Analysis of Physicians’ Probability Estimates of a Medical Outcome Based on a Sequence of Events

IMPORTANCE: The probability of a conjunction of 2 independent events is the product of the probabilities of the 2 components and therefore cannot exceed the probability of either component; violation of this basic law is called the conjunction fallacy. A common medical decision-making scenario involves estimating the probability of a final outcome resulting from a sequence of independent events; however, little is known about physicians’ ability to accurately estimate the overall probability of success in these situations. OBJECTIVE: To ascertain whether physicians are able to correctly estimate the overall probability of a medical outcome resulting from 2 independent events. DESIGN, SETTING, AND PARTICIPANTS: This survey study consisted of 3 separate substudies, in which 215 physicians were asked via internet-based survey to estimate the probability of success of each of 2 components of a diagnostic or prognostic sequence as well as the overall probability of success of the 2-step sequence. Substudy 1 was performed from April 2 to 4, 2021, substudy 2 from November 2 to 11, 2021, and substudy 3 from May 13 to 19, 2021. All physicians were board certified or board eligible in the primary specialty germane to the substudy (ie, obstetrics and gynecology for substudies 1 and 3 and pulmonology for substudy 2), were recruited from a commercial survey service, and volunteered to participate in the study. EXPOSURES: Case scenarios presented in an online survey. MAIN OUTCOMES AND MEASURES: Respondents were asked to provide their demographic information in addition to 3 probability estimates. The first substudy included a scenario describing a brow presentation discovered during labor; the 2 conjuncts were the probabilities that the brow presentation would resolve and that the delivery would be vaginal. The second substudy involved a diagnostic evaluation of an incidentally discovered pulmonary nodule; the 2 conjuncts were the probabilities that the patient had a malignant condition and that a technically successful transthoracic needle biopsy would reveal a malignant condition. The third substudy included a modification of the first substudy in an attempt to debias the conjunction fallacy prevalent in the first substudy. Respondents’ own probability estimates of the individual events were used to calculate the mathematically correct conjunctive probability. RESULTS: Among 215 respondents, the mean (SD) age was 54.0 (9.5) years; 142 respondents (66.0%) were male. Data on race and ethnicity were not collected. A total of 168 physicians (78.1%) estimated the probability of the 2-step sequence to be greater than the probability of at least 1 of the 2 component events. Compared with the product of their 2 estimated components, respondents overestimated the combined probability by 12.8% (95% CI, 9.6%-16.1%; P < .001) in substudy 1, 19.8% (95% CI, 16.6%-23.0%; P < .001) in substudy 2, and 18.0% (95% CI, 13.4%-22.5%; P < .001) in substudy 3, results that were mathematically incoherent (ie, formally illogical and mathematically incorrect). CONCLUSIONS AND RELEVANCE: In this survey study of 215 physicians, respondents consistently overestimated the combined probability of 2 events compared with the probability calculated from their own estimates of the individual events. This biased estimation, consistent with the conjunction fallacy, may have substantial implications for diagnostic and prognostic decision-making.