Simulated data under Weibull model with Time-Dependent Treatment Effect

This simulated data is and description is taken verbatim from the simsurv.

simdat

Format

A dataframe with 1000 observations and 4 variables:

id

patient id

eventtime

time of event

status

event indicator (1 = event, 0 = censored)

trt

binary treatment indicator

Source

See simsurv vignette: https://cran.r-project.org/package=simsurv/vignettes/simsurv_usage.html

Details

Simulated data under a standard Weibull survival model that incorporates a time-dependent treatment effect (i.e. non-proportional hazards). For the time-dependent effect we included a single binary covariate (e.g. a treatment indicator) with a protective effect (i.e. a negative log hazard ratio), but we will allow the effect of the covariate to diminish over time. The data generating model will be $$h_i(t) = \gamma \lambda (t ^{\gamma - 1}) exp(\beta_0 X_i + \beta_1 X_i x log(t))$$ where where Xi is the binary treatment indicator for individual i, \(\lambda\) and \(\gamma\) are the scale and shape parameters for the Weibull baseline hazard, \(\beta_0\) is the log hazard ratio for treatment when t=1 (i.e. when log(t)=0), and \(\beta_1\) quantifies the amount by which the log hazard ratio for treatment changes for each one unit increase in log(t). Here we are assuming the time-dependent effect is induced by interacting the log hazard ratio with log time. The true parameters are 1. \(\beta_0\) = -0.5 2. \(\beta_1\) = 0.15 3. \(\lambda\) = 0.1 4. \(\gamma\) = 1.5

References

Sam Brilleman (2019). simsurv: Simulate Survival Data. R package version 0.2.3. https://CRAN.R-project.org/package=simsurv

Examples

if (requireNamespace("splines", quietly = TRUE)) {
library(splines)
data("simdat")
mod_cb <- casebase::fitSmoothHazard(status ~ trt + ns(log(eventtime),
                                                      df = 3) +
                                   trt:ns(log(eventtime),df=1),
                                   time = "eventtime",
                                   data = simdat,
                                   ratio = 1)
}