Evaluation of Optimal Cut-Offs and Dichotomous Combinations for Two Biomarkers to Improve Patient Selection

Identifying the right cut-off for continuous biomarkers in clinical trials is crucial for pinpointing subgroups at higher risk or more likely to benefit from treatments. Although the literature typically focuses on single biomarkers, trials often involve multiple biomarkers. Our first aim was to compare three methods-the Youden index, point closest-to-(0,1) corner on the receiving operating characteristic curve (ER) method, and concordance probability-for finding optimal cut-offs with two biomarkers, employing both empirical and non-empirical approaches. Our second and main objective was to use our proposed logic indicator approach to extend the Youden index and evaluate whether a combination of biomarkers is an improvement over a single biomarker. The indicator approach created combinations of both or either biomarker being positive. Simulation studies revealed that non-empirical methods outperformed empirical ones, where the ER-generalized additive model (GAM) and concordance-GAM performed the best overall in terms of bias and mean squared error. We illustrated these approaches with a prostate cancer study and a simulated phase 2 lung cancer study. Results indicated similar cut-offs across methods, albeit higher with non-empirical approaches. In the lung cancer simulation, cut-off values remained relatively stable. A higher cut-off could lead to fewer candidate patients, impacting study recruitment or a diagnostic tool. These insights assist in assessing whether single or combined biomarkers are more effective for identifying patients who are more likely to respond to treatment, highlighting the significance in personalized medicine, where many treatments may not benefit "average" patients.