Exploring the heterogeneity in recurrent episode lengths based on quantile regression

Recurrent episode data frequently arise in chronic disease studies when an event of interest occurs repeatedly and each occurrence lasts for a random period of time. Understanding the heterogeneity in recurrent episode lengths can help guide dynamic and customized disease management. However, there has been relative sparse attention to methods tailored to this end. Existing approaches either do not confer direct interpretation on episode lengths or involve restrictive or unrealistic distributional assumptions, such as exchangeability of within-individual episode lengths. In this work, we propose a modeling strategy that overcomes these limitations through adopting quantile regression and sensibly incorporating time-dependent covariates. Treating recurrent episodes as clustered data, we develop an estimation procedure that properly handles the special complications, including dependent censoring, dependent truncation, and informative cluster size. Our estimation procedure is computationally simple and yields estimators with desirable asymptotic properties. Our numerical studies demonstrate the advantages of the proposed method over naive adaptations of existing approaches.