Quantile set-regression with application in precision medicine

Abstract

Quantile regression is commonly used in statistical analysis. It is more general than the ordinary regression. However in some practical investigations, the interest is the conditional quantile of the response given the covariates belonging to some set. For example in subgroup analysis, the goal is to classify the patients into two subgroups, one with whom benefit the most from the treatment and the other not so beneficial. This is equivalent to finding an optimal set in the covariate space, such that a patient is favored for the treatment if his/her covariates fall in this set, and otherwise not. Motivated by this practical problem we extend our recent work on set-regression to quantile set regression, defined as the conditional quantile of the response given the covariates belonging to a given set. This extends the notion of the classical quantile regression and is particularly suitable for precision medicine and other applications. The method is easy to use and in principle it works for sets of any shapes, but our current codes only work for certain particular shaped sets, the balls and rectangles. Simulation studies are conducted to evaluate the performance of the proposed method, which show superior promising results of the proposed method. Then the method is applied to analyze an AIDS Clinical Trials Group data.