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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 responseadaptive
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
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