The importance of varying the event generation process in simulation studies of statistical methods for recurrent events

Abstract

Statistical methods for the analysis of recurrent events are often evaluated in simulation studies. A factor rarely varied in such studies is the underlying event generation process. If the relative performance of statistical methods differs across generation processes, then studies based upon one process may mislead. This paper describes the simulation of recurrent events data using four models of the generation process: Poisson, mixed Poisson, autoregressive, and Weibull. For each model four commonly used statistical methods for the analysis of recurrent events (Cox's proportional hazards method, the Andersen-Gill method, negative binomial regression, the Prentice-Williams-Peterson method) were applied to 200 simulated data sets, and the mean estimates, standard errors, and confidence intervals obtained. All methods performed well for the Poisson process. Otherwise, negative binomial regression only performed well for the mixed Poisson process, as did the Andersen-Gill method with a robust estimate of the standard error. The Prentice-Williams-Peterson method performed well only for the autoregressive and Weibull processes. So the relative performance of statistical methods depended upon the model of event generation used to simulate data. In conclusion, it is important that simulation studies of statistical methods for recurrent events include simulated data sets based upon a range of models for event generation.