Generalized accelerated recurrence time model for multivariate recurrent event data with missing event type

Recurrent events data are frequently encountered in biomedical follow-up studies. The generalized accelerated recurrence time (GART) model (Sun et al., 2016), which formulates covariate effects on the time scale of the mean function of recurrent events (i.e., time to expected frequency), has arisen as a useful secondary analysis tool to provide meaningful physical interpretations. In this article, we investigate the GART model in a multivariate recurrent events setting, where subjects may experience multiple types of recurrent events and some event types may be missing. We propose methods for the GART model that utilize the inverse probability weighting technique or the estimating equation projection strategy to handle event types that are missing at random. The new methods do not require imposing any parametric model for the missing mechanism, and thus are robust; moreover, they enjoy easy and stable implementation. We establish the uniform consistency and weak convergence of the resulting estimators and develop appropriate inferential procedures. Extensive simulation studies and an application to a dataset from Cystic Fibrosis Foundation Patient Registry (CFFPR) illustrate the validity and practical utility of the proposed methods.