🤖 AI Summary
This study addresses the limitations of traditional Markov queueing models in health economics, which rely on precisely specified transition matrices that are often not uniquely identifiable from available data, thereby undermining decision robustness. The authors introduce a set of evidence-compatible transition matrices and formulate a finite-horizon Markov queueing model under imprecise probabilities, marking the first application of imprecise probability methods to cumulative health economic outcomes. Under row-wise independence and compactness assumptions, they develop an efficient computational approach for bounding expected outcomes using Bellman-type upper and lower transition operators combined with an imprecise Dirichlet model, and establish corresponding envelope and consistency theorems. Applied to a cost-effectiveness analysis of patent foramen ovale closure, the proposed method reveals that the net monetary benefit interval straddles zero—contrasting with the modest support for intervention suggested by conventional methods—and highlights substantial sensitivity of policy decisions to unidentified transition probabilities.
📝 Abstract
In applied health research, Markov cohort models are built on a precisely specified transition probability matrix. However, in many applications, the available evidence -- transition counts, structural constraints, and treatment-effect data -- identifies a set of admissible matrices rather than one uniquely justified matrix. This paper formulates an imprecise-probability extension in which inference yields lower and upper expectations over an evidence-compatible set of precise Markov cohort models. The contribution differs from existing imprecise Markov-chain work by focusing on finite-horizon cohort trajectories, additive accumulated outcomes, and transition matrices constructed from empirical transition counts. Under non-empty compact separately specified outgoing-row sets, the lower and upper accumulated outcomes are computed exactly by Bellman-style lower and upper transition operators. We prove the envelope theorem, reduction to the classical model, coherence properties of the lower transition operator, and algebraic conditions under which a single selected matrix yields a non-robust decision. We then show how multinomial transition counts induce admissible matrix sets through the Imprecise Dirichlet Model. A real-world cost-effectiveness example of patent foramen ovale closure after cryptogenic stroke illustrates the practical consequence: the empirical transition matrix slightly favors closure, whereas the imprecise analysis yields an incremental net monetary benefit interval crossing zero. The method provides both a rigorous lower-expectation formulation and a practical diagnostic for decisions that depend on transition probabilities not fully resolved by the evidence.