,1.165) 1.3761 (1.2671,1.494)
## Fracture - Fracture
## Fracture - Death 0.9458 (0.8517,1.050) 1.2494 (1.1117,1.404)
## hypertension copd
## Well - Well
## Well - Fracture 1.070 (0.9879,1.158) 1.133 (1.0274,1.249)
## Well - Death 1.328 (1.2314,1.433) 1.132 (1.0262,1.248)
## Fracture - Fracture
## Fracture - Death 1.309 (1.1777,1.455) 1.096 (0.9635,1.247)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.470 (1.265,1.708) 1.0458 (0.9514,1.150)
## Well - Death 1.599 (1.398,1.830) 1.0068 (0.9168,1.106)
## Fracture - Fracture
## Fracture - Death 1.701 (1.416,2.042) 0.9849 (0.8681,1.117)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.342 (1.240,1.453)
## Well - Death 3.200 (2.918,3.509)
## Fracture - Fracture
## Fracture - Death 1.952 (1.636,2.328)
##
## -2 * log-likelihood: 55552hazard.msm(multi.we1)## $ageBase
## HR L U
## Well - Fracture 1.0364 1.0282 1.0446
## Well - Death 1.0975 1.0895 1.1057
## Fracture - Death 1.0901 1.0791 1.1013
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.5873 1.50689 1.6719
## Well - Death 1.0064 0.96078 1.0541
## Fracture - Death 1.1133 1.03661 1.1958
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.15343 1.06183 1.2529
## Well - Death 0.97090 0.89234 1.0564
## Fracture - Death 0.94255 0.84338 1.0534
##
## $fx50
## HR L U
## Well - Fracture 1.48065 1.37034 1.5998
## Well - Death 1.07757 0.99648 1.1653
## Fracture - Death 0.94577 0.85165 1.0503
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.99336 0.90693 1.0880
## Well - Death 1.37608 1.26706 1.4945
## Fracture - Death 1.24937 1.11175 1.4040
##
## $hypertension
## HR L U
## Well - Fracture 1.0697 0.98792 1.1582
## Well - Death 1.3285 1.23144 1.4332
## Fracture - Death 1.3089 1.17767 1.4548
##
## $copd
## HR L U
## Well - Fracture 1.1328 1.02745 1.2489
## Well - Death 1.1317 1.02616 1.2480
## Fracture - Death 1.0959 0.96346 1.2465
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4698 1.2646 1.7082
## Well - Death 1.5994 1.3977 1.8302
## Fracture - Death 1.7008 1.4163 2.0424
##
## $cancer
## HR L U
## Well - Fracture 1.04584 0.95145 1.1496
## Well - Death 1.00679 0.91676 1.1057
## Fracture - Death 0.98493 0.86814 1.1174
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3420 1.2399 1.4526
## Well - Death 3.1998 2.9181 3.5088
## Fracture - Death 1.9515 1.6358 2.3281Age and FNBMD at fracture time:
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 -0.06572 (-0.06781,-0.06369)
## Well - Fracture 0.03463 ( 0.03321, 0.03611) 1.037 (1.028,1.045)
## Well - Death 0.03109 ( 0.02966, 0.03258) 1.099 (1.091,1.107)
## Fracture - Fracture -0.04162 (-0.04628,-0.03743)
## Fracture - Death 0.04162 ( 0.03743, 0.04628) 1.103 (1.093,1.112)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.583 (1.5029,1.668) 1.1468 (1.0554,1.246)
## Well - Death 1.002 (0.9561,1.049) 0.9721 (0.8932,1.058)
## Fracture - Fracture
## Fracture - Death 1.136 (1.0596,1.218) 0.9524 (0.8517,1.065)
## fx50 cvd.nYes
## Well - Well
## Well - Fracture 1.481 (1.3709,1.601) 0.9922 (0.9056,1.087)
## Well - Death 1.074 (0.9932,1.162) 1.3755 (1.2662,1.494)
## Fracture - Fracture
## Fracture - Death 1.038 (0.9349,1.153) 1.2833 (1.1426,1.441)
## hypertension copd
## Well - Well
## Well - Fracture 1.070 (0.9881,1.159) 1.131 (1.0257,1.247)
## Well - Death 1.319 (1.2220,1.423) 1.140 (1.0332,1.257)
## Fracture - Fracture
## Fracture - Death 1.330 (1.1974,1.478) 1.103 (0.9692,1.254)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.464 (1.260,1.703) 1.047 (0.9524,1.151)
## Well - Death 1.609 (1.406,1.841) 1.013 (0.9221,1.112)
## Fracture - Fracture
## Fracture - Death 1.771 (1.474,2.128) 1.051 (0.9260,1.194)
## timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.345 (1.242,1.456)
## Well - Death 3.240 (2.953,3.555)
## Fracture - Fracture
## Fracture - Death 1.276 (1.066,1.526)
##
## -2 * log-likelihood: 55039hazard.msm(multi.we2)## $age
## HR L U
## Well - Fracture 1.0366 1.0284 1.0448
## Well - Death 1.0986 1.0905 1.1068
## Fracture - Death 1.1026 1.0934 1.1119
##
## $Tscore.2
## HR L U
## Well - Fracture 1.5832 1.50291 1.6678
## Well - Death 1.0016 0.95611 1.0492
## Fracture - Death 1.1361 1.05956 1.2183
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.14677 1.05541 1.2460
## Well - Death 0.97207 0.89320 1.0579
## Fracture - Death 0.95240 0.85165 1.0651
##
## $fx50
## HR L U
## Well - Fracture 1.4815 1.37087 1.6010
## Well - Death 1.0743 0.99321 1.1621
## Fracture - Death 1.0384 0.93492 1.1533
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.99219 0.90561 1.0870
## Well - Death 1.37548 1.26618 1.4942
## Fracture - Death 1.28329 1.14265 1.4412
##
## $hypertension
## HR L U
## Well - Fracture 1.0700 0.98806 1.1588
## Well - Death 1.3187 1.22199 1.4230
## Fracture - Death 1.3301 1.19736 1.4775
##
## $copd
## HR L U
## Well - Fracture 1.1310 1.02566 1.2472
## Well - Death 1.1395 1.03324 1.2568
## Fracture - Death 1.1025 0.96917 1.2542
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4644 1.2595 1.7026
## Well - Death 1.6088 1.4059 1.8411
## Fracture - Death 1.7713 1.4741 2.1285
##
## $cancer
## HR L U
## Well - Fracture 1.0471 0.95242 1.1512
## Well - Death 1.0128 0.92207 1.1124
## Fracture - Death 1.0513 0.92598 1.1935
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3451 1.2425 1.4562
## Well - Death 3.2399 2.9528 3.5550
## Fracture - Death 1.2756 1.0663 1.52612.3.4 Multivariable-adjusted model:
All covariates at baseline:
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 -0.05974 (-0.06165,-0.05788)
## Well - Fracture 0.03297 ( 0.03164, 0.03435) 1.032 (1.024,1.041)
## Well - Death 0.02677 ( 0.02548, 0.02812) 1.088 (1.080,1.097)
## Fracture - Fracture -0.05639 (-0.06215,-0.05116)
## Fracture - Death 0.05639 ( 0.05116, 0.06215) 1.087 (1.076,1.099)
## TscoreBase.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.5746 (1.4889,1.665) 1.1479 (1.0559,1.248)
## Well - Death 0.9837 (0.9361,1.034) 1.0005 (0.9192,1.089)
## Fracture - Fracture
## Fracture - Death 1.0594 (0.9808,1.144) 0.9537 (0.8524,1.067)
## fx50 BMI
## Well - Well
## Well - Fracture 1.4770 (1.3657,1.597) 0.9956 (0.9859,1.0053)
## Well - Death 1.0617 (0.9811,1.149) 0.9875 (0.9783,0.9968)
## Fracture - Fracture
## Fracture - Death 0.9278 (0.8341,1.032) 0.9906 (0.9773,1.0041)
## smoke drink.nYes
## Well - Well
## Well - Fracture 0.9919 (0.9143,1.076) 0.9724 (0.8978,1.0532)
## Well - Death 1.3379 (1.2367,1.447) 0.8721 (0.8064,0.9430)
## Fracture - Fracture
## Fracture - Death 1.2315 (1.1025,1.376) 0.8287 (0.7429,0.9245)
## physical cvd.nYes
## Well - Well
## Well - Fracture 0.8314 (0.7660,0.9025) 0.9815 (0.8954,1.076)
## Well - Death 0.5636 (0.5207,0.6102) 1.3224 (1.2169,1.437)
## Fracture - Fracture
## Fracture - Death 0.6515 (0.5840,0.7267) 1.2122 (1.0770,1.364)
## hypertension copd
## Well - Well
## Well - Fracture 1.055 (0.9736,1.144) 1.107 (1.0023,1.223)
## Well - Death 1.315 (1.2176,1.420) 1.043 (0.9437,1.152)
## Fracture - Fracture
## Fracture - Death 1.250 (1.1230,1.391) 1.028 (0.9015,1.173)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.427 (1.224,1.663) 1.062 (0.9653,1.168)
## Well - Death 1.426 (1.242,1.637) 1.056 (0.9613,1.161)
## Fracture - Fracture
## Fracture - Death 1.537 (1.273,1.856) 1.008 (0.8871,1.145)
## renal parkinson
## Well - Well
## Well - Fracture 1.047 (0.7294,1.502) 2.0855 (1.3558,3.208)
## Well - Death 1.222 (0.8821,1.693) 1.2954 (0.7626,2.200)
## Fracture - Fracture
## Fracture - Death 1.553 (1.0252,2.352) 0.9511 (0.5702,1.586)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.125 (0.9799,1.291) 1.369 (1.264,1.483)
## Well - Death 1.029 (0.8938,1.184) 3.370 (3.071,3.698)
## Fracture - Fracture
## Fracture - Death 1.029 (0.8583,1.233) 2.108 (1.762,2.522)
##
## -2 * log-likelihood: 54586hazard.msm(multi.w1)## $ageBase
## HR L U
## Well - Fracture 1.0323 1.0240 1.0407
## Well - Death 1.0881 1.0798 1.0965
## Fracture - Death 1.0875 1.0761 1.0989
##
## $TscoreBase.2
## HR L U
## Well - Fracture 1.57461 1.48892 1.6652
## Well - Death 0.98371 0.93612 1.0337
## Fracture - Death 1.05936 0.98085 1.1442
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.14787 1.05594 1.2478
## Well - Death 1.00053 0.91920 1.0891
## Fracture - Death 0.95368 0.85236 1.0670
##
## $fx50
## HR L U
## Well - Fracture 1.47695 1.36574 1.5972
## Well - Death 1.06175 0.98110 1.1490
## Fracture - Death 0.92777 0.83409 1.0320
##
## $BMI
## HR L U
## Well - Fracture 0.99557 0.98593 1.0053
## Well - Death 0.98749 0.97828 0.9968
## Fracture - Death 0.99061 0.97725 1.0041
##
## $smoke
## HR L U
## Well - Fracture 0.99187 0.91435 1.0760
## Well - Death 1.33793 1.23674 1.4474
## Fracture - Death 1.23152 1.10253 1.3756
##
## $drink.nYes
## HR L U
## Well - Fracture 0.97240 0.89778 1.05323
## Well - Death 0.87206 0.80642 0.94304
## Fracture - Death 0.82871 0.74289 0.92445
##
## $physical
## HR L U
## Well - Fracture 0.83145 0.76596 0.90254
## Well - Death 0.56364 0.52067 0.61016
## Fracture - Death 0.65146 0.58400 0.72672
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.98154 0.89544 1.0759
## Well - Death 1.32238 1.21687 1.4370
## Fracture - Death 1.21217 1.07704 1.3643
##
## $hypertension
## HR L U
## Well - Fracture 1.0552 0.97355 1.1437
## Well - Death 1.3147 1.21761 1.4196
## Fracture - Death 1.2500 1.12304 1.3912
##
## $copd
## HR L U
## Well - Fracture 1.1073 1.00229 1.2234
## Well - Death 1.0425 0.94370 1.1517
## Fracture - Death 1.0283 0.90147 1.1730
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4267 1.2238 1.6632
## Well - Death 1.4256 1.2416 1.6368
## Fracture - Death 1.5372 1.2734 1.8556
##
## $cancer
## HR L U
## Well - Fracture 1.0620 0.96527 1.1683
## Well - Death 1.0565 0.96133 1.1611
## Fracture - Death 1.0078 0.88706 1.1449
##
## $renal
## HR L U
## Well - Fracture 1.0466 0.72943 1.5018
## Well - Death 1.2222 0.88213 1.6934
## Fracture - Death 1.5527 1.02521 2.3516
##
## $parkinson
## HR L U
## Well - Fracture 2.0855 1.35584 3.2077
## Well - Death 1.2954 0.76264 2.2004
## Fracture - Death 0.9511 0.57025 1.5863
##
## $depression
## HR L U
## Well - Fracture 1.1248 0.97986 1.2911
## Well - Death 1.0286 0.89381 1.1838
## Fracture - Death 1.0289 0.85827 1.2335
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3693 1.2641 1.4833
## Well - Death 3.3697 3.0707 3.6978
## Fracture - Death 2.1078 1.7618 2.5218Age and FNBMD at fracture time (other covariates at baseline):
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 -0.06418 (-0.06626,-0.06217)
## Well - Fracture 0.03433 ( 0.03291, 0.03581) 1.033 (1.024,1.041)
## Well - Death 0.02985 ( 0.02844, 0.03133) 1.089 (1.081,1.098)
## Fracture - Fracture -0.03961 (-0.04417,-0.03553)
## Fracture - Death 0.03961 ( 0.03553, 0.04417) 1.104 (1.094,1.113)
## Tscore.2 fall.yesnoYes
## Well - Well
## Well - Fracture 1.5688 (1.4833,1.659) 1.1416 (1.0499,1.241)
## Well - Death 0.9819 (0.9343,1.032) 1.0007 (0.9192,1.090)
## Fracture - Fracture
## Fracture - Death 1.0671 (0.9895,1.151) 0.9603 (0.8576,1.075)
## fx50 BMI
## Well - Well
## Well - Fracture 1.479 (1.3670,1.599) 0.9952 (0.9856,1.0050)
## Well - Death 1.058 (0.9774,1.145) 0.9882 (0.9789,0.9975)
## Fracture - Fracture
## Fracture - Death 1.021 (0.9176,1.136) 0.9868 (0.9735,1.0003)
## smoke drink.nYes
## Well - Well
## Well - Fracture 0.9957 (0.9178,1.080) 0.9716 (0.8969,1.0525)
## Well - Death 1.3477 (1.2456,1.458) 0.8734 (0.8075,0.9447)
## Fracture - Fracture
## Fracture - Death 1.2864 (1.1512,1.438) 0.8076 (0.7236,0.9014)
## physical cvd.nYes
## Well - Well
## Well - Fracture 0.8326 (0.7668,0.9039) 0.9804 (0.8941,1.075)
## Well - Death 0.5689 (0.5255,0.6160) 1.3206 (1.2150,1.436)
## Fracture - Fracture
## Fracture - Death 0.6357 (0.5702,0.7087) 1.2400 (1.1022,1.395)
## hypertension copd
## Well - Well
## Well - Fracture 1.056 (0.9743,1.145) 1.105 (1.0000,1.221)
## Well - Death 1.306 (1.2093,1.411) 1.048 (0.9484,1.158)
## Fracture - Fracture
## Fracture - Death 1.267 (1.1385,1.409) 1.030 (0.9033,1.175)
## diabetes.nYes cancer
## Well - Well
## Well - Fracture 1.422 (1.220,1.659) 1.063 (0.9661,1.170)
## Well - Death 1.433 (1.248,1.646) 1.061 (0.9655,1.166)
## Fracture - Fracture
## Fracture - Death 1.570 (1.299,1.897) 1.079 (0.9492,1.227)
## renal parkinson
## Well - Well
## Well - Fracture 1.050 (0.7314,1.506) 2.092 (1.3600,3.218)
## Well - Death 1.229 (0.8876,1.703) 1.305 (0.7692,2.214)
## Fracture - Fracture
## Fracture - Death 1.760 (1.1605,2.668) 1.098 (0.6580,1.833)
## depression timeperiod[5,Inf)
## Well - Well
## Well - Fracture 1.122 (0.9774,1.289) 1.373 (1.267,1.487)
## Well - Death 1.033 (0.8978,1.189) 3.397 (3.094,3.730)
## Fracture - Fracture
## Fracture - Death 1.077 (0.8972,1.292) 1.399 (1.166,1.680)
##
## -2 * log-likelihood: 54080hazard.msm(multi.w2)## $age
## HR L U
## Well - Fracture 1.0326 1.0242 1.0410
## Well - Death 1.0894 1.0810 1.0979
## Fracture - Death 1.1038 1.0943 1.1133
##
## $Tscore.2
## HR L U
## Well - Fracture 1.56884 1.48333 1.6593
## Well - Death 0.98191 0.93431 1.0319
## Fracture - Death 1.06713 0.98952 1.1508
##
## $fall.yesnoYes
## HR L U
## Well - Fracture 1.1416 1.04986 1.2413
## Well - Death 1.0007 0.91917 1.0895
## Fracture - Death 0.9603 0.85759 1.0753
##
## $fx50
## HR L U
## Well - Fracture 1.4786 1.36704 1.5993
## Well - Death 1.0580 0.97738 1.1452
## Fracture - Death 1.0209 0.91760 1.1359
##
## $BMI
## HR L U
## Well - Fracture 0.99522 0.98556 1.00497
## Well - Death 0.98818 0.97894 0.99752
## Fracture - Death 0.98678 0.97345 1.00029
##
## $smoke
## HR L U
## Well - Fracture 0.9957 0.91777 1.0802
## Well - Death 1.3477 1.24555 1.4583
## Fracture - Death 1.2864 1.15120 1.4376
##
## $drink.nYes
## HR L U
## Well - Fracture 0.97158 0.89687 1.05251
## Well - Death 0.87344 0.80751 0.94474
## Fracture - Death 0.80762 0.72357 0.90143
##
## $physical
## HR L U
## Well - Fracture 0.83255 0.76682 0.90392
## Well - Death 0.56894 0.52546 0.61602
## Fracture - Death 0.63574 0.57025 0.70875
##
## $cvd.nYes
## HR L U
## Well - Fracture 0.98036 0.89412 1.0749
## Well - Death 1.32065 1.21497 1.4355
## Fracture - Death 1.23997 1.10224 1.3949
##
## $hypertension
## HR L U
## Well - Fracture 1.0562 0.97428 1.1451
## Well - Death 1.3061 1.20933 1.4107
## Fracture - Death 1.2667 1.13851 1.4094
##
## $copd
## HR L U
## Well - Fracture 1.1050 1.00001 1.2211
## Well - Death 1.0477 0.94835 1.1575
## Fracture - Death 1.0304 0.90329 1.1754
##
## $diabetes.nYes
## HR L U
## Well - Fracture 1.4224 1.2197 1.6589
## Well - Death 1.4335 1.2484 1.6460
## Fracture - Death 1.5700 1.2990 1.8975
##
## $cancer
## HR L U
## Well - Fracture 1.0630 0.96608 1.1697
## Well - Death 1.0612 0.96550 1.1664
## Fracture - Death 1.0792 0.94918 1.2270
##
## $renal
## HR L U
## Well - Fracture 1.0496 0.73143 1.5061
## Well - Death 1.2295 0.88761 1.7030
## Fracture - Death 1.7597 1.16055 2.6682
##
## $parkinson
## HR L U
## Well - Fracture 2.0919 1.3600 3.2176
## Well - Death 1.3051 0.7692 2.2145
## Fracture - Death 1.0983 0.6580 1.8331
##
## $depression
## HR L U
## Well - Fracture 1.1223 0.97743 1.2887
## Well - Death 1.0333 0.89783 1.1892
## Fracture - Death 1.0766 0.89716 1.2920
##
## $`timeperiod[5,Inf)`
## HR L U
## Well - Fracture 1.3726 1.2669 1.4872
## Well - Death 3.3973 3.0942 3.7300
## Fracture - Death 1.3992 1.1656 1.67962.3.4 Transition risks
# 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 0.98955 0.0033404 0.0071075
## Fracture 0.00000 0.9905056 0.0094944
## Death 0.00000 0.0000000 1.0000000 pmatrix.msm(multi.w2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -1.5), 2)## Well Fracture Death
## Well 0.91466 0.018168 0.067176
## Fracture 0.00000 0.946187 0.053813
## 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 0.79179 0.03606 0.17215
## Fracture 0.00000 0.88510 0.11490
## Death 0.00000 0.00000 1.00000# Osteoporosis:
pmatrix.msm(multi.w2, t = 1, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)## Well Fracture Death
## Well 0.99063 0.002131 0.0072356
## Fracture 0.00000 0.991100 0.0088998
## Death 0.00000 0.000000 1.0000000 pmatrix.msm(multi.w2, t = 5, ci = "none", covariates = list(age = 60, Tscore.2 = -2.5), 2)## Well Fracture Death
## Well 0.91992 0.011636 0.068442
## Fracture 0.00000 0.949485 0.050515
## 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 0.80128 0.023216 0.17551
## Fracture 0.00000 0.891921 0.10808
## 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 0.99006 0.0022639 0.0076772
## Fracture 0.00000 0.9903988 0.0096012
## 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 0.91521 0.012318 0.072469
## Fracture 0.00000 0.945595 0.054405
## 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 0.79044 0.02442 0.18514
## Fracture 0.00000 0.88388 0.11612
## Death 0.00000 0.00000 1.000002.3.5 Check the model goodness-of-fit
Model validation
prevalence.msm(multi.w2, times = seq(0,20,1), covariates = "mean", ci = "normal")## $Observed
## State 1 State 2 State 3 Total
## 0 7273 0 0 7273
## 1 6950 246 74 7270
## 2 6623 428 205 7256
## 3 6349 558 342 7249
## 4 5969 729 529 7227
## 5 5616 867 713 7196
## 6 5245 983 934 7162
## 7 4914 1079 1134 7127
## 8 4576 1155 1359 7090
## 9 4216 1216 1591 7023
## 10 3867 1205 1862 6934
## 11 3501 1227 2109 6837
## 12 3137 1202 2422 6761
## 13 2824 1176 2663 6663
## 14 2468 1123 2956 6547
## 15 2171 1086 3206 6463
## 16 1901 1030 3459 6390
## 17 1603 917 3661 6181
## 18 1163 738 3840 5741
## 19 909 626 4034 5569
## 20 381 300 4156 4837
##
## $Expected
## $Expected$estimates
## Well Fracture Death Total
## 0 7273.00 0.00 0.00 7273
## 1 6945.66 205.08 119.26 7270
## 2 6623.01 393.48 239.51 7256
## 3 6321.43 566.78 360.79 7249
## 4 6021.08 724.20 481.72 7227
## 5 5727.78 866.42 601.79 7196
## 6 5180.81 1036.66 944.53 7162
## 7 4685.31 1177.70 1263.98 7127
## 8 4235.90 1292.73 1561.36 7090
## 9 3813.21 1379.22 1830.58 7023
## 10 3421.53 1440.54 2071.93 6934
## 11 3065.98 1481.83 2289.18 6837
## 12 2755.39 1511.92 2493.69 6761
## 13 2467.80 1523.56 2671.64 6663
## 14 2203.69 1519.36 2823.95 6547
## 15 1977.02 1512.71 2973.27 6463
## 16 1776.42 1500.38 3113.20 6390
## 17 1561.61 1449.23 3170.16 6181
## 18 1318.16 1338.76 3084.08 5741
## 19 1162.05 1287.08 3119.87 5569
## 20 917.26 1104.51 2815.23 4837
##
## $Expected$ci
## , , 2.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 7273.00 0.00 0.00 7273
## [2,] 6928.94 192.25 109.61 7270
## [3,] 6591.17 369.35 220.61 7256
## [4,] 6275.90 532.29 332.15 7249
## [5,] 5963.32 680.90 444.46 7227
## [6,] 5659.19 816.01 555.44 7196
## [7,] 5113.85 987.61 898.16 7162
## [8,] 4615.29 1130.26 1216.63 7127
## [9,] 4163.40 1244.31 1508.69 7090
## [10,] 3737.50 1328.71 1773.28 7023
## [11,] 3345.69 1388.04 2010.09 6934
## [12,] 2989.76 1426.29 2223.92 6837
## [13,] 2679.19 1453.71 2425.07 6761
## [14,] 2393.17 1462.67 2600.01 6663
## [15,] 2131.18 1457.53 2747.92 6547
## [16,] 1907.06 1449.58 2894.37 6463
## [17,] 1708.07 1435.61 3031.12 6390
## [18,] 1496.99 1384.22 3088.05 6181
## [19,] 1260.18 1276.64 3006.39 5741
## [20,] 1107.82 1223.27 3042.51 5569
## [21,] 871.95 1047.83 2747.15 4837
##
## , , 97.5%
##
## [,1] [,2] [,3] [,4]
## [1,] 7273.0 0.00 0.00 7273
## [2,] 6961.4 218.90 129.11 7270
## [3,] 6653.1 419.69 258.83 7256
## [4,] 6364.5 604.03 389.47 7249
## [5,] 6075.9 772.41 519.87 7227
## [6,] 5793.0 925.18 648.23 7196
## [7,] 5244.8 1092.43 990.63 7162
## [8,] 4748.5 1232.04 1315.91 7127
## [9,] 4299.9 1347.08 1617.73 7090
## [10,] 3880.2 1434.09 1890.07 7023
## [11,] 3490.8 1498.22 2135.43 6934
## [12,] 3136.3 1541.32 2355.93 6837
## [13,] 2827.3 1573.26 2562.88 6761
## [14,] 2540.9 1586.96 2742.93 6663
## [15,] 2275.6 1584.32 2897.67 6547
## [16,] 2047.3 1581.88 3049.20 6463
## [17,] 1844.5 1572.38 3191.17 6390
## [18,] 1626.8 1521.33 3248.38 6181
## [19,] 1377.7 1407.92 3158.97 5741
## [20,] 1218.0 1355.69 3193.20 5569
## [21,] 964.4 1165.93 2880.80 4837
##
##
##
## $`Observed percentages`
## State 1 State 2 State 3
## 0 100.0000 0.0000 0.0000
## 1 95.5983 3.3838 1.0179
## 2 91.2762 5.8986 2.8252
## 3 87.5845 7.6976 4.7179
## 4 82.5931 10.0872 7.3198
## 5 78.0434 12.0484 9.9083
## 6 73.2337 13.7252 13.0410
## 7 68.9491 15.1396 15.9113
## 8 64.5416 16.2906 19.1678
## 9 60.0313 17.3145 22.6541
## 10 55.7687 17.3781 26.8532
## 11 51.2067 17.9465 30.8469
## 12 46.3985 17.7784 35.8231
## 13 42.3833 17.6497 39.9670
## 14 37.6967 17.1529 45.1505
## 15 33.5912 16.8033 49.6054
## 16 29.7496 16.1189 54.1315
## 17 25.9343 14.8358 59.2299
## 18 20.2578 12.8549 66.8873
## 19 16.3225 11.2408 72.4367
## 20 7.8768 6.2022 85.9210
##
## $`Expected percentages`
## $`Expected percentages`$estimates
## Well Fracture Death
## 0 100.000 0.0000 0.0000
## 1 95.539 2.8209 1.6405
## 2 91.276 5.4228 3.3008
## 3 87.204 7.8187 4.9771
## 4 83.314 10.0207 6.6656
## 5 79.597 12.0403 8.3629
## 6 72.338 14.4744 13.1881
## 7 65.740 16.5245 17.7351
## 8 59.745 18.2332 22.0221
## 9 54.296 19.6385 26.0654
## 10 49.344 20.7751 29.8807
## 11 44.844 21.6737 33.4823
## 12 40.754 22.3623 36.8835
## 13 37.037 22.8659 40.0967
## 14 33.660 23.2070 43.1334
## 15 30.590 23.4057 46.0045
## 16 27.800 23.4801 48.7198
## 17 25.265 23.4465 51.2888
## 18 22.960 23.3193 53.7202
## 19 20.866 23.1115 56.0220
## 20 18.963 22.8346 58.2019
##
## $`Expected percentages`$ci
## , , 2.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.0000 0.0000
## [2,] 95.309 2.6444 1.5077
## [3,] 90.837 5.0903 3.0404
## [4,] 86.576 7.3430 4.5820
## [5,] 82.514 9.4216 6.1500
## [6,] 78.643 11.3397 7.7188
## [7,] 71.402 13.7896 12.5407
## [8,] 64.758 15.8588 17.0707
## [9,] 58.722 17.5502 21.2792
## [10,] 53.218 18.9194 25.2495
## [11,] 48.251 20.0179 28.9890
## [12,] 43.729 20.8613 32.5278
## [13,] 39.627 21.5014 35.8685
## [14,] 35.917 21.9521 39.0216
## [15,] 32.552 22.2625 41.9722
## [16,] 29.507 22.4288 44.7837
## [17,] 26.730 22.4666 47.4353
## [18,] 24.219 22.3947 49.9604
## [19,] 21.950 22.2372 52.3669
## [20,] 19.893 21.9657 54.6329
## [21,] 18.027 21.6628 56.7944
##
## , , 97.5%
##
## [,1] [,2] [,3]
## [1,] 100.000 0.0000 0.0000
## [2,] 95.755 3.0110 1.7759
## [3,] 91.691 5.7840 3.5671
## [4,] 87.799 8.3325 5.3727
## [5,] 84.072 10.6878 7.1934
## [6,] 80.504 12.8569 9.0082
## [7,] 73.231 15.2532 13.8318
## [8,] 66.626 17.2869 18.4637
## [9,] 60.647 18.9998 22.8170
## [10,] 55.250 20.4200 26.9126
## [11,] 50.344 21.6068 30.7965
## [12,] 45.872 22.5438 34.4586
## [13,] 41.818 23.2696 37.9068
## [14,] 38.135 23.8175 41.1667
## [15,] 34.758 24.1992 44.2595
## [16,] 31.677 24.4760 47.1794
## [17,] 28.865 24.6068 49.9401
## [18,] 26.319 24.6130 52.5543
## [19,] 23.997 24.5240 55.0247
## [20,] 21.871 24.3435 57.3389
## [21,] 19.938 24.1044 59.5575plot.prevalence.msm(multi.w2, mintime = 0, maxtime = 20, legend.pos = c(10, 80), col.obs = "gray",
col.exp = "black")
Diagnostic plots for survival
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)")