Abstract:

Accuracy of medical tests are often assessed using the Receiver Operating Characteristic (ROC) curve. Parametric methods to estimate the ROC curve generally assume binormality. However, often the population with disease is heterogeneous and may represent a mixture of normal distributions. In this case the ROC curve is a mixture of the ROC curves corresponding to components of the mixture. To use the medical test for diagnosis, one must identify a threshold/optimal point (OP). To date, nobody has determined what the OP for this mixture of ROC curves should be. Assuming the distribution of those without disease is Normal, and those with disease is a mixture of Normal distributions, we estimated the OP as the value maximizing the Youden Index (YI). Here the sensitivity term is a sum of sensitivities from each of the component ROC curves; the Youden index is a mixture of the individual YI’s. No closed form solution for the OP exists, but a grid search can be used to find the OP. Confidence intervals around the OP can be determined through bootstrapping. As an example, data from Wieand et al regarding the biomarker CA199 for pancreatic cancer was used.
