Determining the Optimal Sequence of Multiple Tests

The use of multiple tests can improve medical decision making by balancing the benefits of correctly treating ill patients and avoiding unnecessary treatment for healthy individuals against the potential harms of missed diagnoses, inappropriate treatments, and the costs and risks associated with testing. We quantify the incremental net benefit (INB) of single and multiple tests by accounting for a patient's pre-test probability of disease and the associated benefits, harms, and cost of treatment and testing. We decompose the INB into two components: one that captures the value of information provided by the test, independent of the cost and possible harm of testing, and another that accounts for test costs and harm. Next, we examine conjunctive, disjunctive, and majority aggregation functions, demonstrating their application through examples in prostate cancer, colorectal cancer, and stable coronary artery disease diagnostics. Our approach complements traditional threshold and decision-curve analysis by varying both the pre-test probability of disease and the cost-benefit trade-off of treatment to identify the region over which a given test provides the highest INB. Using empirical test and cost data, we compute decision boundaries to determine when conjunctive, disjunctive, majority, or even single tests are optimal, and, for combinations of tests, in what order they should be administered. In all three application examples, we find that the optimal choice and sequence of tests jointly depend on the probability of disease and the cost-benefit trade-off of treatment. An online tool that visualizes the INB for combined tests is available at https://optimal-testing.streamlit.app/.