Safety data from randomized controlled trials: applying models for recurrent events.

Simple descriptive listings and inference statistics based on 2×2 tables are still the most common way of summarizing and reporting adverse events data from randomized controlled trials, although these methods do not account for differences in observation times between treatment groups. Using standard methods from survival analysis such as the Cox model or Kaplan-Meier estimates would overcome this problem but limit the analysis to the first safety-related event of each subject. As an alternative, we discuss two models for recurrent events data-the Andersen-Gill and Prentice-Williams-Peterson model-regarding their applicability to safety data from randomized controlled trials. We argue that these models can be used to estimate two different quantities: a direct treatment effect on the risk of an event (Prentice-Williams-Peterson) and a total treatment effect as sum of the direct effect and the treatment's indirect effect via the event history (Anderson-Gill). Using simulated data, we illustrate the difference between these treatment effects and analyze the performance of both models in different scenarios. Because both models are limited to the analysis of cause-specific hazards if competing risks are present, we suggest to incorporate estimates of the mean frequency of events in the analysis to additionally allow the comparison of treatment effects on absolute event probabilities. We demonstrate the application of both models and the mean frequency function to safety endpoints with an illustrative analysis of data from a randomized phase-III study.