Weighted NPMLE for the Marginal Mean of Recurrent Events with a Competing Terminal Event

2026-05-25

AI Summary

This study addresses the challenges posed by unverifiable dependence structures and overly restrictive proportional intensity assumptions in settings involving recurrent events subject to competing terminal events. The authors propose a weighted likelihood–based semiparametric regression model that directly targets the marginal mean of recurrent events while accommodating external time-varying covariates. Innovatively integrating weighted nonparametric maximum likelihood estimation (NPMLE), sandwich variance estimation, and a novel simulation algorithm tailored to the marginal mean, the method avoids untestable assumptions about inter-event dependence and circumvents traditional proportional intensity constraints. Demonstrating robust performance under independent right censoring, the approach is successfully applied to the STATCOPE clinical trial to enable personalized prediction of acute exacerbation frequency in COPD patients and to reassess the efficacy of simvastatin specifically in GOLD stage 4 patients.

Abstract

Regression modeling of recurrent and terminal events continues to present methodological challenges in survival analysis. Existing approaches either make unverifiable assumptions about the dependency structure between the two event types or rely on the proportional intensity assumption for the marginal mean. A semiparametric regression model is proposed that is based on a novel weighted likelihood function, thereby targeting directly the marginal mean of the recurrent event. Our general model captures a large class of semiparametric regression models and accommodates external time-dependent covariate effects on the marginal mean intensity. We establish the consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. We propose a novel simulation procedure that directly targets the marginal mean intensity of the recurrent events. In simulation studies, we demonstrate a strong performance of the weighted NPMLE under independent right-censoring. The practical utility of the proposed methodology is demonstrated through application to data from the STATCOPE trial, a large randomized clinical trial that investigated the efficacy of simvastatin for COPD exacerbations. We provide personalized predictions for the number of exacerbations and reassess the effect of simvastatin treatment, accounting for death as a competing terminal event for patients with GOLD stage 4.

Problem

• recurrent events
• competing terminal event
• marginal mean
• survival analysis
• dependency structure

Innovation

• weighted NPMLE
• marginal mean
• recurrent events
• competing terminal event
• semiparametric regression