Mathematical tools for demonstrating the clinical usefulness of biochemical markers.

Various approaches have been proposed for evaluating the diagnostic value of biochemical markers. Careful design of experimental protocol is key in carrying out any evaluation of clinical diagnostic value. A prospective cohort study is the best clinical trial design and should include an appropriate reference (gold) standard applied in every patient, the results of which are assessed blindly. The spectrum of patients evaluated should reflect the population in which the test will be used, be appropriately broad to avoid bias, and include both symptomatic and asymptomatic patients. The handling of indeterminate results and the eligibility criteria for inclusion in the study should be carefully defined. Although sensitivity, specificity, and predictive value have long been used as indices of test accuracy, newer methods such as receiver operating characteristic curve (ROC) analysis, logistic regression analysis and likelihood ratios are more robust indicators that overcome many limitations of the traditional indices. The area under the ROC curve (AUC) is the best global indicator of test accuracy, but comparisons of AUC for different tests must take correlation between the tests into account if they have been performed in the same patients. Logistic regression analysis allows the diagnostic information from several tests to be evaluated multivariately, provides a probability estimate for a given outcome, and requires few assumptions regarding the underlying distributions of test data. Logistic regression also provides a straightforward method for calculating likelihood ratios. Likelihood ratios are useful for interpreting test results in the individual patient because they provide a convenient means to directly determine predictive value without having to calculate sensitivity and specificity for a given decision limit. Application of these methods is demonstrated using specific examples.