A bootstrap resampling procedure for model building: application to the Cox regression model

Abstract

A common problem in the statistical analysis of clinical studies is the selection of those variables in the framework of a regression model which might influence the outcome variable. Stepwise methods have been available for a long time, but as with many other possible strategies, there is a lot of criticism of their use. Investigations of the stability of a selected model are often called for, but usually are not carried out in a systematic way. Since analytical approaches are extremely difficult, data-dependent methods might be an useful alternative. Based on a bootstrap resampling procedure, Chen and George investigated the stability of a stepwise selection procedure in the framework of the Cox proportional hazard regression model. We extend their proposal and develop a bootstrap-model selection procedure, combining the bootstrap method with existing selection techniques such as stepwise methods. We illustrate the proposed strategy in the process of model building by using data from two cancer clinical trials featuring two different situations commonly arising in clinical research. In a brain tumour study the adjustment for covariates in an overall treatment comparison is of primary interest calling for the selection of even 'mild' effects. In a prostate cancer study we concentrate on the analysis of treatment-covariate interactions demanding that only 'strong' effects should be selected. Both variants of the strategy will be demonstrated analysing the clinical trials with a Cox model, but they can be applied in other types of regression with obvious and straightforward modifications.