Inverse decision theory: Characterizing losses for a decision rule with applications in cervical cancer screening

Identifying an optimal decision rule using Bayesian decision theory requires priors, likelihoods, and losses. In many medical settings, we can develop priors and likelihoods, but specifying losses can be difficult, especially when considering both patient outcomes and economic costs. If there is a widely accepted treatment strategy, then we can consider the inverse problem and find a region in the space of losses where the procedure is optimal. We call this approach inverse decision theory (IDT). We apply IDT to the standard of care for diagnosis and treatment of precancerous lesions of the cervix, and consider an alternative procedure that has been proposed. We use a Bayesian approach to estimate the probabilities associated with the diagnostic tests and make inferences about the region in loss space where these medical procedures are optimal. In particular, we find evidence supporting the current standard of care.