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.

翻译：复发事件与终止事件的回归建模在生存分析中持续面临方法学挑战。现有方法要么对两类事件间的依赖结构作出不可验证的假设，要么依赖边际均值的比例强度假设。本文提出一种基于新型加权似然函数的半参数回归模型，直接针对复发事件的边际均值。该通用模型涵盖了一大类半参数回归模型，并能容纳外部时变协变量对边际均值强度的影响。我们证明了估计量的一致性和渐近正态性，并提出了方差的三明治估计量。同时提出了一种直接针对复发事件边际均值强度的新型模拟程序。在模拟研究中，我们验证了加权NPMLE在独立右删失下的优异性能。通过STATCOPE试验数据（一项探究辛伐他汀对COPD急性加重疗效的大型随机临床试验）的应用，展示了所提出方法论的实际效用。我们提供了急性加重次数的个性化预测，并重新评估了辛伐他汀治疗的效果，将死亡视为GOLD 4期患者的竞争性终止事件。