A Fast Nonparametric Sampling Method for Time to Event in Individual-Level Simulation Models

Purpose. Individual-level simulation models often require sampling times to events; however, efficient parametric distributions for many processes may often not exist. For example, time to death from life tables cannot be accurately sampled from existing parametric distributions. We propose an efficient nonparametric method to sample times to events that does not require any parametric assumption on the hazards. Methods. We developed a nonparametric sampling (NPS) approach that simultaneously draws multiple time-to-event samples from a categorical distribution. This approach can be applied to univariate and multivariate processes. We discretize the entire period into equal-length time intervals and then derived the interval-specific probabilities. The times to events can then be used directly in individual-level simulation models. We compared the accuracy of our approach in sampling time-to-events from common parametric distributions, including exponential, gamma, and Gompertz. In addition, we evaluated the method’s performance in sampling age to death from US life tables and sampling times to events from parametric baseline hazards with time-dependent covariates. Results. The NPS method estimated similar expected times to events from 1 million draws for the 3 parametric distributions, 100,000 draws for the homogenous cohort, 200,000 draws from the heterogeneous cohort, and 1 million draws for the parametric distributions with time-varying covariates, all in less than 1 second. Conclusion. Our method produces accurate and computationally efficient samples for time to events from hazards without requiring parametric assumptions. Highlights The nonparametric sampling method is generic and can sample times to an event from any discrete (or discretizable) hazard without requiring any parametric assumption. The method is showcased with 5 commonly used distributions in discrete-event simulation models. The method produced very similar expected times to events, as well as their probability distribution, compared with analytical results. We provide a multivariate categorical sampling function for R and Python programming languages to sample times to events from processes with different hazards simultaneously.