  We consider a setting in which we have a treatment and a 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 valid inferences in a variety of settings. It can be
useful for 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 gene expression studies of cancer.
The modified data 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.
