Differential Diagnosis: Models, Heuristics, and Bounds

Physicians regularly face the challenge of differential diagnosis, i.e., differentiating between diseases with similar symptoms. As a first step, a physician forms an initial belief for each possible disease. In the second step, the physician conducts more tests and examinations over multiple periods to arrive at a single diagnosis. Although many computer-aided diagnosis (CADx) algorithms have been developed recently to generate standard prior probabilities of diseases (first step), minimal effort has focused on standardizing the second step. Toward this end, we model the second step of the multi-period differential diagnosis problem as a Markov Decision Process. We use the qualitative insights from the structure of the optimal policy to characterize conditions under which common rules of thumb used by physicians, such as "confirmation bias" (only considering the test for the most probable disease) and "restricted rule-out" (only considering the tests for the most probable disease or the disease with the greatest reward from correct diagnosis) may or may not be optimal. We discuss two approaches to constructing computationally tractable heuristics. We also use our analytical results to develop an economic index for tests and use it to construct a tailored heuristic. Further, we propose a novel integration of information relaxation and a regression-based functional approximation technique to formulate a tractable mixed-integer linear program to obtain an upper bound. Our extensive numerical experiments show that the index-based heuristic outperforms the rules of thumb and the standard limited look ahead heuristic under various values of parameters. As tests' accuracy approaches $100\%$, the heuristics that prune the breadth of the search by evaluating only a restricted set of tests for running in each period, i.e., the index-based heuristic and the physician rules of thumb, converge to the optimal policy. In contrast, the limited look-ahead heuristic that prunes the depth of the search by assuming that the diagnostic process will continue only for a small, fixed number of time horizons diverges from the optimal policy. The performance gap between the heuristics/rules and the optimal policy decreases and increases as the costs of tests increase, under low and high accuracies, respectively. Our work leverages dynamic optimization and qualitative analysis of the optimal policy to efficiently aid differential diagnosis under multiple diseases and broadens the existing research on diagnostic testing in operations that has only considered one disease.