Abstract

The treatment allocation mechanism in a randomized clinical trial can be optimized by

maximizing the nonparametric efficiency bound for a specific measure of treatment effect.

Optimal treatment allocations which may or may not depend on baseline covariates have

been derived for a variety of effect measures focusing on the trial population, the patient

population represented by the trial participants. Frequently, clinical trial data are used to

estimate treatment effects in a target population that is related to but different from the

trial population. This article provides optimal treatment allocations that account for the

impact of such population differences. We consider three cases with different data configurations: transportation, generalization, and post-stratification. Our results indicate that,

for general effect measures, optimal treatment allocations may depend on the covariate disdescribes the target covariate distribution. For estimating average treatment effects, there

is a unique covariate-dependent allocation that achieves maximal efficiency regardless of the

target covariate distribution and the associated data configuration.

Key words and phrases: covariate adjustment; covariate-dependent randomization; generalizability; op- timal design; propensity score; transportability 1 Introduction The treatment allocation mechanism in a randomized clinical trial can be optimized for statistical efficiency. A well-known result in this domain is the Neyman allocation (Neyman, 1934), which makes the size of each treatment group proportional to the standard deviation of the outcome of interest in the same treatment group. The Neyman allocation is optimal, in the sense of minimum asymptotic variance, for estimating the average treatment effect (ATE) with the sample mean difference. The sample mean difference is commonly used but not fully efficient in the presence of baseline covariates associated with treatment outcomes. Motivated by semiparametric theory (Bickel et al., 1993; Tsiatis, 2006), more efficient estimators have been developed to incorporate information from baseline covariates (e.g., Tsiatis et al., 2008; Zhang et al., 2008; Moore and van der Laan, 2009; Rosenblum and van der Laan, 2010; Tian et al., 2012; Zhang and Ma, 2019; Ye et al., 2023; Bannick et al., 2025). Some of these estimators leverage modern machine learning and ensemble learning methods (e.g., Hastie et al., 2009; Polley et al., 2011) and have a better chance (than those based on parametric models) to attain or approach the nonparametric efficiency bound for treatment effect estimation. In optimize treatment allocation for an efficient estimator attaining the nonparametric efficiency bound. Optimal treatment allocations that maximize the nonparametric efficiency bound have been derived by Zhang et al. (2023), who considered both the traditional covariate- independent randomization (CIR) design and a covariate-dependent randomization (CDR) design that resembles observational studies except that the propensity score is specified and known by the investigator. These efforts to improve statistical efficiency generally aim at a treatment effect measure, such as the ATE, in the trial population (i.e., the patient population represented by the trial participants)

Information

Preprint No.SS-2025-0330
Manuscript IDSS-2025-0330
Complete AuthorsWei Zhang, Zhiwei Zhang, Aiyi Liu
Corresponding AuthorsWei Zhang
Emailszhangwei@amss.ac.cn

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Acknowledgments

The research of Wei Zhang was supported by the National Key R&D Program of China

[grant number 2022YFA1004800]. The research of Aiyi Liu was supported by the Intramural

Research Program of the National Institutes of Health (NIH). The contributions of the NIH

author were made as part of their official duties as NIH federal employees, are in compliance

with agency policy requirements, and are considered Works of the United States Government.

However, the findings and conclusions presented in this paper are those of the author and do

not necessarily reflect the views of the NIH or the U.S. Department of Health and Human

Services.