Biomarker-driven optimal designs for patient enrollment restriction

The rapidly developing field of personalized medicine is giving the opportunity to treat patients with a specific regimen according to their individual demographic, biological, or genomic characteristics, known also as biomarkers. While binary biomarkers simplify subgroup selection, challenges arise in the presence of continuous ones, which are often categorized based on data-driven quantiles. In the context of binary response trials for treatment comparisons, this paper proposes a method for determining the optimal cutoff of a continuous predictive biomarker to discriminate between sensitive and insensitive patients, based on their relative risk. We derived the optimal design to estimate such a cutoff, which requires a set of equality constraints that involve the unknown model parameters and the patients' biomarker values and are not directly attainable. To implement the optimal design, a novel covariate-adjusted response-adaptive randomization is introduced, aimed at sequentially minimizing the Euclidean distance between the current allocation and the optimum. An extensive simulation study shows the performance of the proposed approach in terms of estimation efficiency and variance of the estimated cutoff. Finally, we show the potential severe ethical impact of adopting the data-dependent median to identify the subpopulations.