Semiparametric varying-coefficient regression analysis of recurrent events with applications to treatment switching

This paper investigates the semiparametric statistical methods for recurrent events. The mean number of the recurrent events are modeled with the generalized semiparametric varying-coefficient model that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects. We assume that the time-varying effects are unspecified functions of time and the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. Different link functions can be selected to provide a rich family of models for recurrent events data. The profile estimation methods are developed for the parametric and nonparametric components. The asymptotic properties are established. We also develop some hypothesis testing procedures to test validity of the parametric forms of covariate-varying effects. The simulation study shows that both estimation and hypothesis testing procedures perform well. The proposed method is applied to analyze a data set from an acyclovir study and investigate whether acyclovir treatment reduces the mean relapse recurrences.