D‐Optimal Designs for Comparative Experiments When Different Models for the Treatment Effects Are Assumed in the Competing Arms

Traditional clinical trials have been designed to estimate an average treatment effect across a homogeneous patient population; however, with the advent of personalized medicine, treatments are developed to target groups of patients with specific characteristics identified, for instance, by predictive biomarkers. Thus, we focus on an experimental scenario in which the treatment effect of a new drug depends on covariates, while the control group, representing standard care or placebo, is assumed to be unaffected by these patient-specific factors. Under this setting, the D-optimal design is characterized by (i) an unbalanced allocation that favours the new treatment and by (ii) equality constraints imposed on the empirical moments of the covariates in the treatment groups. Because patient covariates are observed only at the time of enrolment, the optimal allocation can be achieved sequentially. The impact of the proposed strategy is further demonstrated by a simulation study, illustrating how balanced allocations can significantly reduce estimation efficiency.