Generalized likelihood ratio concept and logistic regression analysis for multiple diagnostic categories.

Albert (Clin Chem 1982;28:1113-9) has proposed estimation of likelihood ratios by logistic regression analysis. The usual likelihood-ratio approach for estimation of post-test probability of disease from sensitivity and specificity data of a diagnostic test has been extended by Birkett (J Clin Epidemiol 1988; 41:491-4) for situations with more than two diagnostic categories. We suggest here a combination of these ideas, demonstrating this by a re-evaluation of previously published data on the validity of neopterin as a tool for differential diagnosis between chronic non-A, non-B hepatitis and fatty liver. Analysis of neopterin data in combination with the ratio between serum concentrations of aspartate aminotransferase and of alanine aminotransferase yielded a good discrimination between three mutually exclusive diagnostic categories, namely, fatty liver and chronic persistent and chronic aggressive non-A, non-B hepatitis. The approach is flexibly applicable to situations with different pre-test probabilities. The sum of estimated post-test probabilities deviates slightly from the sum of pre-test probabilities. This deviation is a function of the coefficients obtained in logistic regression, and an analytical expression for the deviation is given. The generalized likelihood-ratio approach appears promising in complex diagnostic situations when multiple diagnostic tests are available.