sim_survival
Yunqi Yang
2/1/2023
Last updated: 2023-02-09
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. Let’s first simulate data without censoring. The full explanation about simulation is at: https://yunqiyang0215.github.io/survival-susie/sim_survival.html
Here I try different correlations between \(x_1\) and \(x_2\) where \(x_1\) has an effect on survival time, and \(x_2\) doesn’t have. That is, the true model is: \(\log T_i = \beta_0+\beta_1x_{i1} +\epsilon_i\).
Results: (1) For r = 0.9, and r = 0.8. Susie seems work marginally. (2) For r = 0.7, Susie gives rediculous results. Seems something wrong in the code.
library(mvtnorm)
library(survival)
# Modified Karl's code for intercept part
devtools::load_all("/Users/nicholeyang/Desktop/logisticsusie")ℹ Loading logisticsusieSimulation functions:
# Here we use parametric model to simulate data with survival time,
# assuming survival time is exponentially distributed.
# We first simulate the mean of exponential from linear combinations
# of variables, and then simulate survival time.
# T\sim 1/u*exp(-t/u), and the true model is:
# log(T) = \mu + e = b0 + Xb + e
# @param b: vector of length (p+1) for true effect size, include intercept.
# @param X: variable matrix of size n by p.
# @param status: censoring status. 1 = censored, 2 = event observed.
sim_dat <- function(b, X){
n = nrow(X)
mu <- exp(cbind(rep(1,n), X) %*% b)
surT <- rexp(n, rate = 1/mu)
dat <- data.frame(cbind(surT, X))
names(dat) = c("surT", "x1", "x2")
dat$status <- rep(2, n)
return(dat)
}Functions for running IBSS
# Function to calculate approximate BF based on Wakefield approximation
# @param z: zscore of the regression coefficient
# @param s: standard deviation of the estimated coefficient
compute_abf <- function(z, s, prior_variance){
abf <- sqrt(s^2/(s^2+prior_variance))*exp(z^2/2*(prior_variance/(s^2+prior_variance)))
return(abf)
}
compute_approx_post_var <- function(z, s, prior_variance){
post_var <- 1/(1/s^2 + 1/prior_variance)
return(post_var)
}
# @param post_var: posterior variance
# @param s: standard deviation of the estimated coefficient
# @param bhat: estimated beta effect
compute_approx_post_mean <- function(post_var, s, bhat){
mu <- post_var/(s^2)*bhat
return(mu)
}surv_uni_fun <- function(x, y, o, prior_variance, estimate_intercept = 0, ...){
fit <- coxph(y~ x + o)
bhat <- summary(fit)$coefficients[1, 1]
sd <- summary(fit)$coefficients[1, 3]
zscore <- summary(fit)$coefficients[1, 4]
bf <- compute_abf(zscore, sd, prior_variance)
var <- compute_approx_post_var(zscore, sd, prior_variance)
mu <- compute_approx_post_mean(var, sd, bhat)
lbf <- log(bf)
return(list(mu = mu, var=var, lbf=lbf, intercept=0))
}
fit_coxph <- ser_from_univariate(surv_uni_fun)Sim1: r = 0.9.
set.seed(2)
r = 0.9
n <- 50
b <- c(1, 3, 0)
X <- rmvnorm(n, sigma = matrix(c(1, r, r, 1), ncol = 2, nrow = 2))
dat <- sim_dat(b, X)
hist(dat$surT, breaks = 20)
# Fit cox ph
## Create survival object. status == 2 is death
dat$y <- with(dat, Surv(surT, status == 2))
cox <- coxph(y ~ x1 + x2, data = dat)
summary(cox)Call:
coxph(formula = y ~ x1 + x2, data = dat)
n= 50, number of events= 50
coef exp(coef) se(coef) z Pr(>|z|)
x1 -2.55832 0.07743 0.44590 -5.737 9.61e-09 ***
x2 -0.43372 0.64809 0.32930 -1.317 0.188
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
x1 0.07743 12.914 0.03231 0.1856
x2 0.64809 1.543 0.33989 1.2358
Concordance= 0.902 (se = 0.021 )
Likelihood ratio test= 102.1 on 2 df, p=<2e-16
Wald test = 54.51 on 2 df, p=1e-12
Score (logrank) test = 73.13 on 2 df, p=<2e-16X = as.matrix(dat[, c(2:3)])
y = dat$y
fit <- ibss_from_ser(X, y, L = 10, prior_variance = 1., prior_weights = rep(1/2, 2), tol = 1e-3, maxit = 100, estimate_intercept = TRUE, ser_function = fit_coxph)4.083 sec elapsedfit$alpha [,1] [,2]
[1,] 0.06669668 0.9333033
[2,] 0.65530739 0.3446926
[3,] 0.65575846 0.3442415
[4,] 0.65615088 0.3438491
[5,] 0.65632170 0.3436783
[6,] 0.65619941 0.3438006
[7,] 0.65583822 0.3441618
[8,] 0.65539917 0.3446008
[9,] 0.65507624 0.3449238
[10,] 0.65500422 0.3449958Sim2: r = 0.8
set.seed(2)
r = 0.8
n <- 50
b <- c(1, 3, 0)
X <- rmvnorm(n, sigma = matrix(c(1, r, r, 1), ncol = 2, nrow = 2))
dat <- sim_dat(b, X)
hist(dat$surT, breaks = 20)
# Fit cox ph
## Create survival object. status == 2 is death
dat$y <- with(dat, Surv(surT, status == 2))
cox <- coxph(y ~ x1 + x2, data = dat)
summary(cox)Call:
coxph(formula = y ~ x1 + x2, data = dat)
n= 50, number of events= 50
coef exp(coef) se(coef) z Pr(>|z|)
x1 -2.70130 0.06712 0.40618 -6.651 2.92e-11 ***
x2 -0.37518 0.68717 0.23165 -1.620 0.105
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
x1 0.06712 14.899 0.03028 0.1488
x2 0.68717 1.455 0.43639 1.0821
Concordance= 0.898 (se = 0.023 )
Likelihood ratio test= 101.5 on 2 df, p=<2e-16
Wald test = 53.8 on 2 df, p=2e-12
Score (logrank) test = 73.14 on 2 df, p=<2e-16X = as.matrix(dat[, c(2:3)])
y = dat$y
fit <- ibss_from_ser(X, y, L = 10, prior_variance = 1., prior_weights = rep(1/2, 2), tol = 1e-3, maxit = 100, estimate_intercept = TRUE, ser_function = fit_coxph)4.654 sec elapsedfit$alpha [,1] [,2]
[1,] 0.05557329 0.9444267
[2,] 0.73050163 0.2694984
[3,] 0.73079335 0.2692067
[4,] 0.73119270 0.2688073
[5,] 0.73153210 0.2684679
[6,] 0.73167064 0.2683294
[7,] 0.73154912 0.2684509
[8,] 0.73121998 0.2687800
[9,] 0.73083015 0.2691698
[10,] 0.73055282 0.2694472Sim3: r = 0.7
set.seed(2)
r = 0.7
n <- 50
b <- c(1, 3, 0)
X <- rmvnorm(n, sigma = matrix(c(1, r, r, 1), ncol = 2, nrow = 2))
dat <- sim_dat(b, X)
hist(dat$surT, breaks = 20)
# Fit cox ph
## Create survival object. status == 2 is death
dat$y <- with(dat, Surv(surT, status == 2))
cox <- coxph(y ~ x1 + x2, data = dat)
summary(cox)Call:
coxph(formula = y ~ x1 + x2, data = dat)
n= 50, number of events= 50
coef exp(coef) se(coef) z Pr(>|z|)
x1 -2.63840 0.07148 0.37615 -7.014 2.31e-12 ***
x2 -0.37759 0.68551 0.20131 -1.876 0.0607 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
x1 0.07148 13.991 0.0342 0.1494
x2 0.68551 1.459 0.4620 1.0171
Concordance= 0.888 (se = 0.021 )
Likelihood ratio test= 99.48 on 2 df, p=<2e-16
Wald test = 54.83 on 2 df, p=1e-12
Score (logrank) test = 73.46 on 2 df, p=<2e-16X = as.matrix(dat[, c(2:3)])
y = dat$y
fit <- ibss_from_ser(X, y, L = 10, prior_variance = 1., prior_weights = rep(1/2, 2), tol = 1e-3, maxit = 100, estimate_intercept = TRUE, ser_function = fit_coxph)0.198 sec elapsedfit$alpha [,1] [,2]
[1,] 1 3.208481e-11
[2,] 1 3.208481e-11
[3,] 1 3.208481e-11
[4,] 1 3.208481e-11
[5,] 1 3.208481e-11
[6,] 1 3.208481e-11
[7,] 1 3.208481e-11
[8,] 1 3.208481e-11
[9,] 1 3.208481e-11
[10,] 1 3.208481e-11
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] logisticsusie_0.0.0.9004 testthat_3.1.0 survival_3.2-11
[4] mvtnorm_1.1-3 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] tidyselect_1.1.1 xfun_0.27 bslib_0.4.1 remotes_2.4.1
[5] purrr_0.3.4 splines_4.1.1 lattice_0.20-44 generics_0.1.2
[9] vctrs_0.3.8 usethis_2.1.3 htmltools_0.5.2 yaml_2.2.1
[13] utf8_1.2.2 rlang_1.0.6 pkgbuild_1.2.0 jquerylib_0.1.4
[17] later_1.3.0 pillar_1.6.4 glue_1.4.2 withr_2.5.0
[21] sessioninfo_1.1.1 matrixStats_0.63.0 lifecycle_1.0.1 stringr_1.4.0
[25] tictoc_1.1 devtools_2.4.2 evaluate_0.14 memoise_2.0.1
[29] knitr_1.36 callr_3.7.0 fastmap_1.1.0 httpuv_1.6.3
[33] ps_1.6.0 fansi_0.5.0 highr_0.9 Rcpp_1.0.8.3
[37] promises_1.2.0.1 cachem_1.0.6 desc_1.4.0 pkgload_1.2.3
[41] jsonlite_1.7.2 fs_1.5.0 digest_0.6.28 stringi_1.7.5
[45] dplyr_1.0.7 processx_3.5.2 rprojroot_2.0.2 grid_4.1.1
[49] cli_3.1.0 tools_4.1.1 magrittr_2.0.1 sass_0.4.4
[53] tibble_3.1.5 crayon_1.4.1 whisker_0.4 pkgconfig_2.0.3
[57] ellipsis_0.3.2 Matrix_1.5-3 prettyunits_1.1.1 rmarkdown_2.11
[61] rstudioapi_0.13 R6_2.5.1 git2r_0.28.0 compiler_4.1.1