A penalized algorithm for event-specific rate models for recurrent events

TL;DR

This paper proposes a covariate-specific total variation penalty for semiparametric models of recurrent event rates, improving estimation accuracy especially in small to moderate samples, with theoretical guarantees and real data application.

Contribution

It introduces a novel penalized estimation method for stratified Cox and Aalen models, enhancing their performance for recurrent event rate analysis.

Findings

Penalized estimators are consistent and asymptotically normal.

Our method outperforms classical estimators in simulations.

Application to bladder tumour data demonstrates practical utility.

Abstract

We introduce a covariate-specific total variation penalty in two semiparametric models for the rate function of recurrent event process. The two models are a stratified Cox model, introduced in Prentice et al. (1981), and a stratified Aalen's additive model. We show the consistency and asymptotic normality of our penalized estimators. We demonstrate, through a simulation study, that our estimators outperform classical estimators for small to moderate sample sizes. Finally an application to the bladder tumour data of Byar (1980) is presented.