sim_survival
Yunqi Yang
2/1/2023
Last updated: 2023-02-05
Checks: 7 0
Knit directory: survival-susie/
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Description:
Simulate time-to-event data based on exponential model. And fit proportional hazard model to data.
library(mvtnorm)
library(EnvStats)
Attaching package: 'EnvStats'The following objects are masked from 'package:stats':
predict, predict.lmThe following object is masked from 'package:base':
print.defaultlibrary(survival)# Function to construct block like covariance matrix.
# x1 and x2 are correlated; x3, x4 correlated and x5, x6 correlated
block_cov <- function(r = c(0.98, 0.8, 0.5)){
cov = matrix(0, ncol = 6, nrow = 6)
diag(cov[2:6, 1:5]) = diag(cov[1:5, 2:6]) = c(r[1], 0, r[2], 0, r[3])
diag(cov) = rep(1, 6)
return(cov)
}
# Here I simulate 6 variables from Gaussian,
# using block like covariance matrix.
# @param n: sample size
sim_X <- function(n, cov){
X <- rmvnorm(n, sigma = cov)
return(X)
}
# Here we use parametric model to simulate data with survival time,
# assuming survival time is exponentially distributed.
# T\sim 1/u*exp(-t/u), and the true model is:
# log(T) = b0 + b1*x1 + b3*x3 + b5*x5 + e.
# e\sim extreme value distribution, f(e) = exp(e)*exp(-exp(e))
# @param b: vector of length (p+1) for true effect size, include intercept.
# @param X: variable matrix of size n by p.
sim_dat <- function(b, X){
n = nrow(X)
e = -revd(n, location = 0, scale = 1)
log_surT <- cbind(rep(1,n), X) %*% b + e
surT <- exp(log_surT)
dat <- data.frame(cbind(surT, X))
names(dat) = c("surT", "x1", "x2", "x3", "x4","x5", "x6")
return(dat)
}set.seed(1)
n = 50
cov <- block_cov()
print(cov) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00 0.98 0.0 0.0 0.0 0.0
[2,] 0.98 1.00 0.0 0.0 0.0 0.0
[3,] 0.00 0.00 1.0 0.8 0.0 0.0
[4,] 0.00 0.00 0.8 1.0 0.0 0.0
[5,] 0.00 0.00 0.0 0.0 1.0 0.5
[6,] 0.00 0.00 0.0 0.0 0.5 1.0X <- sim_X(n, cov)
dat <- sim_dat(b = c(0.5, 3, 0, 2, 0, 2, 0), X)
head(dat) surT x1 x2 x3 x4 x5
1 0.12938514 -0.3688273 -0.2542623 -0.03397769 1.05315805 0.1059272
2 74.28497285 0.8446532 0.8801352 0.37842066 -0.01565043 1.5611673
3 0.12629957 -1.8825864 -2.1079356 0.98607388 0.46289456 0.2286442
4 42.42740818 1.0117009 0.9795530 1.17174034 1.11054315 -0.4428579
5 0.01542759 0.4443932 0.3487988 -0.79708820 -1.38515479 -0.3536863
6 0.08744163 0.9869396 0.7802569 0.32268168 0.12524732 -1.4375459
x6
1 -0.7072287
2 0.7678374
3 0.9074854
4 -1.9022673
5 0.2799462
6 -0.7572632dat$status <- rep(2, n)hist(dat$surT, breaks = 20)
## Add survival object. status == 2 is death
dat$SurvObj <- with(dat, Surv(surT, status == 2))
## Check data
head(dat) surT x1 x2 x3 x4 x5
1 0.12938514 -0.3688273 -0.2542623 -0.03397769 1.05315805 0.1059272
2 74.28497285 0.8446532 0.8801352 0.37842066 -0.01565043 1.5611673
3 0.12629957 -1.8825864 -2.1079356 0.98607388 0.46289456 0.2286442
4 42.42740818 1.0117009 0.9795530 1.17174034 1.11054315 -0.4428579
5 0.01542759 0.4443932 0.3487988 -0.79708820 -1.38515479 -0.3536863
6 0.08744163 0.9869396 0.7802569 0.32268168 0.12524732 -1.4375459
x6 status SurvObj
1 -0.7072287 2 0.12938514
2 0.7678374 2 74.28497285
3 0.9074854 2 0.12629957
4 -1.9022673 2 42.42740818
5 0.2799462 2 0.01542759
6 -0.7572632 2 0.08744163saveRDS(dat, "./data/sim1.rds")Cox regression using coxph
## Fit Cox regression
res.cox <- coxph(SurvObj ~ x1 + x2 + x3 + x4 + x5 + x6, data = dat)
res.coxCall:
coxph(formula = SurvObj ~ x1 + x2 + x3 + x4 + x5 + x6, data = dat)
coef exp(coef) se(coef) z p
x1 -3.22922 0.03959 1.03367 -3.124 0.00178
x2 0.34129 1.40675 0.96286 0.354 0.72300
x3 -1.92631 0.14569 0.35632 -5.406 6.44e-08
x4 -0.39133 0.67616 0.25498 -1.535 0.12484
x5 -2.67193 0.06912 0.45889 -5.823 5.79e-09
x6 0.02514 1.02546 0.25402 0.099 0.92115
Likelihood ratio test=116.8 on 6 df, p=< 2.2e-16
n= 50, number of events= 50 res.cox2 <- coxph(SurvObj ~ x2, data = dat)
res.cox2Call:
coxph(formula = SurvObj ~ x2, data = dat)
coef exp(coef) se(coef) z p
x2 -0.8959 0.4082 0.1985 -4.514 6.36e-06
Likelihood ratio test=21.14 on 1 df, p=4.265e-06
n= 50, number of events= 50 res.cox3 <- coxph(SurvObj ~ x1, data = dat)
res.cox3Call:
coxph(formula = SurvObj ~ x1, data = dat)
coef exp(coef) se(coef) z p
x1 -0.8410 0.4313 0.2049 -4.104 4.06e-05
Likelihood ratio test=18.67 on 1 df, p=1.553e-05
n= 50, number of events= 50
sessionInfo()R version 4.1.1 (2021-08-10)
Platform: x86_64-apple-darwin20.6.0 (64-bit)
Running under: macOS Monterey 12.0.1
Matrix products: default
BLAS: /usr/local/Cellar/openblas/0.3.18/lib/libopenblasp-r0.3.18.dylib
LAPACK: /usr/local/Cellar/r/4.1.1_1/lib/R/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] survival_3.2-11 EnvStats_2.7.0 mvtnorm_1.1-3 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] Rcpp_1.0.8.3 highr_0.9 pillar_1.6.4 compiler_4.1.1
[5] bslib_0.4.1 later_1.3.0 jquerylib_0.1.4 git2r_0.28.0
[9] tools_4.1.1 digest_0.6.28 lattice_0.20-44 jsonlite_1.7.2
[13] evaluate_0.14 lifecycle_1.0.1 tibble_3.1.5 pkgconfig_2.0.3
[17] rlang_1.0.6 Matrix_1.5-3 cli_3.1.0 rstudioapi_0.13
[21] yaml_2.2.1 xfun_0.27 fastmap_1.1.0 stringr_1.4.0
[25] knitr_1.36 fs_1.5.0 vctrs_0.3.8 sass_0.4.4
[29] grid_4.1.1 rprojroot_2.0.2 glue_1.4.2 R6_2.5.1
[33] fansi_0.5.0 rmarkdown_2.11 magrittr_2.0.1 whisker_0.4
[37] splines_4.1.1 promises_1.2.0.1 ellipsis_0.3.2 htmltools_0.5.2
[41] httpuv_1.6.3 utf8_1.2.2 stringi_1.7.5 cachem_1.0.6
[45] crayon_1.4.1