Inverse decision theory with medical applications
Davies, Kalatu R.
Cox, Dennis D.
Doctor of Philosophy
Medical decision makers would like to use decision theory to determine optimal treatment strategies for patients, but it can be very difficult to specify loss functions in the medical setting, especially when trying to assign monetary value to health outcomes. These issues led to the development of an alternative approach, called Inverse Decision Theory (IDT), in which given a probability model and a specific decision rule, we determine the set of losses for which that decision rule is optimal. This thesis presents the evolution of the IDT method and its applications to medical treatment decision rules. There are two ways in which we can use the IDT method. Under the first approach, we operate under the assumption that the decision rule of interest is optimal, and use the prior information that we have to make inferences on the losses. The second approach involves the use of the prior information to derive an optimal region and determine if the losses in this region are reasonable based on our prior information. We illustrate the use of IDT by applying it to the current standard of care (SOC) for the detection and treatment of cervical neoplasias. First, we model the diagnostic and treatment process as a Bayesian sequential decision procedure. Then, we determine the Bayes risk expression for all decision rules and compare the Bayes risk expression for the current SOC decision rule to the Bayes risk expressions of all other decision rules, forming linear inequality constraints on a region under which the current SOC is optimal. The current standard of care has been in use for many years, but we find another decision rule to be optimal. We question whether the current standard of care is the optimal decision rule and will continue to examine these implications and the practicality of implementing this new decision rule. The IDT method provides us with a mathematical technique for dealing with the challenges in formally quantifying patient experiences and outcomes. We believe that it will be applicable to many other disease conditions and become a valuable tool for determining optimal medical treatment standards of care.