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

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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.