Finding the optimal multiple-test strategy using a method analogous to logistic regression: The diagnosis of hepatolenticular degeneration (Wilson's disease)

Finding the optimal strategy among a battery of tests may be cumbersome for decision-analytic models. The authors present a method of examining multiple test combinations that is based on a modified Bayes' formula analogous to logistic regression. They examined all 16 combinations of four tests used to diagnose hepatolenticular degeneration. The four tests examined were: serum ceruloplasmin level, 24-hour urinary copper excretion, free serum copper level, and liver biopsy copper concentration. They also simulated the diagnostic workup of the disease for a hypothetical cohort of 15,000 patients at risk. Assuming the disutilities of false positives and false negatives to be equal, and considering sensitivity analysis of test characteristics, the following test combinations were found to be optimal for making the diagnosis at a prior probability of disease equal to 0.05: positive serum ceruloplasmin and 24-hour urinary copper excretion, combined with either positive liver biopsy or free serum copper (or both). The strategies obtained by the modified Bayes' formula were the same as those found using the simulated data set with a standard logistic-regression software package. The logistic model's diagnostic accuracy is 0.98 as measured by the area under the receiver operating characteristic curve. The optimal strategy for diagnosing hepatolenticular degeneration varies with the prior probability of disease. For prior probabilities of 0.05, 0.25, and 0.9, and the optimal strategy, model sensitivities are 0.801, 0.880, and 0.997, and model specificities are 0.991, 0.985, and 0.814, respectively. The new method provides a convenient alternative to decision trees when examining multiple diagnostic tests.