Optimal Treatment Selection Using the Covariate-Specific Treatment Effect Curve with High-dimensional Covariates
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In this paper, 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, with a large number of baseline covariates. 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 proposed method is quite flexible to depict both local and global associations between the treatment and baseline covariates, and thus is robust against model mis-specification in the presence of high-dimensional covariates. We also establish the theoretical properties of our proposed procedure. They provide a sound basis for conducting statistical inference in making individualized treatment decisions. Our proposed method is further illustrated by simulation studies and analysis of a real data example.
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