Generalizing Quantile Regression for Counting Processes With Applications to Recurrent Events

Abstract

In survival analysis, quantile regression has become a useful approach to account for covariate effects on the distribution of an event time of interest. In this paper, 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. We demonstrate the utility of our proposals via simulation studies and an application to a dataset from the US Cystic Fibrosis Foundation Patient Registry (CFFPR).

Generalized Accelerated Recurrence Time Model for Multivariate Recurrent Event Data with Missing Event Type

“…The ART model extends the AFT model by allowing for evolving covariate effects on time to expected frequency. More recently, Sun et al (2016) derived the generalized accelerated recurrence time (GART) model from a counting process modeling perspective. The GART model is a strict extension of the ART model, permitting a more flexible transformation from the frequency scale to the time scale of the mean function.…”

“…The GART model is a strict extension of the ART model, permitting a more flexible transformation from the frequency scale to the time scale of the mean function. The inferential methods developed by Sun et al (2016) accommodate recurrent events data subject to observation windows that take the form of general time interval(s).…”

“…Our estimators also have explicit closed forms despite the incorporation of covariates, which are not available in Lin et al (2013)’s method. As another appealing feature, the two methods derived from the IPW and EEP strategies can be unified in an inferential framework that resembles Sun et al (2016)’s method. This entails simple and stable implementations of the proposed methods.…”

“…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.…”

Quantile Regression Models and Their Applications: A Review

“…Peng and Huang [60] developed an estimator which is very close to Nelson-Aalen estimator. Most recently, great work is still expanding this area to recurrent events [61][62][63], various censoring types [64][65][66], competing risks [65,[67][68][69].…”