Optimal marker-adaptive designs for targeted therapy based on imperfectly measured biomarkers

type="main" xml:id="rssc12092-abs-0001"> Targeted therapy revolutionizes the way that physicians treat cancer and other diseases, enabling them to select individualized treatment adaptively according to the patient's biomarker profile. The implementation of targeted therapy requires that the biomarkers are accurately measured, which may not always be feasible in practice. We propose two optimal marker-adaptive trial designs in which the biomarkers are subject to measurement errors. The first design focuses on a patient's individual benefit and minimizes the treatment assignment error so that each patient has the highest probability of being assigned to the treatment that matches his or her true biomarker status. The second design focuses on the group benefit, which maximizes the overall response rate for all the patients enrolled in the trial. We develop a Wald test to evaluate the treatment effects for marker subgroups at the end of the trial and derive the corresponding asymptotic power function. Simulation studies and an application to a lymphoma cancer trial show that the optimal designs proposed achieve our design goal and obtain desirable operating characteristics.