Treatment recommendation and parameter estimation under single-index contrast function

In this article, we consider a semiparametric model for contrast function which is defined as the conditional expected outcome difference under comparative treatments. The contrast function can be used to recommend treatment for better average outcomes. Existing approaches model the contrast function either parametrically or nonparametrically. We believe our approach improves interpretability over the non-parametric approach while enhancing robustness over the parametric approach. Without explicit estimation of the nonparametric part of our model, we show that a kernel-based method can identify the parametric part up to a multiplying constant. Such identification suffices for treatment recommendation. Our method is also extended to high-dimensional settings. We study the asymptotics of the resulting estimation procedure in both low- and high-dimensional cases. We also evaluate our method in simulation studies and real data analyses.