Optimizing Sequential Diagnostic Testing under Uncertainty: Models, Heuristics, and Bounds for Differential Diagnosis

Abstract

Physicians regularly face the challenge of differential diagnosis---distinguishing among multiple diseases with overlapping symptoms---by ordering diagnostic tests to identify the underlying condition. In non-urgent outpatient settings, where patients present with chronic symptoms such as cough, fatigue, or headaches, clinical constraints and insurance prior authorization rules dictate that tests are conducted sequentially across encounters, each test is administered at most once, and parallel testing is precluded. Clinical guidelines often do not comprehensively prescribe test sequencing and stopping rules across broad differentials, and physician heuristics fail to fully capture economic trade-offs. To bridge this gap, we formalize a finite-horizon Markov Decision Process (MDP) where a physician sequentially selects costly, imperfect tests, updates Bayesian beliefs, and decides when to declare a diagnosis, maximizing expected reward net of testing costs and misdiagnosis penalties. The state space and problem complexity grow exponentially in the number of candidate diseases (N), and specifically targeted tests that are informative only about their corresponding diseases cannot be ordered by Blackwell informativeness for N>=3, precluding classical sequencing rules. We present a novel decomposition of the optimal policy into test subset selection, sequencing, and declaration, so that the expected net reward is supermodular over test subsets, enabling a polynomial-time algorithm for general asymmetric rewards, penalties, and costs under perfect tests. Building on this, we develop the Economic Index Policy (EIP), a polynomial-time heuristic for imperfect tests that synthesizes priors, test accuracies, rewards, penalties, and costs into a single sequencing criterion. To benchmark performance at scale, we derive a mixed-integer linear program upper bound on the optimal value using the information relaxation technique. In a clinically calibrated case study of pediatric chronic cough with 16 candidate diseases, EIP outperforms the prior-based heuristic (testing by descending probability) by 17.7%, the cost-adjusted prior-based heuristic (testing by descending probability-to-cost ratio) by 15.7%, the information gain heuristic (testing by expected uncertainty reduction) by 68.6%, and the cost-adjusted information gain heuristic by 31.7%, with gaps between EIP and the upper bound frequently below 10%. These improvements arise from three mechanisms: severity-weighted rebalancing of initial tests toward rare but critical conditions, cost-effective prioritization of cheap and accurate tests, and adaptive stopping calibrated to reward heterogeneity.

Keywords: Differential Diagnosis, Diagnostic Test Sequencing, Information Relaxation, Heuristics