Weighted NPMLE for the Marginal Mean of Recurrent Events with a Competing Terminal Event
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.
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BibTeX
@misc{bellach2026weighted,
title = {{Weighted NPMLE for the Marginal Mean of Recurrent Events with a Competing Terminal Event}},
author = {Anna Bellach and Michael R. Kosorok},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.25934},
eprint = {2605.25934},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25934},
}
RIS
TY - UNPB
TI - Weighted NPMLE for the Marginal Mean of Recurrent Events with a Competing Terminal Event
AU - Anna Bellach
AU - Michael R. Kosorok
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2605.25934
UR - https://arxiv.org/abs/2605.25934
AB - 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.
ER -