  With a large number of baseline covariates, we propose a new semi-parametric
modeling strategy for heterogeneous treatment effect estimation and
individualized treatment selection, which are two major goals in personalized
medicine. We achieve the first goal through estimating a covariate-specific
treatment effect (CSTE) curve modeled as an unknown function of a weighted
linear combination of all baseline covariates. The weight or the coefficient
for each covariate is estimated by fitting a sparse semi-parametric logistic
single-index coefficient model. The CSTE curve is estimated by a
spline-backfitted kernel procedure, which enables us to further construct a
simultaneous confidence band (SCB) for the CSTE curve under a desired
confidence level. Based on the SCB, we find the subgroups of patients that
benefit from each treatment, so that we can make individualized treatment
selection. The innovations of the proposed method are three-fold. First, the
proposed method can quantify variability associated with the estimated optimal
individualized treatment rule with high-dimensional covariates. Second, the
proposed method is very flexible to depict both local and global associations
between the treatment and baseline covariates in the presence of
high-dimensional covariates, and thus it enjoys flexibility while achieving
dimensionality reduction. Third, the SCB achieves the nominal confidence level
asymptotically, and it provides a uniform inferential tool in making
individualized treatment decisions.
