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

在各种回归问题中，面对含有大量潜在影响协变量的高维复杂数据变得越来越重要。一种可能的解决方案是应用评估方法，允许选择相关的预测因素，或者更广泛地说，解决模型选择的各个方面。例如，这些方法基于适当的增压技术。在目前的奖学金申请范围内，我们希望在特定的事件间隔时间数据回归模型，即所谓的Cox Frailty模型中，实现这样一种基于似然的分量增强方法的发展，用于变量和模型的选择。由于在许多应用中，一些协变量的影响随时间变化，我们也考虑了时变效应。然后，推动方法应涵盖以下主要模型选择问题：单一效应应作为时变效应包括在内，应以恒定效应的形式包括在内，或完全排除。为了实现这一目标，我们建议使用逐个组件的提升。此外，该方法应该包含一类强大而灵活的乘性脆弱分布，特别是对数正态分布。总之，该方法的目的是产生非常灵活和稀疏的比例风险模型来建模生存数据。最后，从长远来看，计划在统计程序R中的相应软件包中实施该方法。

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.