Empirical Simulation of Survival and Mixed-Type Data for Clinical Trial Design

2026-08-12

AI Summary

Traditional parametric approaches often fail to accurately model complex time-to-event data in clinical trials due to their reliance on prespecified hazard function forms. This work proposes a joint simulation framework based on empirical copulas that integrates nonparametric reconstruction with parametric tail modeling. The method handles right censoring via conditional Kaplan–Meier imputation, models marginal distributions through log-scale location–scale transformations and power distortion of quantile functions, and preserves multivariate rank correlation structures using a Gaussian copula. Remarkably, the approach can reproduce treatment-group survival curves using only a few target quantiles. Applied to a non-small cell lung cancer trial, it successfully replicated both overall survival and progression-free survival curves, yielding a simulated censored Kendall’s tau of 0.522—closely approximating the observed value of 0.549.

Abstract

Simulating realistic time-to-event data is essential for planning and evaluating complex clinical trial designs. Conventional approaches often sample event times from parametric families, such as Weibull or log-normal distributions, which restrict hazard shapes and may poorly represent observed survival data. We propose an empirical copula-based framework for simulating multivariate data containing continuous, binary, count, and right-censored time-to-event variables. The method completes censored historical survival data using a two-zone procedure that combines conditional Kaplan-Meier imputation with a parametric tail. It matches a target survival distribution through a log-scale location-scale transformation and a power distortion of the empirical percentile function, while preserving historical dependence through a Gaussian copula fitted to rank correlations. In an oncology trial of previously treated non-small-cell lung cancer, the method reconstructs overall survival and progression-free survival curves for the experimental arm using control-arm data and a small set of target percentiles. Simulations preserve rank correlations among baseline covariates and the dependence between progression-free and overall survival, with censored Kendall's tau of 0.522 compared with 0.549 in the observed data. The method is implemented in the R package EmpiricalSim.

Problem

• survival simulation
• mixed-type data
• clinical trial design
• right-censored data
• empirical simulation

Innovation

• empirical copula
• survival simulation
• censored data imputation
• mixed-type data
• rank correlation preservation