Is What You Call Probable…Impossible?

Physicians tend to excel in science and math, so it’s a bit surprising that, in a new study, nearly 8 in 10 ― 78% ― committed a gaffe called the conjunction fallacy.

Researchers asked doctors to estimate the probability of a sequence of events in a clinical scenario. But most gave answers that were logically impossible, the study found.

In medicine, this type of mistake can lead to clinical missteps, including overtreatment of patients, said Scott K. Aberegg, MD, MPH, associate professor of medicine at the University of Utah, Salt Lake City, who is a co-author of the new study.

The impetus for the research, published this week in JAMA Network Open, was a real obstetrics case.

If a physician overestimates the likelihood of successful vaginal delivery as a result of this type of error in thinking, they might not recognize cases in which an immediate cesarean delivery is warranted. The result can have “catastrophic” consequences for the mother and child, the researchers write.

Committing the Conjunction Fallacy

To examine the ability of clinicians to accurately estimate the probability of a medical outcome that results from two independent events, Aberegg and his colleagues Hal R. Arkes, PhD, and Kevin A. Arpin, PhD, asked 215 physicians to complete online surveys.

Participants estimated the likelihood of a main medical outcome ― which depended on two events occurring first. In addition to estimating the probability of the main outcome, physicians assigned each event its own probability.

Doctors consistently estimated that the main outcome was more likely than one or both of the component events.

Mathematically, that does not compute.

And in so doing, the doctors were committing the conjunction fallacy.

Obstetricians and Pulmonologists

The study included three surveys. One, taken by 67 obstetricians, asked about the likelihood of successful vaginal delivery after brow presentation was discovered during labor. The main outcome in this case ― successful vaginal delivery ― depended on the likelihood of conversion to a deliverable position and the odds of delivering vaginally from that new position.

A second survey, taken by 84 pulmonologists, asked about the odds that a biopsy of a pulmonary nodule would reveal cancer. In this scenario, the main outcome hinged on “the probability that the nodule is cancerous and the probability of the biopsy successfully detecting cancer in the presence of a cancerous nodule,” according to the researchers.

A third survey, taken by 64 obstetricians, was similar to the first survey, but the researchers reordered the questions in a way that they thought might lead to fewer illogical responses: they asked about the two component events first.

In the first survey, 74.6% of the respondents committed the conjunction fallacy. In the pulmonary nodule survey, 86.9% committed the conjunction fallacy. In the third survey, 70.3% committed the conjunction fallacy.

Only one physician estimated a main outcome probability that equaled the product of the component event estimates, in accordance with the multiplication rule for probability.

“Physicians did not know (or did not recognize when to use) the multiplication rule for probability,” the researchers concluded.

Consequences and Applications

Estimating probabilities is a key element of day-to-day medical practice, said Aartik Sarma, MD, of the University of California, San Francisco.

Sarma said he plans to incorporate the concepts from the study into his clinical teaching in the intensive care unit.

“This study suggests we need to improve how we teach medical students and physicians about probability, especially in multistep processes,” Sarma told Medscape Medical News. “Doctors balance probabilities of risks and benefits every day. If their intuitions about probability are incorrect, this could harm patients.”

Adam Rodman, MD, an internist at Beth Israel Deaconess Medical Center and instructor at Harvard Medical School, Boston, noted that the study assumed that the component events were truly independent. In other contexts, that may not be the case.

“That being said, the fundamental principle remains even if there are varying degrees of independence,” Rodman said. “If, as the paper shows, physicians fundamentally misunderstand the multiplication rule of probability due to innumeracy, they are dramatically overestimating the post-test probabilities of disease ― and drastically overtreating people.”

Apart from the frequent commissions of the conjunction fallacy, the probability estimates that doctors gave were widely scattered.

“It really seems as though ― in this study and in my experience in medicine ― that when asked to predict a probability, physicians either are completely unwilling to do so or provide nothing more than a wild guess,” Aberegg said. “That sounds pejorative. It sounds like I’m poking at my fellow physicians, and I don’t want it to seem that way. But I think that’s just reflective of a general discomfort with or lack of facility with probabilities and simple numbers.”

To fix this problem, Aberegg said, medical education should redouble its focus on estimating probabilities: “You can’t minimize your patients’ risks unless you understand and estimate the risks.”

The researchers funded the study. They have disclosed no relevant financial relationships.

JAMA Netw Open. Published online June 27, 2022. Full text

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