The statistical framework used in medical decision making is based on the theory of errors developed 200 years ago by Legendre, Gauss and Laplace. This framework was developed to combine observations with experimental or observational errors in astronomy, geodesy and physics. The costs of errors were assumed to be symmetric and quadratic. In medical decision making, costs of false negative errors are quite different from the costs of false positive errors. Some errors have no consequence for the final decision. Another problem with many traditional statistical methods is that parameter estimates are developed to minimize the estimation errors and not the prediction errors for a specific class of decision problems. In this project, a new approach to medical decision making is proposed. When the number of feasible medical conditions is m, with one least cost treatment for each, the total number of correct decision is m and the maximum number of errors is m(m-1). Parameter estimates and threshold probabilities will be developed jointly to minimize the total cost of errors and correct decisions. The popular estimation methods such as the least squares and the maximum likelihood are special cases in this approach. The estimates will in general be biased, but will minimize the costs of treatment. It is similar to using weights in an estimation procedure with a crucial difference: the weights here are not exogenously specified, but endogenously determined and sensitive to the decision context. The efficiency of the new approach will be studied using Monte Carlo techniques as well as real data relating to two medical conditions, brain cancer and diabetes. According to preliminary studies, this approach leads to a cost reduction of 6.4% when compared with the logistic regression models. While these methods can be used to determine the least cost decision rules, they can even be used to diagnose the diagnostician's own behavior using actual cost to point out the areas for improvement such as sensitivity and specificity. Algorithms to compute the decision rules will be developed for frequently used probability distributions.
