Probabilistic reasoning and clinical decision-making: do doctors overestimate diagnostic probabilities?

Background: The 'threshold approach' is based on a physician's assessment of the likelihood of a disease expressed as a probability. The use of Bayes' theorem to calculate disease probability in patients with and without a particular characteristic, may be hampered by the presence of subadditivity (i.e. the sum of probabilities concerning a single case scenario exceeding 100%). Aim: To assess the presence of subadditivity in physicians' estimations of probabilities and the degree of concordance among doctors in their probability assessments. Design: Prospective questionnaire. Methods: Residents and trained physicians in Family Medicine, Internal Medicine and Cardiology (n = 84) were asked to estimate the probability of each component of the differential diagnosis in a case scenario describing a patient with chest pain. Results: Subadditivity was exhibited in 65% of the participants. The total sum of probabilities given by each participant ranged from 44% to 290% (mean 137%). There was wide variability in the assignment of probabilities for each diagnostic possibility (SD 16-21%). Discussion: The finding of substantial subadditivity, coupled with the marked discordance in probability estimates, questions the applicability of the threshold approach. Physicians need guidance, explicit tools and formal training in probability estimation to optimize the use of this approach in clinical practice.