Simulating Survival Data

Survival Analysis

simulation

inverse-hazard

Generating realistic censored time-to-event datasets for power analysis and method validation

Published

April 17, 2026

Introduction

Simulating censored time-to-event data is essential for three classes of work: power and sample-size calculations for trials with non-standard designs, validation of new statistical methods (does the estimator recover the truth?), and pedagogy. The inverse-hazard method generates event times from any specified hazard function and lets you build realistic datasets that match a target survival pattern, censoring distribution, and covariate-effect structure.

Prerequisites

A working understanding of hazard and cumulative hazard functions, the inverse-CDF method for random-number generation, and the relationship between proportional-hazards models and exponentiated covariate effects.

Theory

For a hazard \(h(t \mid x)\) with cumulative hazard \(H(t \mid x)\) and a uniform variate \(U \sim \mathrm{Uniform}(0, 1)\),

\[T = H^{-1}\bigl(-\log U \mid x\bigr)\]

has the target distribution. Under proportional hazards \(H(t \mid x) = H_0(t) \exp(x^\top \beta)\), so

\[T_i = H_0^{-1}\!\left(-\log U_i / \exp(x_i^\top \beta)\right).\]

Censoring is added by drawing an independent censoring time \(C_i\) from a chosen distribution (administrative, exponential, or empirical from a real cohort) and recording \(\min(T_i, C_i)\) as the observation time and \(\mathbf 1\{T_i \le C_i\}\) as the event indicator.

Assumptions

The specified baseline hazard and covariate-effect structure are the truth being simulated; the censoring distribution is independent of \(T_i\) unless the simulation explicitly handles informative censoring.

R Implementation

library(simsurv)

set.seed(2026)
n <- 300
x <- data.frame(id = 1:n, arm = factor(rep(c("A", "B"), each = n/2)))
x$arm_num <- as.numeric(x$arm) - 1

# Weibull baseline: lambda = 0.1, gamma = 1.2
sim <- simsurv(lambdas = 0.1, gammas = 1.2,
               x = x, betas = c(arm_num = -0.5),
               maxt = 10)

# Merge with covariates
d <- merge(sim, x, by = "id")
head(d)

# Kaplan-Meier
library(survival)
fit_km <- survfit(Surv(eventtime, status) ~ arm, data = d)
plot(fit_km)

Output & Results

simsurv() returns a tibble with one row per subject containing the simulated event time, the censoring indicator (here taken at maxt = 10), and the subject id. Merging back with the covariate frame gives a complete simulated dataset ready for analysis. The Kaplan-Meier plot shows the two arms separating with the designed effect size.

Interpretation

A reporting sentence: “Simulated Weibull data with shape 1.2, baseline scale 0.1, and a treatment hazard ratio of \(\exp(-0.5) = 0.61\); a Cox model on the simulated data recovered an HR of 0.59 (95 % CI 0.46 to 0.76), confirming the simulation is correctly calibrated.” Always confirm that the analysis pipeline recovers the simulation parameters before using the simulator for power calculations.

Practical Tips

simsurv supports Weibull and Gompertz baselines plus user-defined hazard functions; for arbitrary parametric shapes, supply hazard or loghazard directly.
For competing risks, simulate each cause’s event time independently and record the cause that occurred first; the resulting data have the correct cumulative incidence functions.
Match the censoring distribution to the real-study target: administrative censoring at study end, plus loss-to-follow-up exponentials with rates calibrated to historical drop-out.
For power calculations, run thousands of simulated datasets, fit the planned model on each, and record the proportion of times the test rejects at the chosen alpha; this is the standard Monte Carlo power estimator.
For time-varying covariates, simulate via piecewise-constant hazards across pre-specified intervals; simsurv supports tdefunction for time-dependent covariate effects.
For validation of new methods, re-simulate under several scenarios (PH violation, heavy censoring, sparse events) and check robustness; a method that works only on its design assumptions is brittle.

R Packages Used

simsurv for the canonical inverse-hazard simulator with Weibull, Gompertz, and user-defined baselines; flexsurv for rflexsurv() simulation from fitted flexible models; coxed for Cox-model-based simulations; survSim for additional simulation extensions including frailty and time-dependent effects.