  Progression of chronic disease is often manifested by repeated occurrences of
disease-related events over time. Delineating the heterogeneity in the risk of
such recurrent events can provide valuable scientific insight for guiding
customized disease management. In this paper, we present a new modeling
framework for recurrent event data, which renders a flexible and robust
characterization of individual multiplicative risk of recurrent event through
quantile regression that accommodates both observed covariates and unobservable
frailty. The proposed modeling requires no distributional specification of the
unobservable frailty, while permitting the exploration of dynamic covariate
effects. We develop estimation and inference procedures for the proposed model
through a novel adaptation of the principle of conditional score. The
asymptotic properties of the proposed estimator, including the uniform
consistency and weak convergence, are established. Extensive simulation studies
demonstrate satisfactory finite-sample performance of the proposed method. We
illustrate the practical utility of the new method via an application to a
diabetes clinical trial that explores the risk patterns of hypoglycemia in Type
2 diabetes patients.
