Proportional hazards frailty models have been extensively investigated and used to analyze clustered and recurrent failure times data. However, the proportional hazards assumption in the models may not always hold in practice. In this paper, we propose an additive hazards frailty model with semi-varying coefficients, which allows some covariate effects to be time-invariant while other covariate effects to be time-varying. The time-varying and time-invariant regression coefficients are estimated by a set of estimating equations, whereas the frailty parameter is estimated by the moment method. The large sample properties of the proposed estimators are established. The finite sample performance of the estimators is examined by simulation studies. The proposed model and estimation are illustrated with an analysis of data from a rehospitalization study of colorectal cancer patients.

比例危险脆弱模型已被广泛研究并用于分析聚类和重复故障时间数据。然而，模型中的比例风险假设在实践中可能并不总是成立。在本文中，我们提出了一种具有半变系数的加性风险脆弱模型，该模型允许一些协变量效应是时不变的，而其他协变量效应是时变的。时变和非时变回归系数由一组估计方程估计，而脆弱参数由矩法估计。所提出的估计器的大样本特性被建立。通过模拟研究检查估计器的有限样本性能。