Aalen's linear hazard rate regression model is a useful and increasingly popular alternative to Cox' multiplicative hazard rate model. It postulates that an individual has hazard rate function $h(s)=z_1α_1(s)+\cdots+z_rα_r(s)$ in terms of his covariate values $z_1,\ldots,z_r$. These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions $α_j(s)$ are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model's parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study.

翻译：Aalen的线性风险率回归模型是Cox乘性风险率模型的一种实用且日益流行的替代方案。该模型假设个体具有风险率函数$h(s)=z_1α_1(s)+\cdots+z_rα_r(s)$，其中$z_1,\ldots,z_r$为其协变量值。这些协变量通常代表不同风险因素的水平，也可能具有时间依赖性。风险因子函数$α_j(s)$是模型的参数，需从数据中估计。传统上，这一过程完全以非参数化方式实现。本文发展了当部分风险因子函数采用参数化建模而其余部分保持非参数化时的估计方法。在这一部分参数化、部分非参数化的框架内，我们得到了大样本结果，该框架还使我们能够评估模型参数化部分的拟合优度。此外，这些结果被用于量化相较于标准非参数方法，采用参数-非参数模型所能提升的精度程度。本文包含一个实际数据应用案例及简要的模拟研究。