Robust Estimation of Additive Shared‐Frailty Models for Recurrent Event Data With Dependent Censoring

Recurrent event data with dependent censoring frequently arise in medical follow‐up studies. In analyzing such data, one main challenge is addressing the complex dependencies among the recurrent events, failure events, and censoring events. In this paper, we focus on additive shared‐frailty models for recurrent event processes and failure times, and propose a robust estimation procedure that accommodates censoring times dependent on both recurrent and failure events, even after conditioning on observed covariates. Notably, our method does not require specifying the exact dependence structure between censoring and recurrent/failure times, nor does it assume a particular frailty distribution. We show that the resulting estimates are consistent and asymptotically normal. We further assess the method's finite‐sample performance through simulation studies, and illustrate its practical utility with a hospitalization dataset.