Estimating the receiver operating characteristic curve in studies that match controls to cases on covariates

Studies evaluating a new diagnostic imaging test may select control subjects without disease who are similar to case subjects with disease in regard to factors potentially related to the imaging result. Selecting one or more controls that are matched to each case on factors such as age, comorbidities, or study site improves study validity by eliminating potential biases due to differential characteristics of readings for cases versus controls. However, it is not widely appreciated that valid analysis requires that the receiver operating characteristic (ROC) curve be adjusted for covariates. We propose a new computationally simple method for estimating the covariate-adjusted ROC curve that is appropriate in matched case-control studies.

We provide theoretical arguments for the validity of the estimator and demonstrate its application to data. We compare the statistical properties of the estimator with those of a previously proposed estimator of the covariate-adjusted ROC curve. We demonstrate an application of the estimator to data derived from a study of emergency medical services encounters where the goal is to diagnose critical illness in nontrauma, non-cardiac arrest patients. A novel bootstrap method is proposed for calculating confidence intervals.

The new estimator is computationally very simple, yet we show it yields values that approximate the existing, more complicated estimator in simulated data sets. We found that the new estimator has excellent statistical properties, with bias and efficiency comparable with the existing method.

In matched case-control studies, the ROC curve should be adjusted for matching covariates and can be estimated with the new computationally simple approach.