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Optimal designs for the development of personalized treatment rules
Author(s) -
Azriel David,
Rinott Yosef,
Posch Martin
Publication year - 2023
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12621
Subject(s) - covariate , homoscedasticity , mathematics , statistics , contrast (vision) , population , sample size determination , econometrics , clinical trial , medicine , computer science , artificial intelligence , heteroscedasticity , environmental health
We study the design of multi‐armed parallel group clinical trials to estimate personalized treatment rules that identify the best treatment for a given patient with given covariates. Assuming that the outcomes in each treatment arm are given by a homoscedastic linear model, with possibly different variances between treatment arms, and that the trial subjects form a random sample from an unselected overall population, we optimize the (possibly randomized) treatment allocation allowing the allocation rates to depend on the covariates. We find that, for the case of two treatments, the approximately optimal allocation rule does not depend on the value of the covariates but only on the variances of the responses. In contrast, for the case of three treatments or more, the optimal treatment allocation does depend on the values of the covariates as well as the true regression coefficients. The methods are illustrated with a recently published dietary clinical trial.