Clinical Trials: A 250-Year-Old Interpretation

Henry R. Black, MD; George A. Diamond, MD


November 13, 2013

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Explaining the Bayesian Prior

Henry R. Black, MD: Hi. I am Dr. Henry Black, Adjunct Professor of Medicine at the New York University School of Medicine. I am here today with my friend and colleague, Dr. George Diamond.

George A. Diamond, MD: I am Professor of Medicine at the University of California in Los Angeles and Emeritus Senior Research Scientist at the Cedars-Sinai Medical Center.

Dr. Black: I always associate with you with Bayesian interpretation of clinical trials. I have heard you speak about this several times. Could you explain what a Bayesian interpretation is, starting with who Bayes was, what he said and did, and how you have applied that to clinical trials?

Dr. Diamond: I was introduced to Thomas Bayes of "Bayes' theorem" fame back as an early postdoctoral student, when I was looking for ways to analyze cardiac stress test data. A seminal article was published in [the New England Journal of Medicine] back in 1975[1] that for the first time explained some of the paradoxes that we had been observing in stress test data.

Stress testing was extremely accurate in predicting coronary disease in patients with typical angina pectoris, but was very inaccurate in predicting the same coronary disease in asymptomatic individuals or those with very minimal symptoms. It turns out that Bayes' theorem explains that paradox.

Dr. Black: How so?

Dr. Diamond: The paradox is founded on the differences in the prior probability of disease in those 2 populations. If you knew nothing else other than the fact that the patient was suffering from typical angina, about 90% of the time you would be correct if you predicted that the patient had coronary disease. But if it was an asymptomatic individual and you predicted that this person had coronary disease and referred the patient to a catheterization to prove it, you would be right only about 5% of the time.

Dr. Black: This is based on what the stress test showed, right?

Dr. Diamond: No, before the stress test. This represents the prior probability of disease, a concept that was introduced by Bayes and that is ignored by classical statisticians. I will make a little bit of a historical extrapolation.

Thomas Bayes came up with these ideas about the interpretation of probability as a belief rather than as a measureable frequency back in the mid-18th century. It was embraced by such luminaries as Laplace throughout the 19th century. But it was always controversial and was criticized by others, such as George Boole, who wrote the book on Boolean analysis and on the laws of thought.

Ronald Fisher picked up the critical ideas and developed a methodology that allowed us to analyze observational data without reference to prior probabilities. He wrote a book on this (several books, in fact), and it became a standard of analysis throughout the 20th century.

Only now are we beginning to question the assumptions under which Fisher's classical school of analysis is based. We can't ignore prior probabilities. We don't ignore them in any other domain of our lives.

If you are sitting on an acceptance committee at a college, you would look at the transcripts of students who were applying for enrollment. That is prior information. If you are buying a new car, you might look at the frequency of repair records for that model before you made your decision -- prior information. If you are a judge sentencing someone in civil court, not in criminal court, you would look at the person's rap sheet on his prior convictions. That's relevant prior information. In fact, in every walk of life we use prior information, save one: the analysis of clinical trials.

Dr. Black: One could ask, if you have a good history, why do the stress test at all?

Dr. Diamond: In many cases, that is absolutely true. You most often refer to testing to confirm a preconception that you have already made on the basis of prior information from the history and the physical examination. So when it comes to using sophisticated diagnostic tests, we naturally apply prior information to the interpretation. We frequently say that if we weren't suspecting a disease was present, that abnormal test result was likely to be a false-positive.


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