Partial summary measures of the predictiveness curve

In the evaluation of a biomarker for risk prediction, one can assess the performance of the biomarker in the population of interest by displaying the predictiveness curve. In conjunction with an assessment of the classification accuracy of a biomarker, the predictiveness curve is an important tool for assessing the usefulness of a risk prediction model. Inference for a single biomarker or for multiple biomarkers can be performed using summary measures of the predictiveness curve. We propose two partial summary measures, the partial total gain and the partial proportion of explained variation, that summarize the predictiveness curve over a restricted range of risk. The methods we describe can be used to compare two biomarkers when there are existing thresholds for risk stratification. We describe inferential tools for one and two samples that are shown to have adequate power in a simulation study. The methods are illustrated by assessing the accuracy of a risk score for predicting the onset of Alzheimer's disease.