Determining the Optimal Sequence of Multiple Tests

The use of multiple tests can improve medical decision making. The patient utility maximizing combination of these tests involves balancing the benefits of correctly treating ill patients and avoiding unnecessary treatment for healthy individuals against the potential harms of missed diagnoses or inappropriate treatments. We quantify the incremental net benefit (INB) of single and multiple tests by accounting for a patients pre-test probability of disease and the associated benefits and harms of treatment. 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. We examine conjunctive, disjunctive, and majority aggregation functions, demonstrating their application through examples in prostate cancer, colorectal cancer, and stable coronary artery disease diagnostics. Using empirical test and cost data, we identify decision boundaries to determine when conjunctive, disjunctive, majority, or even single tests are optimal, based on a patients pre-test probability of disease and the cost-benefit tradeoff of treatment. In all three cases, we find that the optimal choice of combined tests depends on both the cost-benefit tradeoff of treatment and the probability of disease. An online tool that visualizes the INB for combined tests is available at https://optimal-testing.streamlit.app/.