Clinical Trials: A 250-Year-Old Interpretation

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


November 13, 2013

Bayesian Probability in the Clinical Setting

Dr. Black: How does this work with the interpretation of a new clinical trial in light of former clinical trials?

Dr. Diamond: Suppose I had a new diagnostic test, and I came to you and I said, "Henry, I love this test. It's wonderful. It's got a specificity of 95%. It's highly, highly specific. Is that enough information for you to embrace that test? It is.

Dr. Black: I'd want to know the sensitivity too.

Dr. Diamond: Why? I gave you incomplete information, and yet that is the basis for the interpretation of clinical trials. The P value of < .05 is equivalent to a false-positive reading.

Dr. Black: Right.

Dr. Diamond: It's equivalent to my statement that there is a 95% chance that you wouldn't have made these observations if the null hypothesis was true. Therefore, you should reject the null hypothesis.

But that is only specificity. You need to know also how often it would be likely to make those observations in somebody where the hypothesis is true, and how likely that hypothesis was before you even engaged in performing the trial. Bayesian analysis incorporates that additional information. Instead of reporting the results as a false-positive reading, it reports the results as a posterior probability, as a predicted accuracy that the test hypothesis is true -- a much more natural piece of information for our interpretation.

Dr. Black: How does that affect what we recommend to doctors and patients for the interpretation of clinical trials? How do you see this evolving with time? Is this something we should be thinking about?

Dr. Diamond: I have no real faith that things are going to change overnight. We have been debating the use of Bayesian prior probability for 300 years now. But belief, which is the foundation of Bayesian analysis, is what we all reason with in our clinical decision-making. We don't have data to support every decision that we make. Most of our questions are analogous to what the likelihood is that there will be a hurricane tomorrow.

It has never occurred before. Tomorrow has never occurred before, so any statement we make is a belief. It can't be based on empirical evidence. Analysis of clinical trials is also a belief because we don't repeatedly analyze the same test hypothesis in multiple trials. We are lucky if we get a handful of trials and analyze them by meta-analysis. But most of the time, we are dealing with one publication, one hypothesis, and one study at a time.


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