A Simple Method for Variable Selection in Regression with Respect to Treatment Selection

Abstract

In this paper, we compare the method of Gunter et al. (2011) for variable selection in treatment comparison analysis (an approach to regression analysis where treatment-covariate interactions are deemed important) with a simple stepwise selection method that we introduce. The stepwise method has several advantages, most notably its generalization to  regression models that are not necessarily linear, its simplicity and its intuitive nature. We show that the new simple method works surprisingly well compared to the more complex method when compared in the linear regression framework. We use four generative models (explicitly detailed in the paper) for the simulations and compare spuriously identified interactions and where applicable (generative models 3 and 4) correctly identified interactions. We also apply the new method to logistic regression and Poisson regression and illustrate its  performance in Table 2 in the paper. The simple method can be applied to other types of regression models including various other generalized linear models, Cox proportional hazard models and nonlinear models.