A REGRET THEORY APPROACH TO DECISION CURVE ANALYSIS

Purpose: Decision curve analysis (DCA) has been proposed as an alternative method for evaluation of diagnostic tests, prediction models, and molecular markers [MDM 2006;26:565]. We re-formulated DCA from the regret theory point of view to take into consideration decision consequences [MDM 2008;28:540].

Method: First, we constructed a classic decision tree describing three decision alternatives: treat, do not treat, and treat/no treat based on a predictive model. We then computed the expected regret for each of these alternatives as the difference between the utility of the action taken and the utility of the action that should have been taken, in retrospect. We evaluated the expected regret(s) for the tree using different weightings regarding regret associated with “omissions” (e.g. failure to treat) vs. “commissions” (e.g. treating unnecessary). For any pair of strategies, we measure the difference in net expected regret (NERD), by subtracting the expected regret of each alternative from the other. Finally, using the concept of acceptable regret-the range at which potential regret associated with wrong decisions becomes acceptable- we identified the circumstances where acting on a given strategy will be acceptable even if the decision was wrong.

Result: We first showed that NERD is equivalent to net benefits as described in the original DCA. The regret re-formulation of the original DCA model showed an asymmetry in decision-making. That is, the decision-maker seems to weigh (=the threshold probability at which a decision-maker is indifferent between two actions) regret associated with failure to treat much higher than the regret related to unnecessary treatment. This is because the decision-maker weights true positive results to a much greater extent than false-positive results. Similarly, different attitudes toward omissions vs. commissions identified different circumstances when the decision-maker can “live with” regret even if the decision was wrong, in retrospect. The symmetry in the decision-making was re-instated when the weighting for false-positive and false-negative results was identical.

Conclusion: We present an alternative derivation of the DCA based on regret theory. Under assumptions of unequal weighting, the regret approach generates identical results to the original DCA. The regret approach may also be intuitively more appealing to a decision-maker, particularly in those clinical situations when the best management option is the one associated with the least amount of regret (e.g. treatment of advanced cancer, etc).