The Annals of Statistics

Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design

Alessandro Baldi Antognini and Maroussa Zagoraiou

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The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among covariates is adopted. The ensuing compound optimal allocations of the treatments depend on the covariates and their distribution on the population of interest, as well as on the unknown parameters of the model. Therefore, we introduce the reinforced doubly adaptive biased coin design, namely a general class of covariate-adjusted response-adaptive procedures that includes both continuous and discontinuous randomization functions, aimed to target any desired allocation proportion. The properties of this proposal are described both theoretically and through simulations.

Article information

Ann. Statist., Volume 40, Number 3 (2012), 1315-1345.

First available in Project Euclid: 10 August 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs 62L05: Sequential design
Secondary: 62G20: Asymptotic properties 60F05: Central limit and other weak theorems

Balance information criteria ethics CARA designs


Baldi Antognini, Alessandro; Zagoraiou, Maroussa. Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design. Ann. Statist. 40 (2012), no. 3, 1315--1345. doi:10.1214/12-AOS1007.

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Supplemental materials

  • Supplementary material: Supplement to “Multi-objective optimal designs in comparative clinical trials with covariates: the reinforced doubly adaptive biased coin design”. An online supplementary file contains the extension of inferential criteria C1–C5 to the case of several covariates.