## Annals of Statistics

### 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 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.

#### Article information

Source
Ann. Statist., Volume 47, Number 4 (2019), 2348-2377.

Dates
Revised: April 2018
First available in Project Euclid: 21 May 2019

https://projecteuclid.org/euclid.aos/1558425648

Digital Object Identifier
doi:10.1214/18-AOS1750

Mathematical Reviews number (MathSciNet)
MR3953454

Zentralblatt MATH identifier
07082289

Subjects
Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing

#### Citation

Shi, Chengchun; Song, Rui; Lu, Wenbin. On testing conditional qualitative treatment effects. Ann. Statist. 47 (2019), no. 4, 2348--2377. doi:10.1214/18-AOS1750. https://projecteuclid.org/euclid.aos/1558425648

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#### Supplemental materials

• Supplement to “On testing conditional qualitative treatment effects”. Supplementary material includes additional simulation results and some proofs of asymptotic results.