Treatment Decisions Without Diagnostic Tests

Abstract

We consider a medical case which requires a physician’s treatment decision where no diagnostic test is available. The physician knows the particular illness and its treatment, as well as a sick person’s utility gain and a healthy person’s utility loss from treatment. But he is uncertain whether the patient is actually sick or not. To aid his decision, we derive a lower boundary for the a priori probability of the illness at which treatment is indicated. We show that a risk-averse physician should treat at a lower a priori probability than a risk-neutral physician. We also analyze the therapeutic risk, i.e., the risk that treatment fails, and derive the success probability threshold, above which the physician will undertake treatment. In contrast to the diagnostic risk, the threshold for the successful treatment probability is higher for a risk-averse decision maker than for a risk-neutral one. Finally, we consider the diagnostic risk and the therapeutic risk simultaneously and study the thresholds in this extended model.