Optimal Design of Controlled Experiments for Personalized Decision Making in the Presence of Observational Covariates

Li, Yezhuo; Zhang, Qiong; Khademi, Amin; Yang, Boshi

doi:10.51387/23-NEJSDS22

The New England Journal of Statistics in Data Science

Optimal Design of Controlled Experiments for Personalized Decision Making in the Presence of Observational Covariates

Yezhuo Li Qiong Zhang Amin Khademi All authors (4)

https://doi.org/10.51387/23-NEJSDS22

Pub. online: 26 January 2023 Type: Statistical Methodology

Open Access

Accepted
12 January 2023

Published
26 January 2023

Abstract

Controlled experiments are widely applied in many areas such as clinical trials or user behavior studies in IT companies. Recently, it is popular to study experimental design problems to facilitate personalized decision making. In this paper, we investigate the problem of optimal design of multiple treatment allocation for personalized decision making in the presence of observational covariates associated with experimental units (often, patients or users). We assume that the response of a subject assigned to a treatment follows a linear model which includes the interaction between covariates and treatments to facilitate precision decision making. We define the optimal objective as the maximum variance of estimated personalized treatment effects over different treatments and different covariates values. The optimal design is obtained by minimizing this objective. Under a semi-definite program reformulation of the original optimization problem, we use a YALMIP and MOSEK based optimization solver to provide the optimal design. Numerical studies are provided to assess the quality of the optimal design.

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Open access article under the CC BY license.

Keywords

E-optimal design Multiple treatments allocation Semi-definite program

Funding

Khademi is supported by NSF Award 1651912.

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