Best combination of multiple diagnostic tests for screening purposes

In a medical diagnostic testing problem, multiple diagnostic tests are often available in distinguishing between diseased and nondiseased subjects. Different diagnostic tests are usually sensitive to different aspects of the disease. A desirable approach is to combine multiple diagnostic tests so as to obtain an optimal composite diagnostic test with higher sensitivity and specificity that detects the presence of the disease more accurately. To accomplish this, it has been observed via signal detection theory developed in the 1950s and 1960s, that the optimal combination of different diagnostic variables (i.e. the diagnostic test results) is determined by the likelihood ratio function for the diseased and nondiseased groups. The conventional approach is to fit parametric models for the diseased and nondiseased groups separately and then to use the fitted likelihood ratio function for the best combination of test results. However, this approach is not so robust if the underlying distribution functions are misspecified. Since the optimal combination depends only on the likelihood ratio function, it would be more appropriate to model this function directly. A two-sample semiparametric inference technique is applied to the model for the likelihood ratio function. We consider the best combination of multiple diagnostic tests, and study semiparametric likelihood estimation of the optimal receiver operating characteristic curve and the area under the curve. We present a bootstrap procedure along with some results on simulation and on analysis of two real data sets.