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Introduction: Cost-effectiveness analysis (CEA) is used increasingly in medicine to determine whether the health benefit of an intervention is worth the economic cost. Decision trees, the standard decision modeling technique for non-temporal domains, can only perform CEAs for very small problems. Influence diagrams can model much larger problems, but only when the decisions are totally ordered.Objective: To develop a CEA method for problems with unordered or partially ordered decisions, such as finding the optimal sequence of tests for diagnosing a disease.Methods: We explain how to model those problems using decision analysis networks (DANs), a new type of probabilistic graphical model, somewhat similar to Bayesian networks and influence diagrams. We present an algorithm for evaluating DANs with two criteria, cost and effectiveness, and perform some experiments to study its computational efficiency. We illustrate the representation framework and the algorithm using a hypothetical example involving two therapies and several tests and then present a DAN for a real-world problem, the mediastinal staging of non-small cell lung cancer.Results: The evaluation of a DAN with two criteria, cost and effectiveness, returns a set of intervals for the willingness to pay, separated by incremental cost-effectiveness ratios (ICERs). The cost, the effectiveness, and the optimal intervention are specific for each interval, i.e., they depend on the willingness to pay.Conclusion: Problems involving several unordered decisions can be modeled with DANs and evaluated in a reasonable amount of time. OpenMarkov, an open-source software tool developed by our research group, can be used to build the models and evaluate them using a graphical user interface. [ABSTRACT FROM AUTHOR]