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The present paper deals with the problem of allocating patients to twocompeting treatments in the presence of covariates or prognostic factors inorder to achieve a good trade-off among ethical concerns, inferential precisionand randomness in the treatment allocations. In particular we suggest amultipurpose design methodology that combines efficiency and ethical gain whenthe linear homoscedastic model with both treatment/covariate interactions andinteractions among covariates is adopted. The ensuing compound optimalallocations of the treatments depend on the covariates and their distributionon the population of interest, as well as on the unknown parameters of themodel. Therefore, we introduce the reinforced doubly adaptive biased coindesign, namely a general class of covariate-adjusted response-adaptiveprocedures that includes both continuous and discontinuous randomizationfunctions, aimed to target any desired allocation proportion. The properties ofthis proposal are described both theoretically and through simulations.

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