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

Abstract

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. Supplementary materials for this article are available online.

• Efficiency augmentation
• Modified covariates
• Personalized medicine
• Randomized clinical trial
• Subgroup analysis

SUPPLEMENTARY MATERIALS

In the online supplementary materials, we first present the modified covariates method for estimating the personalized treatment effect in terms of the relative risk for binary responses. We also provide detailed theoretical justifications for the optimal efficiency augmentation for continuous, binary and survival outcomes, respectively. Lastly, the supplementary materials contain the numerical algorithms for computing the lasso-regularized solution with efficiency augmentation.