simsurv is an R package that allows the user to simulate survival times from standard parametric survival distributions (exponential, Weibull, and Gompertz), 2-component mixture distributions, or a user-defined hazard function, log hazard function, cumulative hazard function, or log cumulative hazard function. Baseline covariates can be included under a proportional hazards assumption. Time dependent effects (i.e. non-proportional hazards) can be included by interacting covariates with linear time or some transformation of time.
Under the 2-component mixture distributions the baseline survival at time t is taken to be S(t) = p x S_1(t) + (1 - p) x S_2(t) where S_1(t) and S_2(t) are the baseline survival under each component of the mixture distribution and p is the mixing parameter. Each component of the mixture distribution is assumed to be either exponential, Weibull or Gompertz. The 2-component mixture distributions can allow for a variety of flexible baseline hazard functions (see Crowther and Lambert (2013) for some examples).
If the user wishes to provide a user-defined [log] [cumulative] hazard function (instead of using one of the standard parametric survival distributions) then this is also possible. If a user-defined hazard or log hazard function is specified, then this is allowed to be time-dependent, and the resulting cumulative hazard function does not need to have a closed-form solution. The survival times are generated using the approach described in Crowther and Lambert (2013), whereby the cumulative hazard is evaluated using numerical quadrature and survival times are generated using an iterative algorithm which nests the quadrature-based evaluation of the cumulative hazard inside Brent’s (1973) univariate root finder. Not requiring a closed form solution to the cumulative hazard function has the benefit that survival times can be generated for complex models such as flexible (spline-based) baseline hazards or under joint longitudinal and survival models; the package documentation and vignettes provide examples of this.
For further details on the underlying methodology and examples of usage, please see the package vignettes (available here).
Note that this package is modelled on the user-written survsim package available in the Stata software (see Crowther and Lambert (2012)).
Note: Please note that the version available on GitHub is the most
up-to-date development version of the package. A stable version of the
package is available from the Comprehensive R Archive Network (CRAN);
type install.packages("simsurv") into your R session to download it.
You can install the simsurv package directly from CRAN. Just type the following into your R session console:
install.packages("simsurv")If, for some reason, you wish to download the development version from GitHub, then this can be done easily using the devtools package. To do this you should first check you have devtools installed by executing the following commands from within your R session:
if (!require(devtools)) {
install.packages("devtools")
}Then execute the following commands to install simsurv:
library(devtools)
install_github("sambrilleman/simsurv")Please also see the package vignettes for more detailed examples and a description of the methodology underpinning the simsurv package.
Generate times from a Weibull model including a binary treatment variable, with log hazard ratio of -0.5, and censoring after 5 years:
set.seed(13579)
covs <- data.frame(id = 1:1000, trt = stats::rbinom(1000, 1L, 0.5))
s1 <- simsurv(lambdas = 0.1, gammas = 1.5,
x = covs, betas = c(trt = -0.5), maxt = 5)
head(s1)
#> id eventtime status
#> 1 1 5.000000 0
#> 2 2 5.000000 0
#> 3 3 2.805715 1
#> 4 4 5.000000 0
#> 5 5 5.000000 0
#> 6 6 2.276330 1Generate times from a Gompertz model:
s2 <- simsurv(dist = "gompertz", lambdas = 0.1, gammas = 0.05, x = covs)Generate times from a 2-component mixture Weibull model:
s3 <- simsurv(lambdas = c(0.1, 0.05), gammas = c(1, 1.5),
mixture = TRUE, pmix = 0.5, x = covs, maxt = 5)Generate times from user-defined log hazard function:
fn <- function(t, x, betas, ...)
(-1 + 0.02 * t - 0.03 * t ^ 2 + 0.005 * t ^ 3)
s4 <- simsurv(loghazard = fn, x = covs, maxt = 1.5)In this section we present an example showing how the simsurv package’s main function can be used to simulate survival times based on a joint longitudinal and survival model. (In most instances, simulating survival times from a joint longitudinal and survival model can pose difficulties since time-dependency in the hazard function leads to there not being a general closed form solution to the integral when evaluating the cumulative hazard).
First we define the hazard function to pass to simsurv. This function
must be defined by the user and must use three named arguments: t,
which is the time variable; x, which is a data frame with each row
containing the covariate values for one individual; betas, which is a
data frame with each row containing the “true” parameter values for one
individual. The function must return the hazard evaluated at time t.
We will define the hazard function for a Weibull proportional hazards
regression submodel from a joint longitudinal and survival model with a
so-called “current value” association structure, where the hazard at
time t depends on the expected value of the longitudinal outcome also
evaluated at time t.
haz <- function(t, x, betas, ...) {
betas[["shape"]] * (t ^ (betas[["shape"]] - 1)) * exp(
betas[["betaEvent_intercept"]] +
betas[["betaEvent_binary"]] * x[["Z1"]] +
betas[["betaEvent_continuous"]] * x[["Z2"]] +
betas[["betaEvent_assoc"]] * (
betas[["betaLong_intercept"]] +
betas[["betaLong_slope"]] * t +
betas[["betaLong_binary"]] * x[["Z1"]] +
betas[["betaLong_continuous"]] * x[["Z2"]]
)
)
}Then we construct data frames with the true parameter values and the covariate data for each individual:
set.seed(5454) # set seed before simulating data
N <- 20 # number of individuals
# Population (fixed effect) parameters
betas <- data.frame(
shape = rep(2, N),
betaEvent_intercept = rep(-11.9,N),
betaEvent_binary = rep(0.6, N),
betaEvent_continuous = rep(0.08, N),
betaEvent_assoc = rep(0.03, N),
betaLong_binary = rep(-1.5, N),
betaLong_continuous = rep(1, N),
betaLong_intercept = rep(90, N),
betaLong_slope = rep(2.5, N)
)
# Individual-specific (random effect) parameters
b_corrmat <- matrix(c(1, 0.5, 0.5, 1), 2, 2)
b_sds <- c(20, 3)
b_means <- rep(0, 2)
b_z <- MASS::mvrnorm(n = N, mu = b_means, Sigma = b_corrmat)
b <- sapply(1:length(b_sds), function(x) b_sds[x] * b_z[,x])
betas$betaLong_intercept <- betas$betaLong_intercept + b[,1]
betas$betaLong_slope <- betas$betaLong_slope + b[,2]
# Covariate data
covs <- data.frame(
Z1 = rbinom(N, 1, 0.45), # a binary covariate
Z2 = rnorm(N, 44, 8.5) # a continuous covariate
)Then we simulate the survival times based on the hazard function (passed
to the hazfn argument), the covariate values for each individual
(passed to the x argument), and true parameter values for each
individual (passed to the betas argument). We will also censor
individuals with survival times greater than 10 years (or whatever time
units we have assumed to be using) by specifying the maxt argument:
s1 <- simsurv(hazard = haz, x = covs, betas = betas, maxt = 10)
head(s1)
#> id eventtime status
#> 1 1 4.328229 1
#> 2 2 8.630500 1
#> 3 3 4.608717 1
#> 4 4 1.638580 1
#> 5 5 3.183835 1
#> 6 6 7.715658 1If you find any bugs, please file an issue on GitHub.
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Brilleman SL, Wolfe R, Moreno-Betancur M, and Crowther MJ. Simulating survival data using the simsurv R package. Journal of Statistical Software 2021; 96(9), 1–27. doi:10.18637/jss.v097.i03. https://www.jstatsoft.org/article/view/v097i03
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Crowther MJ, and Lambert PC. Simulating biologically plausible complex survival data. Statistics in Medicine 2013; 32, 4118–4134. doi:10.1002/sim.5823
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Bender R, Augustin T, and Blettner M. Generating survival times to simulate Cox proportional hazards models. Statistics in Medicine 2005; 24(11), 1713–1723.
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Brent R. (1973) Algorithms for Minimization without Derivatives. Englewood Cliffs, NJ: Prentice-Hall.
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Crowther MJ, and Lambert PC. Simulating complex survival data. The Stata Journal 2012; 12(4), 674–687. https://www.stata-journal.com/sjpdf.html?articlenum=st0275