Subtrees, Use in Constructing Decision Trees

Symmetry

A common error made in building decision tree models is to neglect to include the same chance events in all strategies of the decision tree. This may occur in several contexts. For instance, in a tree examining diagnostic testing, the modeler may neglect to consider a chance node representing the presence or absence of disease (i.e., disease prevalence) in the strategy that does not involve testing. In a tree examining different treatment options, the modeler may neglect to include a chance node representing treatment-related adverse events in the Do Not Treat strategy. While this may be reasonable in some clinical circumstances, there are many diseases in which the same adverse events may occur in both treated and untreated patients. For instance, patients with atrial fibrillation who receive anticoagulation or blood thinning treatment may have bleeding complications. However, even patients who do not receive this therapy may suffer from similar bleeding events, albeit at a lower risk. Similarly, patients receiving radiation therapy for prostate cancer may suffer from difficulty in urinating. However, even patients who do not receive radiation may have similar problems, albeit at a lower rate. The use of common subtrees to model these events ensures symmetry and reduces the risk of conceptual or programming errors. Of note, an alternative representational notation for decision models is the influence diagram, which by its very nature enforces complete syntactic symmetry. An automated decision-tree-critiquing program, BUNYAN, takes advantage of the principle of symmetry to diagnose common errors in decision tree models.

Consider the simple decision tree shown in Figure 1, where the underlying presence or absence of disease is explicitly modeled only on [Page 1095]the upper Treat branch. If one were to perform a sensitivity analysis on the parameter representing the probability of disease (pDisease), increasing pDisease would decrease the expected utility or value of the Treat strategy by shifting patients from well to sick. However, variations in pDisease would have no impact on the No Treat strategy because this factor is left implicit in the outcome prognosis. This would result in clinically nonsensical sensitivity analysis results—the more likely the patient was to have disease, the worse treatment would appear to be compared with no treatment; whereas in reality patients more likely to have disease are the ones who benefit most from treatment.

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