A Quantitative Concordance Measure for Comparing and Combining Treatment Selection Markers.

Motivated by an HIV example, we consider how to compare and combine treatment selection markers, which are essential to the notion of precision medicine. The current literature on precision medicine is focused on evaluating and optimizing treatment regimes, which can be obtained by dichotomizing treatment selection markers. In practice, treatment decisions are based not only on efficacy but also on safety, cost and individual preference, making it difficult to choose a single cutoff value for all patients in all settings. It is therefore desirable to have a statistical framework for comparing and combining treatment selection markers without dichotomization. We provide such a framework based on a quantitative concordance measure, which quantifies the extent to which higher marker values are predictive of larger treatment effects. For a given marker, the proposed concordance measure can be estimated from clinical trial data using a U-statistic, which can incorporate auxiliary covariate information through an augmentation term. For combining multiple markers, we propose to maximize the estimated concordance measure among a specified family of combination markers. A cross-validation procedure can be used to remove any re-substitution bias in assessing the quality of an optimized combination marker. The proposed methodology is applied to the HIV example and evaluated in simulation studies.