Theoretical considerations on the health checkup accuracy of combination testing

To find basic theoretical evidence for an optimum combination of multi-phasic health checkup testing obtained by considering how the health checkup accuracy changes with the number of tests (n) and kinds of combination methods (A, B, C, D and E).

To find how the health checkup accuracy changes with the number of tests and type of combination method, generalized formulas as functions of the number of tests, are obtained to calculate the over-all health checkup accuracy which is defined by sensitivity (alpha), specificity (beta) and odds-ratio (gamma), based on the two-by-two table. Five kinds of combination methods were considered: A) Sequential tests. B) Sequential tests after changing the order in A. C) Simultaneous tests using the Believe-the-Negative Rule. D) Simultaneous tests using the Believe-the-Positive Rule. E) Simultaneous tests using the Believe-all-Positive-all-Negative Rule.

It was proved that combination methods A, B and C are "equivalent" for health checkup accuracy. Therefore, the five methods could be summarized into three patterns. For A, B and C: beta and gamma increased but a decreased with increasing n. For D: alpha increased but beta and gamma decreased with n. For E: alpha, beta and gamma increased with n.

Health checkup accuracy of combination testing is the best in case of E, although problems exist concerning how to judge the borderline subjects.