An ROC comparison of four methods of combining information from multiple images of the same patient

Variance of diagnostic information contained in an image degrades diagnostic accuracy. Acquiring multiple images of the same patient (e.g., mediolateral oblique and craniocaudal view mammograms) can, in principle, help reduce this degradation. We demonstrate how this can be accomplished in the context of computer-aided diagnosis (CAD). Assuming that computer outputs obtained from multiple images of the same patient can be transformed monotonically to the same pair of truth-conditional normal distributions and, for simplicity, ignoring correlation among images, we investigate theoretically four methods of combining the computer outputs: taking the average, the median, the maximum, or the minimum. We found, as one would expect, that both the average and the median always produce an improved area under the receiver operating characteristic (ROC) curve (AUC) compared to the single-view images, while the average always produces better performance than the median. However, the maximum and minimum also can produce improved AUCs in some situations, and under certain conditions can outperform the average. Surprisingly, we found that the maximum and minimum of normally-distributed decision variables produce nearly binormal ROC curves. These results can be used as a guide in attempting to increase the efficacy of CAD when multiple images are available from the same patient.