by imposing restrictions on the numbers of variables, on the probability distributions assumed, or on the shapes and configurations of the regions. There are six main approaches: (1) linear or quadratic discrimination; (2) logistic regression; (3) nearest neighbor and kernel methods; (4) recursive partitioning (e.g., classification and regression trees, CART); (5) Bayes independence models; (6) artificial neural networks. The first two approaches are discussed in Appendix F. Hastie, Tibshirani, and Friedman (2001) and Hand (1992, 1998) give useful overviews. All these methods have proponents and critics and are supported by examples of excellent performance in which they equaled or surpassed that of experienced clinicians in a reasonably narrowly defined domain of disease or treatment. These methods have been applied in many areas, not just to problems of medical classification.
Two simple special cases of the logistic regression method reduce to simple calculations and do not require the technical details of logistic regression to describe. We describe these here because they exemplify some common aspects of methods for combining information and are often considered to provide useful guidance in medical diagnostic analyses. They also have relevance for polygraph screening.
Independent parallel testing assumes that a fixed collection of diagnostically informative dichotomous variables is obtained for each subject. The disease or other feature that is the target of detection is inferred to be present if any of the individual tests is positive. Consequently, the parallel combination test is negative only when all of its component tests are negative. In personnel security screening, one might consider the polygraph test, the background investigation for clearance, and various psychological tests administered periodically as the components of a parallel test: security risk is judged to be absent only if all the screens are negative for indications of security risk.
Under the assumed independence among tests, the specificity (1 – false positive rate) of the parallel combination test is the product of the specificities of the individual component tests. Since the component specificities are below 1, the combined or joint specificity must be lower than that of any components. Similarly, the false negative rate of the parallel combination test is the product of the false negative rates of the individual component tests, hence, also lower than that of any component. Consequently, the sensitivity of the parallel combination test is higher than the sensitivity of any component test, and the parallel combination yields a test of higher sensitivity but lower specificity than any component.