Applications of Bayesian sequential decision theory to medical decision-making
Swartz, Richard J.
Cox, Dennis D.
Doctor of Philosophy
This thesis considers the use of Bayesian sequential decision theory for the diagnosis of pre-cancerous lesions of the cervix otherwise known as cervical intraepithelial neoplasia (CIN). We consider a sequence of n diagnostic tests where the ordering of the tests is predetermined. After each test in the sequence, the clinician must either make a treatment decision based on available information or continue testing. Our method allows the use of the previously collected information along with the new information collected at each level. In addition, we apply Bayesian sequential decision theory in a setting where the observations are not independent and identically distributed. Before this theory can be applied to the medical setting, a satisfactory method of attaining the costs of diagnostic tests and losses associated with treatment decisions must be specified. These costs and losses must be in the same units of measurement and they should include monetary considerations and both positive and negative patient outcomes. This thesis provides a method to determine bounds on relative costs and losses for medical decisions. First the medical decision process is modelled as a Bayesian sequential decision problem. Then we assume the current standard of care for detection of CIN is optimal, and use the model to determine bounds for the costs associated with testing and the losses associated with treatment. Unlike several other approaches, the costs and losses from our analysis potentially incorporate both monetary considerations and patient outcomes associated with testing and treatment or non-treatment. We estimate the probabilities necessary for the model from data collected at the University of Texas M. D. Anderson Cancer Center. We use both maximum likelihood estimates and Bayesian posterior mean estimates, with a prior developed from the literature. We also randomly sampled from the posterior distribution and compared our empirical bounds on the losses to values for the bounds on the losses reported in the cancer literature. The implications are discussed further in the thesis.