The Pivotal Role of Semiparametric Methods in Model-agnostic Framework for Biomedical Applications

In studies ranging from clinical medicine to policy research, complete data are usually available from a population P, but the quantity of interest is often sought for a related but different population Q. In this talk, we consider the unsupervised domain adaptation setting under the label shift assumption. We estimate a parameter of interest in population Q by leveraging information from P, where three ingredients are essential: (a) the common conditional distribution of X given Y, (b) the regression model of Y given X in P, and (c) the density ratio of the outcome Y between the two populations. We propose an estimation procedure that only needs some standard nonparametric technique to approximate the conditional expectations with respect to (a), while by no means needs an estimate or model for (b) or (c); i.e., doubly flexible to the model misspecifications of both (b) and (c). We rigorously study the theoretical properties of our proposed methods. Empirically, we illustrate our proposed methods in the MIMIC-III database. 

Change-point regression is linear regression where the regression coefficients change depending on whether another covariate is above or below an unknown threshold. Change-plane regression is a generalization of this where the regression cofficents change depending on whether another vector of covariates is above or below an unknown hyperplane. Since the residual error in this setting is assumed to be mean zero with finite variance, but is otherwise unspecified, this model is semiparametric. In this presentation, we derive for the first time the limiting distribution of the unknown parameters, under least-squares estimation, and when some of the covariates are allowed to be discrete. The limiting distribution is new and has not been previously characterized. In addition to theoretical results, we also present simulation studies and an illustrative data analysis of AIDS data for precision medicine.