Decision rules for subgroup selection based on a predictive biomarker

When investigating a new therapy, there is often some plausibility that the treatment is more efficient (or efficient only) in a subgroup as compared to the total patient population. In this situation, the target population for the proof of efficacy is commonly selected in a data-dependent way, for example, based on the results of a pilot study or a planned interim analysis. The performance of the applied selection rule is crucial for the success of a clinical trial or even a drug development program. We consider the situation in which the selection of the patient population is based on a biomarker and where the diagnostic that evaluates the biomarker may be perfect, that is, with 100% sensitivity and specificity, or not. We develop methods that allow an evaluation of the operational characteristics of rules for selecting the target population, thus enabling the choice of an appropriate strategy. Especially, the proposed procedures can be used to calculate the sample size required to achieve a specified selection probability. Furthermore, we derive optimal selection rules by modeling the uncertainty about parameters by prior distributions. Throughout, there is a strong impact of sensitivity and specificity of the biomarker on the results. It is therefore essential to evaluate the rules for patient selection before applying them, thereby bearing in mind that the diagnostic that evaluates the applied biomarker may be imperfect.