Electronic Journal of Statistics

High-dimensional inference for personalized treatment decision

X. Jessie Jeng, Wenbin Lu, and Huimin Peng

Full-text: Open access

Abstract

Recent development in statistical methodology for personalized treatment decision has utilized high-dimensional regression to take into account a large number of patients’ covariates and described personalized treatment decision through interactions between treatment and covariates. While a subset of interaction terms can be obtained by existing variable selection methods to indicate relevant covariates for making treatment decision, there often lacks statistical interpretation of the results. This paper proposes an asymptotically unbiased estimator based on Lasso solution for the interaction coefficients. We derive the limiting distribution of the estimator when baseline function of the regression model is unknown and possibly misspecified. Confidence intervals and p-values are derived to infer the effects of the patients’ covariates in making treatment decision. We confirm the accuracy of the proposed method and its robustness against misspecified function in simulation and apply the method to STAR∗D study for major depression disorder.

Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 2074-2089.

Dates
Received: October 2017
First available in Project Euclid: 21 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1529568040

Digital Object Identifier
doi:10.1214/18-EJS1439

Mathematical Reviews number (MathSciNet)
MR3816967

Zentralblatt MATH identifier
06917431

Subjects
Primary: 62J05: Linear regression 62F35: Robustness and adaptive procedures
Secondary: 62P10: Applications to biology and medical sciences

Keywords
Large $p$ small $n$ model misspecification optimal treatment regime robust regression

Rights
Creative Commons Attribution 4.0 International License.

Citation

Jeng, X. Jessie; Lu, Wenbin; Peng, Huimin. High-dimensional inference for personalized treatment decision. Electron. J. Statist. 12 (2018), no. 1, 2074--2089. doi:10.1214/18-EJS1439. https://projecteuclid.org/euclid.ejs/1529568040


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