Preliminary, Comments Welcome PROFIT MAXIMIZING ESTIMATORS AND MEDICAL DECISION RULES

When outcomes of actions are random variables with unknown parameters, a popular approach to choose an optimal action involves two steps: 1. Estimate the parameters of a probability distribution using some criterion such as minimizing the sum of squared errors or maximum likelihood. 2. Choose an action to minimize the expected loss (or maximize the expected proÞt) using the criterion relevant for the outcome of the action. In this two step procedure, the choice of estimation and prediction rules are based two different loss functions. In this paper we present a method for simultaneous estimation and prediction that minimizes costs of estimation and prediction errors using a common loss function. This non-parametric method is the frequentist’s analogue of the Bayesian procedures using predictive densities. This technique outperforms the conventional two-step method in both small and large samples. Disease management typically involves problem of joint estimation (diagnosis) and prediction (treatment). In an application to diagnosing hypoand hyperglycemia in diabetic patients and choosing optimal insulin doses, it is shown that average cost of treatment errors is lower with the approach presented in this paper.