Effect of correlation on combining diagnostic information from two images of the same patient

We have shown previously, in the context of computer-aided diagnosis (CAD), that information derived from multiple images of the same patient can be used to improve diagnostic performance. In that work, we ignored the correlation among multiple images of the same patient. In the present study, we investigate theoretically, within the framework of receiver operating characteristic (ROC) analysis, the effect of correlation on three methods for combining quantitative diagnostic information from two images: taking the average, the maximum, and the minimum of a pair of normally distributed decision variables. We assume, as in our previous work, that the quantitative diagnostic information obtained from the two images of a given patient can be transformed monotonically to two latent decision variables that are normally distributed. Similar to the situation of uncorrelated images, we found that (1) the average always improves the area under the ROC curve (AUC) compared to the single-view image; (2) the maximum and the minimum can also, but not always, improve the AUC; and (3) each method can be the best method in certain situations. In addition, as the correlation strength increases, the average performs the best less often, whereas the maximum and the minimum perform the best more often. These theoretical results are illustrated with analysis of a mammography study.