Identifying optimal approaches to early termination in two-stage biomarker validation studies

Group sequential study designs have been proposed as an approach to conserve resources in biomarker validation studies. Typically, group sequential study designs allow both ‘early termination to reject the null hypothesis’ and ‘early termination for futility’ if there is evidence against the alternative hypothesis. In contrast, several researchers have advocated for using group sequential study designs that allow only early termination for futility in biomarker validation studies because of the desire to obtain a precise estimate of marker performance at study completion. This suggests a loss function that heavily weights the precision of the estimate that is obtained at study completion at the expense of an increased sample size when there is strong evidence against the null hypothesis. We propose a formal approach to comparing designs that allow early termination for futility, superiority or both by developing a loss function that incorporates the expected sample size under the null and alternative hypotheses, as well as the mean-squared error of the estimate that is obtained at study completion. We then use our loss function to compare several candidate designs and derive optimal two-stage designs for a recently reported validation study of a novel prostate cancer biomarker.