Using Bayes theorem to estimate positive and negative predictive values for continuously and ordinally scaled diagnostic tests

Abstract

Objectives: Positive predictive values (PPVs) and negative predictive values (NPVs) are frequently reported to put estimates of accuracy of a diagnostic test in clinical context and to obtain risk estimates for a given patient taking into account baseline prevalence in the population. In order to calculate PPV and NPV, tests with ordinally or continuously scaled results are commonly dichotomized at the expense of a loss of information. Methods: Extending the rationale for the calculation of PPV and NPV, Bayesian theorem is used to calculate the probability of disease given the outcome of a continuously or ordinally scaled test. Probabilities of test results conditional on disease status are modeled in a Bayesian framework and subsequently transformed to probabilities of disease status conditional on test result. Results: Using publicly available data, probability of a clinical depression diagnosis given PROMIS Depression scores was estimated. Comparison with PPV and NPV based on dichotomized scores shows that a more fine-grained interpretation of test scores is possible. Conclusions: The proposed method bears the chance to facilitate accurate and meaningful interpretation of test results in clinical settings by avoiding unnecessary dichotomization of test scores.