Recurrent event data analysis with intermittently observed time-varying covariates

Although recurrent event data analysis is a rapidly evolving area of research, rigorous studies on estimation of the effects of intermittently observed time-varying covariates on the risk of recurrent events have been lacking. Existing methods for analyzing recurrent event data usually require that the covariate processes are observed throughout the entire follow-up period. However, covariates are often observed periodically rather than continuously. We propose a novel semiparametric estimator for the regression parameters in the popular proportional rate model. The proposed estimator is based on an estimated score function where we kernel smooth the mean covariate process. We show that the proposed semiparametric estimator is asymptotically unbiased, normally distributed, and derives the asymptotic variance. Simulation studies are conducted to compare the performance of the proposed estimator and the simple methods carrying forward the last covariates. The different methods are applied to an observational study designed to assess the effect of group A streptococcus on pharyngitis among school children in India.