Test and Treatment Decisions

We extend the analysis of the treatment decision to include the diagnostic test. Because information is not perfect, the physician generally has to decide (again) under uncertainty whether to not use a test, to test and act according to the test results (i.e., treat if the test result is positive and abstain from treatment if the test result is negative), or to treat directly without a test. Under these circumstances, the core descriptive concept guiding the physician’s decision is the value of information of the test. This is the expected utility to be gained from testing. For very low and very high prior probabilities of disease, the value of information is zero; thus, it is preferable not to test. The test threshold and the test-treatment thresholds can then be identified. While the test threshold indicates the prior probability of disease at which the physician should start testing, the test-treatment threshold is the prior probability at which immediate treatment without testing is indicated. We also explore the relatedness of the threshold analysis to the decision curve analysis, an approach that has been recommended by epidemiologists for the evaluation of new tests. Finally, we study the influence of risk aversion on the propensity to use a test. For risk-averse decision makers, the diagnostic test and the treatment serve as insurance devices, and they will use them more often than risk-neutral decision makers.