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On testing conditional qualitative treatment effects

Shi, Chengchun, Song, Rui and Lu, Wenbin (2019) On testing conditional qualitative treatment effects. Annals of Statistics, 47 (4). 2348 - 2377. ISSN 0090-5364

[img] Text (CQTEaccept) - Accepted Version
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Identification Number: 10.1214/18-AOS1750

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 nonnegligible 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.

Item Type: Article
Official URL: https://projecteuclid.org/info/euclid.aos
Additional Information: © 2019 Institute of Mathematical Statistics
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 15 Oct 2019 12:21
Last Modified: 20 Nov 2020 02:47
URI: http://eprints.lse.ac.uk/id/eprint/102109

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