Purpose: To develop a method of cost-effectiveness analysis (CEA) that avoids the typical restriction that there is only one decision to be made or that the decision is the root node in the tree.

Statement of the problem: Cost-effectiveness analyses (CEAs) usually assume that the problem involves only one decision. When the analysis is performed by means of a decision tree, that decision is the root node. However, many medical problems involve several decisions. For instance, we may be interested in the cost-effectiveness of a test, whose result may guide the choice of the best therapy. In this case “Therapy” would be an “embedded decision node” in the decision tree. The cost-effectiveness of the test depends on which treatment will be selected, and this in turn may depend on lambda, a parameter that determines how much money the decision maker is willing to pay per each QALY gained. The problem is that lambda is unknown when performing a cost-effectiveness analysis—otherwise a one-dimensional analysis based on the net health benefit (NHB) would replace the two-dimensional CEA. A similar problem may arise when there is only one decision but the root node is a chance variable: each context in which the decision has to be made is represented in the tree by an embedded decision node.

Methods: We have developed an algorithm for computing the cost and the effectiveness in decision trees with embedded decision nodes. The method is similar to the traditional evaluation of decision trees, but instead of returning a single utility value for each branch, it returns a list of lambda intervals, each having a cost and an effectiveness. The limits of those intervals are obtained from the incremental cost-effectiveness ratios (ICERs) stemming from posterior decisions.

Results: We have built a decision support software tool for performing CEA in decision trees with embedded nodes. It displays the results of the analysis in the form of text or in the form of a cost-effectiveness plot for each decision node and each lambda interval.

Conclusions: The method and the software tool that we have developed will permit to perform CEAs for many problems that could not be solved with traditional methods and tools.