Semiparametric and nonparametric analysis of recurrent events with observation gaps

This paper considers statistical analysis of recurrent event data when there exist observation gaps. By observation gaps, we mean that some study subjects are out of the study for a period of time for various reasons and then are back in the study again and this may happen more than once. Most of existing studies of recurrent events discuss situations where study subjects are under observation over continuous time periods. For recurrent event data with observation gaps, a naive analysis method is to treat them as usual recurrent events without gaps by either censoring observations at times when subjects first leave the study or ignoring the gaps. As expected and shown below, this could yield biased and misleading results. In this paper, we present some appropriate methods for the problem. In particular, we consider estimation of the underlying mean function and regression analysis of recurrent event data in the presence of observation gaps. The presented analysis methods are evaluated and compared to the naive approach that ignores observation gaps using extensive simulation studies and an example.