The power-integrated discriminant improvement: An accurate measure of the incremental predictive value of additional biomarkers

The predictive performance of biomarkers is a central concern in biomedical research. This is often evaluated by comparing two statistical models: a "new" model incorporating additional biomarkers and an "old" model without them. In 2008, the integrated discrimination improvement (IDI) was proposed for cases when the response variable is binary, and it is now widely applied as a promising alternative to conventional measures, such as the difference of the area under the receiver operating characteristic curve. However, the IDI can erroneously identify a significant improvement in the new model even if no additional information has been provided by new biomarkers. In order to overcome problems with existing measures, in this study, we propose the power-IDI as a measure of incremental predictive value. Our study explains why the IDI cannot avoid false detection of apparent improvements in a new model and we show that our proposed measure is better able to capture improvements in prediction. Numerical simulations and examples using real empirical data reveal that the power-IDI is not only more powerful but also incurs fewer false detections of improvement.