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Introduction: Cost-effectiveness analysis (CEA) is used increasingly in medicine to determine whether the health benefit of an intervention outweighs the economic cost. Decision trees, the standard decision modeling technique for non-temporal domains, can only perform CEAs for very small problems. Objective: To develop a method for CEA in problems involving several dozen variables. Methods: We explain how to build influence diagrams (IDs) that explicitly represent cost and effectiveness. We propose an algorithm for evaluating cost-effectiveness IDs directly, i.e., without expanding an equivalent decision tree. Results: The evaluation of an ID returns a set of intervals for the willingness to pay-separated by incremental cost-effectiveness ratios (ICERs)-and, for each interval, the cost, the effectiveness, and the optimal intervention. The algorithm that evaluates the ID directly is in general much more efficient than the brute-force method, which is in turn more efficient than the expansion of an equivalent decision tree. Using OpenMarkov, an open-source software tool that implements this algorithm, we have been able to perform CEAs on two medical IDs whose equivalent decision trees contain billions of branches. Conclusion: IDs can perform CEA on many problems that could not be analyzed with decision trees.

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OpenMarkov is a Java open-source tool for creating and evaluating probabilistic graphical models, including Bayesian networks, influence diagrams, and some Markov models. With more than 100,000 lines of code, it offers some features for interactive learning, explanation of reasoning, and cost-effectiveness analysis, which are not available in any other tool. OpenMarkov has been used at universities, research centers, and large companies in more than 30 countries on four continents. Several models, some of them for real-world medical applications, built with OpenMarkov, are publicly available on Internet.

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