When biomarker studies involve patients at multiple centers and the goal is to develop biomarker combinations for diagnosis, prognosis, or screening, we consider evaluating the predictive capacity of a given combination with the center-adjusted AUC (aAUC), a summary of conditional performance. Rather than using a general method to construct the biomarker combination, such as logistic regression, we propose estimating the combination by directly maximizing the aAUC. Furthermore, it may be desirable to have a biomarker combination with similar predictive capacity across centers. To that end, we allow for penalization of the variability in center-specific performance. We demonstrate good asymptotic properties of the resulting combinations. Simulations provide small-sample evidence that maximizing the aAUC can lead to combinations with greater predictive capacity than combinations constructed via logistic regression. We further illustrate the utility of constructing combinations by maximizing the aAUC while penalizing variability. We apply these methods to data from a study of acute kidney injury after cardiac surgery.



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