Precision medicine is a medical paradigm that focuses on making effective treatment decision based on individual patient characteristics. When there are a large amount of patient information, such as patient’s genetic information, medical records and clinical measurements, available, it is of interest to select the covariates which have interactions with the treatment, for example, in determining the individualized treatment regime where only a subset of covariates with treatment interactions involves in decision making. We propose a marginal feature ranking and screening procedure for measuring interactions between the treatment and covariates. The method does not require imposing a specific model structure on the regression model and is applicable in a high dimensional setting. Theoretical properties in terms of consistency in ranking and selection are established. We demonstrate the finite sample performance of the proposed method by simulation and illustrate the applications with two real data examples from clinical trials.

We propose two variable selection methods in multivariate linear regression with highdimensional covariates. The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level. The second method extends the univariate forward regression of Wang [(2009). Forward regression for ultra-high dimensional variable screening.