Penalized robust learning for optimal treatment regimes with heterogeneous individualized treatment effects.

The growing popularity of personalized medicine motivates people to explore individualized treatment regimes according to heterogeneous characteristics of the patients. For the large-scale data analysis, however, the data are collected at different times and different locations, i.e. subjects are usually from a heterogeneous population, which causes that the optimal treatment regimes also vary for patients across different subgroups. In this paper, we mainly focus on the estimation of optimal treatment regimes for subjects come from a heterogeneous population with high-dimensional data. We first remove the main effects of the covariates for each subgroup to eliminate non-ignorable residual confounding. Based on the centralized outcome, we propose a penalized robust learning that estimates the coefficient matrix of the interactions between covariates and treatment by penalizing pairwise differences of the coefficients of any two subgroups for the same covariate, which can automatically identify the latent complex structure of the coefficient matrix with heterogeneous and homogeneous columns. At the same time, the penalized robust learning can also select the important variables that truly contribute to the individualized treatment decisions with commonly used sparsity structure penalty. Extensive simulation studies show that our proposed method outperforms current popular methods, and it is further illustrated in the real analysis of the Tamoxifen breast cancer data.