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 \(h(s)=z_1\alpha _1(s)+\cdots +z_r\alpha _r(s)\) 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 \(\alpha _j(s)\) 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.

Aalen 的线性风险率回归模型是 Cox 乘法风险率模型的有用且日益流行的替代模型。它假设个体的协变量值\(z_1,\ldots ,z_r)具有危险率函数\(h(s)=z_1\alpha _1(s)+\cdots +z_r\alpha _r(s)\) \) 。这些通常是各种危险因素的水平，并且也可能与时间相关。危险因子函数\(\alpha _j(s)\)是模型的参数，是根据数据估计的。传统上，这是通过完全非参数的方式完成的。本文开发了一种估计危险因素函数的方法，其中一些是参数化建模的，而另一些则未指定。大样本结果是在这个部分参数、部分非参数的框架内得出的，这也使我们能够评估模型参数组件的拟合优度。此外，这些结果还用于确定使用参数-非参数模型相对于标准非参数方法可以获得多少精度。其中包括真实数据应用程序以及简短的模拟研究。