Non-parametric analysis of gap times for multiple event data: An overview

Multiple event data are frequently encountered in medical follow-up, engineering and other applications when the multiple events are considered as the major outcomes. They may be repetitions of the same event (recurrent events) or may be events of different nature. Times between successive events (gap times) are often of direct interest in these applications. The stochastic-ordering structure and within-subject dependence of multiple events generate statistical challenges for analysing such data, including induced dependent censoring and non-identifiability of marginal distributions. This paper provides an overview of a class of existing non-parametric estimation methods for gap time distributions for various types of multiple event data, where sampling bias from induced dependent censoring is effectively adjusted. We discuss the statistical issues in gap time analysis, describe the estimation procedures and illustrate the methods with a comparative simulation study and a real application to an AIDS clinical trial. A comprehensive understanding of challenges and available methods for non-parametric analysis can be useful because there is no existing standard approach to identifying an appropriate gap time method that can be used to address research question of interest. The methods discussed in this review would allow practitioners to effectively handle a variety of real-world multiple event data.