Trust Me, I'm a Doctor?
Clinical trials usually target average treatment effects, but treatment decisions are made for individuals. This tension motivates a common criticism of evidence-based medicine: a treatment that is beneficial on average may be inappropriate for a particular patient, and skilled physicians may outperform rigid adherence to the strategy that performed best in a randomized trial. We consider how randomized and observational data from the same target population can be used to assess that possibility. Specifically, we study settings in which trial and/or observational data yield estimates of average outcomes under `treat all', `treat none', and usual care strategies in the population of interest. We derive sharp bounds on the proportion of encounters with physicians whose personal strategies outperform the better of `treat all' or `treat none' under the assumption that no physician's strategy is worse than always choosing the worse performing of `treat all' and `treat none'. These results clarify when clinical data support relying on physician discretion over the trial-average recommendation and when stronger justification is required.