A Simple Method for Estimating Interactions between a Treatment and a Large Number of Covariates

We consider a setting in which we have a treatment and a potentially large number of covariates for a set of observations, and wish to model their relationship with an outcome of interest. We propose a simple method for modeling interactions between the treatment and covariates. The idea is to modify the covariate in a simple way, and then fit a standard model using the modified covariates and no main effects. We show that coupled with an efficiency augmentation procedure, this method produces clinically meaningful estimators in a variety of settings. It can be useful for practicing personalized medicine: determining from a large set of biomarkers the subset of patients that can potentially benefit from a treatment. We apply the method to both simulated datasets and real trial data. The modified covariates idea can be used for other purposes, for example, large scale hypothesis testing for determining which of a set of covariates interact with a treatment variable.