Evaluating Risk Prediction with Data Collection Costs: Novel Estimation of Test Tradeoff Curves

Abstract

Background The test tradeoff curve helps investigators decide if collecting data for risk prediction is worthwhile when risk prediction is used for treatment decisions. At a given benefit-cost ratio (the number of false-positive predictions one would trade for a true positive prediction) or risk threshold (the probability of developing disease at indifference between treatment and no treatment), the test tradeoff is the minimum number of data collections per true positive to yield a positive maximum expected utility of risk prediction. For example, a test tradeoff of 3,000 invasive tests per true-positive prediction of cancer may suggest that risk prediction is not worthwhile. A test tradeoff curve plots test tradeoff versus benefit-cost ratio or risk threshold. The test tradeoff curve evaluates risk prediction at the optimal risk score cutpoint for treatment, which is the cutpoint of the risk score (the estimated risk of developing disease) that maximizes the expected utility of risk prediction when the receiver-operating characteristic (ROC) curve is concave. Methods Previous methods for estimating the test tradeoff required grouping risk scores. Using individual risk scores, the new method estimates a concave ROC curve by constructing a concave envelope of ROC points, taking a slope-based moving average, minimizing a sum of squared errors, and connecting successive ROC points with line segments. Results The estimated concave ROC curve yields an estimated test tradeoff curve. Analyses of 2 synthetic data sets illustrate the method. Conclusion Estimating the test tradeoff curve based on individual risk scores is straightforward to implement and more appealing than previous estimation methods that required grouping risk scores. Highlights The test tradeoff curve helps investigators decide if collecting data for risk prediction is worthwhile when risk prediction is used for treatment decisions. At a given benefit-cost ratio or risk threshold, the test tradeoff is the minimum number of data collections per true positive to yield a positive maximum expected utility of risk prediction. Unlike previous estimation methods that grouped risk scores, the method uses individual risk scores to estimate a concave ROC curve, which yields an estimated test tradeoff curve.