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Abstract:
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Various measures quantifying the predictiveness of a continuous marker for a binary outcome have been proposed, including the area under the ROC curve, proportion of variation explained, correlation of outcome with risk, Brier score, and concordance index. We argue that the predictive capacity of a marker has to do with the population distribution of risk, given the marker, and suggest a graphical tool---the predictiveness curve---to display this distribution. This provides a common scale to compare markers that may not be comparable on their original scales. Some existing measures of predictiveness are shown to be summary indexes derived from the predictiveness curve. Other measures are concerned with the performance of decision rules based on the marker, which we argue is different from its predictiveness. Applications to cancer biomarkers will be discussed.
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