Recurrent Events Analysis in the Presence of Time Dependent Covariates and Dependent Censoring

Maja Miloslavsky, Division of Biostatistics, School of Public Health, University of California, Berkeley
Sunduz Keles, Division of Biostatistics, School of Public Health, University of California, Berkeley
Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Steve Butler, Genentech, Inc., South San Francisco, CA

Abstract

Recurrent events models have lately received a lot of attention in the literature. The majority of approaches discussed show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates included into the model. We provide an overview of available recurrent events analysis methods, and present an inverse probability of censoring weighted estimator for the regression parameters in the Andersen-Gill model that is commonly used for recurrent event analysis. This estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently, and generally improves on the naive estimator for the Anderson-Gill model in the case of independent censoring. We illustrate the bias of ad hoc estimators in the presence of informative censoring with a simulation study and provide a data analysis of recurrent lung exacerbations in cystic fibrosis patients when some patients are lost to follow up.