Decision Trees and Thresholds
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Case Description
A hypothetical new treatment for a neurologic disease that blocks a certain cell receptor decreases the mortality associated with the disease from 50/1000 to 15/1000. In other words, individuals who must wait to get the treatment, incur this mortality. However, if the person ultimately turns out not to have that cell receptor type, the treatment has a mortality risk of 1%. There is a perfectly accurate deep brain biopsy that allows the collection of the type of tissue required to determine if the receptor is present, but the biopsy carries a mortality risk of 0.5%.
Case Instructions
Construct a decision tree to model the trade-offs of options for patients, using mortality as the outcome. Feel free to use Excel, Amua, or construct the tree on paper.
Calculate the following from the decision tree you constructed above. Note that the first three will be in algebraic form since we do not know the \(Pr(D+\):
- Expected mortality, no treat
- Expected mortality, treat
- Expected mortality, test
- Treatment threshold (interpret result)
- No treat-test threshold (interpret result)
- Test-treat threshold (interpret result)