Generalizing Quantile Regression for Counting Processes With Applications to Recurrent Events

In this article, we discuss how quantile regression can be extended to model counting processes and thus lead to a broader regression framework for survival data. We specifically investigate the proposed modeling of counting processes for recurrent events data.

We show that the new recurrent events model retains the desirable features of quantile regression such as easy interpretation and good model flexibility, while accommodating various observation schemes encountered in observational studies. We develop a general theoretical and inferential framework for the new counting process model, which unifies with an existing method for censored quantile regression. As another useful contribution of this work, we propose a sample-based covariance estimation procedure, which provides a useful complement to the prevailing bootstrapping approach.