Likelihood-based Component-wise Boosting Methods for Effects Selection in Cox Frailty Models

在各种回归问题中，面对具有大量潜在影响协变量的高维复杂数据变得越来越重要。一个可能的解决方案是应用允许选择相关预测者的估计方法，或者更一般地说，处理模型选择的各个方面。例如，这些方法是基于合适的增强技术。在当前奖学金应用程序的范围内，我们希望实现这样一种基于似然的组件智能增强方法的开发，用于在特定的时间到事件数据的回归模型中选择变量和模型，即所谓的Cox脆弱性模型。由于在许多应用中，一些协变量的影响随时间而变化，我们也考虑时变效应。然后，增强方法应涵盖以下主要的模型选择问题：单一效应应作为时变效应包括在内，以恒定效应的形式包括在内，或者完全排除。为了实现这一目标，我们建议使用组件增强。此外，该方法应纳入一类强大而灵活的乘法脆弱性分布，特别是对数正态分布。总之，该方法旨在产生非常灵活和稀疏的比例风险模型，用于建模生存数据。最后，从长远来看，我们计划在统计程序R中的相应软件包中实现该方法。

In all sorts of regression problems it has become more and more relevant to face high dimensional and complex data with lots of potentially influential covariates. A possible solution is to apply estimation methods that allow to select the relevant predictors or, more generally, to address aspects of model choice. These methods are based, for example, on suitable boosting techniques. Within the scope of the current fellowship application we want to realize the development of such a likelihood-based component-wise boosting approach for variable and model selection in a particular regression model for time-to-event data, the so-called Cox frailty model. As in many applications the influence of some covariates changes over time, we also consider time-varying effects. The boosting approach should then cover the following major model selection issues: single effects should either be included as time-varying, be included in the form of a constant effect or be totally excluded. In order to achieve this goal, we propose to use component-wise boosting. Besides, the methodology should incorporate a powerful and flexible class of multiplicative frailty distributions, in particular, the log-normal distribution. Altogether, the approach is aimed to result in very flexible and sparse proportional hazards models for modeling survival data. Finally, in the long run, an implementation of the method in a corresponding software package in the statistical program R is planned.