The likelihood approach for the comparison of medical diagnostic system with multiple binary tests

Detection (diagnosis) techniques play an important role in clinical medicine. Early detection of diseases could be life-saving, and the consequences of false-positives and false-negatives could be costly. Using multiple measurements strategy is a popular tool to increase diagnostic accuracy. In addition to the new diagnostic technology, recent advances in genomics, proteomics, and other areas have allowed some of these newly developed individual biomarkers measured by non-invasive and inexpensive procedures (e.g. samples from serum, urine or stool) to progress from basic discovery research to assay development. As more tests become commercially available, there is an increasing interest for clinicians to request combinations of various non-invasive and inexpensive tests to increase diagnostic accuracy. Using information regarding individual test sensitivities and specificities, we proposed a likelihood approach to combine individual test results and to approximate or estimate the combined sensitivities and specificities of various tests taking into account the conditional correlations to quantify system performance. To illustrate this approach, we considered an example using various combinations of diagnostic tests to detect bladder cancer.