Conditional estimation after a two-stage diagnostic biomarker study that allows early termination for futility

Many biomarkers identified in marker discovery are shown to have inadequate performance in validation studies. This motivates the use of group sequential designs that allow early termination for futility. However, an option for early termination will lead to biased estimates for studies that reach full enrollment. We propose conditional estimators and confidence intervals that correct for this bias assuming that an unadjusted estimator exists that has an independent increments covariance structure. The proposed estimators and confidence intervals are applied to conditional estimation of the receiver operating characteristic curve and the positive predictive value curve after a two-stage study that allows early termination for futility, and their performance is evaluated by simulation.