Joint modeling of recurrent event processes and intermittently observed time-varying binary covariate processes

When conducting recurrent event data analysis, it is common to assume that the covariate processes are observed throughout the follow-up period. In most applications, however, the values of time-varying covariates are only observed periodically rather than continuously. A popular ad-hoc approach is to carry forward the last observed covariate value until it is measured again. This simple approach, however, usually leads to biased estimation. To tackle this problem, we propose to model the covariate effect on the risk of the recurrent events through jointly modeling the recurrent event process and the longitudinal measures. Despite its popularity, estimation of the joint model with binary longitudinal measurements remains a challenge, because the standard linear mixed effects model approach is not appropriate for binary measures. In this paper, we postulate a Markov model for the binary covariate process and a random-effect proportional intensity model for the recurrent event process. We use a Markov chain Monte Carlo algorithm to estimate all the unknown parameters. The performance of the proposed estimator is evaluated via simulations. The methodology is applied to an observational study designed to evaluate the effect of Group A streptococcus on pharyngitis among school children in India.