A Bayesian approach to the analysis of clinical trial data using logistic regression: example from a randomized placebo-controlled crossover trial of propranolol for migraine prevention

Abstract

Bayesian methods enable the "prior" (or informative) beliefs of an audience to be combined with the results of a clinical trial to arrive at a final "posterior" belief. This example concerns previously published data from a double-blind placebo-controlled trial of propranolol to reduce the number of episodes of migraine, where subjects were crossed-over after 3 months of treatment. The informative prior range was supplied by an educated audience (members of our Faculty of Neurology) who were given review papers on propranolol in migraine prophylaxis and placebo responses in migraine trials. We used logistic regression models to try to predict those whose symptoms improved (based on treatment or on the time period under consideration; ie, the first or second 3-month period, or based on both factors considered together). The posterior was generated using the Markov-Chain Monte-Carlo methods. For the original dataset, the Bayesian posteriors tended to be more tightly defined than those with no prior or minimally informative prior beliefs, thus yielding firmer conclusions in light of the trial. When compared with a larger dataset (which was generated from the original, but was arrived at by multiplying the number of observations by 10), the influence of prior beliefs was much less marked, but the posteriors did tend to be marginally more narrowly defined. This finding is in keeping with existing work on Bayesian methods, highlighting their value in aiding interpretation of trials with a small number of observations.

Thymectomy for non-thymomatous myasthenia gravis: a propensity score matched study

“…Since previous data on thymectomy efficacy are inconsistent, we used 2 approaches to estimate our prior possibilities: assuming no knowledge (non-informative prior) and assuming evidence of no efficacy (skeptical prior). The first assumption allowed us to place more emphasis in our observed data, and the second assumption served to incorporate the “worst case scenario” for thymectomy, giving more weight to a previous belief of no efficacy [ 26 ]. Finding an effect in this skeptical model strengthens our findings.…”