On testing conditional qualitative treatment effects

Abstract

Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given another set of variables and provide a class of equivalent representations for the null hypothesis of no CQTE. The proposed definition of CQTE does not assume any parametric form for the optimal treatment rule and plays an important role for assessing the incremental value of a set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. We then propose novel testing procedures for no CQTE based on kernel estimation of the conditional contrast functions. We show that our test statistics have asymptotically correct size and non-negligible power against some nonstandard local alternatives. The empirical performance of the proposed tests are evaluated by simulations and an application to an AIDS data set.

A Sequential Significance Test for Treatment by Covariate Interactions

“…Wager and Athey (2018) investigated a forest-based method for treatment effect estimation and inference. Shi, Song and Lu (2019) proposed a nonparametric test to assess the incremental value of a given set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. These methods focused on the test of non-linear treatment effects, and worked well with a relatively small set of covariates.…”

“…These methods focused on the test of non-linear treatment effects, and worked well with a relatively small set of covariates. Although Shi, Song and Lu (2019) considered application of their method in a forward stepwise fashion and studied its variable selection properties, the derived p-value loses its interpretation when used with for-ward selection. In the presence of large number of covariates, Shen and Cai (2016) proposed a kernel based method to identify whether there is interaction between the treatment and a group of covariates; however, this is applicable only to a randomized trial setting.…”