Bayesian Methods for Evidence Evaluation

Abstract

“First they ignore you, then they laugh at you, then they fight you, then you win,” a saying reportedly misattributed to Mahatma Ghandi,1 might apply to the use of Bayesian statistics in medical research. The idea that Bayesian approaches might be used to “affirm” findings derived from conventional methods, and thereby be regarded as more authoritative, is a dramatic turnabout from an era not very long ago when those embracing Bayesian ideas were considered barbarians at the gate. I remember my own initiation into the Bayesian fold, reading with a mixture of astonishment and subversive pleasure one of George Diamond’s early pieces taking aim at conventional interpretations of large cardiovascular trials of the early 1980s.2 It is gratifying to see that the Bayesian approach, which saw negligible application in biomedical research in the 1980s and began to get traction in the 1990s, is now not just a respectable alternative to standard methods, but sometimes might be regarded as preferable. That said, it is premature to declare a win, and the statistical lingua franca of biomedical research is still firmly frequentist, with P -values, confidence intervals, and type I and II errors dominating the journal landscape. It is helpful to use the thoughtful and thorough Bayesian exercise of Bittl et al3 to reflect on what Bayesian approaches give us, and what they do not. Many introductions to this approach can be found in the literature, and those basics will not be repeated here.4–6 But it is useful to examine the philosophical foundations of Bayesianism, which have their roots not so much in the Bayes theorem, from which the approach gets its name, but in its definition of probability, which Bittl et al allude to. Uncertainty can be roughly divided into 2 types: stochastic and epistemic. …