Developing biomarker combinations in multicenter studies via direct maximization and penalization

Motivated by a study of acute kidney injury, we consider the setting of biomarker studies involving patients at multiple centers where the goal is to develop a biomarker combination for diagnosis, prognosis, or screening. As biomarker studies become larger, this type of data structure will be encountered more frequently. In the presence of multiple centers, one way to assess the predictive capacity of a given combination is to consider the center-adjusted area under the receiver operating characteristic curve (aAUC), a summary of the ability of the combination to discriminate between cases and controls in each center. Rather than using a general method, such as logistic regression, to construct the biomarker combination, we propose directly maximizing the aAUC. Furthermore, it may be desirable to have a biomarker combination with similar performance across centers. To that end, we allow for penalization of the variability in the center-specific AUCs. We demonstrate desirable asymptotic properties of the resulting combinations. Simulations provide small-sample evidence that maximizing the aAUC can lead to combinations with improved performance. We also use simulated data to illustrate the utility of constructing combinations by maximizing the aAUC while penalizing variability. Finally, we apply these methods to data from the study of acute kidney injury.