Statistical Considerations for Evaluating Prognostic Biomarkers: Choosing Optimal Threshold

Abstract

The use of biomarker is increasingly popular in cancer research and various imaging biomarkers have been developed recently as prognostic markers. In practice, a threshold or cutpoint is required for dichotomizing continuous markers to distinguish patients with certain conditions or responses from those who are without. Two popular ROC based methods to establish “optimal” threshold are based on Youdan index J and closest top-left criterion. We have shown in this paper the importance to acknowledge the inherent variance of such estimates. In addition, a purely data-driven approach to search for optimal threshold can produce estimates that are not necessarily meaningful due to the large variance in such estimates. Instead, we propose to estimate the threshold through pre-specified criterion, such as a fixed level of specificity. The confidence intervals of the threshold and sensitivity at the pre-specified specificity are much narrower compared to the quantities measured through either Youdan index J or closest top left criterion. We suggest to estimate the threshold at a pre-specified level of specificity, and the sensitivity at that threshold, all the estimates should be accompanied by appropriate 95 % confidence intervals.