Treatment Decisions

We present the cornerstone of medical decision making under uncertainty. If no diagnostic test is available, the physician faces the risk of a misdiagnosis: They may either treat a patient who is healthy or fail to treat one who is sick. We assume that the physician knows the patient’s utility gain from treatment in the sick state and the patient’s utility loss from treatment in the healthy state. This allows us to derive the treatment threshold, which identifies the prior probability of disease at which the physician is indifferent between treatment and no treatment. This threshold provides for a decision rule: Treat if the prior probability of disease is above the threshold, do not treat if it is below. We show that a risk-averse physician treats the patient at a lower prior probability of disease than a risk-neutral physician because the risk-averse physician values the utility gain to the sick more and the utility loss to the healthy less than the risk-neutral physician. We also analyze the therapeutic risk (i.e., the risk that treatment fails) and derive the threshold of the probability of success above which the physician decides to treat the patient. In contrast to the diagnostic risk, the treatment threshold is higher for a risk-averse physician than for a risk-neutral one. Finally, we combine the diagnostic risk and the therapeutic risk and study the effects on the thresholds if both risks are considered simultaneously.