Threshold Analysis Using Diagnostic Tests with Multiple Results

Abstract

Clinical problems represented by decision trees can be analyzed in terms of the probability threshold model, which provides management recommendations based on the prior prob ability of disease, the test threshold, and the test-treatment threshold. As originally proposed, the threshold model assumes that diagnostic tests provide information about a single event that is relevant to the decision. For some problems, however, a diagnostic test may provide information about more than one such event (e.g., a computed tomography [CT] scan gives information about both mediastinal and hilar metastases in lung cancer). The authors extend the probability threshold model to cases in which a single test provides information about two events that are relevant to the decision. They derive four thresholds that determine the best strategy for any combination of test results. The approach is illustrated for the decision to use a CT scan to stage lung cancer. The analysis reveals that: 1) the range of prior probabilities for which testing is optimal increases; 2) for some prior probabilities only test results about one event are important; 3) for some prior probabilities test results about both events are important; and 4) failure to account fully for information provided by a test can lead to erroneous test and treatment recommendations. Key words: decision theory; Bayes theorem; decision making, computer-assisted; decision support technics; predictive value of tests; lung neoplasms; probability threshold; decision analysis. (Med Decis Making 1989;9:91- 103)