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Absence of Evidence and Evidence of Absence in the FLASH Trial: A Bayesian Reanalysis

Available on https://psyarxiv.com/4pf9j, this is a comment on a recent article in JAMA (Futier et al., 2020).

The multicenter FLASH trial1 concluded that “Among patients at risk of postoperative kidney injury undergoing major abdominal surgery, use of HES [hydroxyethyl starch] for volume replacement therapy compared with 0.9% saline resulted in no significant difference in a composite outcome of death or major postoperative complications within 14 days after surgery.” Indeed, the results were opposite to those expected: death or major complications were more prevalent in the HES group (139 of 389 patients: 35.7%) than in the saline group (125 of 386 patients: 32.4%). An associated editorial2 pointed out that “absence of evidence is not evidence of absence” and concluded that “The results of the FLASH trial corroborate the detrimental kidney effects of HES” suggested by recent meta-analyses.

Rationale and Origin of the One-Sided Bayes Factor Hypothesis Test

The default Bayes factor hypothesis test compares the predictive performance of two rival models, the point-null hypothesis \mathcal{H}_0: \delta = 0 and the alternative hypothesis \mathcal{H}_1: \delta \sim f(\cdot). In the case of the t-test, a popular choice for the prior distribution f is a Cauchy centered on zero with scale parameter 0.707 (for informed alternatives see Gronau et al., in press).

One of the problems with such default prior distributions is that they are not directional — in frequentist lingo, they instantiate a two-sided test. Two-sided tests are sometimes useful, but the theories that provide the inspiration for experimental work generally come with strong directional predictions. In fact, a directional prediction is often all that a ‘theory’ provides. For example, the facial feedback hypothesis states that people who hold a pen between their teeth find cartoons to be more funny –not less funny– than people who hold a pen with their lips (e.g., Strack et al., 1988; but see Wagenmakers et al., 2016). Similarly, arguments have been put forward as to why lonely people take showers that are hotter (not colder) than people who are not lonely (e.g., Bargh & Shalev, 2012; but see Donnellan et al., 2015).

Follow-up: A Bayesian Perspective on the FDA Guidelines for Adaptive Clinical Trials

In September 2018, the American Food and Drug Administration (FDA) issued a draft version of the industry guidance on “Adaptive Designs for Clinical Trials of Drugs and Biologics”. In an earlier blog post we provided some comments from a Bayesian perspective that we also submitted as feedback to the FDA. Two months ago, the FDA released the final version of the guidelines, and of course we were curious to see whether and how any of our feedback was incorporated.

Ramsey’s Farmer

Despite dying at a young age, Frank Ramsey has had a profound impact on the field of probability and inference. In his book Making decisions, Dennis Lindley lionizes Ramsey to the point of hyperbole:

“The basic ideas discussed in this book were essentially discovered by Frank Ramsey, who worked in Cambridge in the 1920s. To my mind Ramsey’s discoveries in the twentieth century are as important to mankind as Newton’s made in the same city in the seventeenth. Newton discovered the laws of mechanics, Ramsey the laws of human action.” (Lindley, 1985, (p. 64))



In the previous post I discussed the famous de Finettti (1974) preface, containing the iconic statement “PROBABILITY DOES NOT EXIST”. As mentioned in that post, many statisticians and philosophers of science believe that, together with Frank Ramsey, de Finetti was the first real subjectivist. Fellow subjectivist Dennis Lindley, for instance, always expressed a fawning admiration for de Finetti, calling him “the great genius of probability” (Lindley, 2000, p. 336).

But was de Finetti really the first subjectivist? I am not sure, especially after reading An Essay on Probabilities and on Their Application to Life Contingencies and Insurance Offices, published by Augustus de Morgan in 1838 (!). Here is the cover of the book:


Together with Frank Ramsey, the Italian “radical probabilist” Bruno de Finetti is widely considered to be the main progenitor and promoter of the idea that probability is inherently subjective. According to this view, all we can do is specify our prior beliefs and then ensure that they remain coherent, that is, free from internal inconsistencies. And the only way to ensure such coherence is to update those beliefs in light of new data through the use of Bayes’ rule.

Dennis Lindley once stated that a decent study of de Finetti would take a statistician one or two years (but that it would be worth the investment). Recently I decided to bite the bullet and order the reprint of de Finetti’s standard work “Theory of Probability”. After browsing the book I must say that it looks much less daunting than I had anticipated; perhaps this is because I have already accepted the main Bayesian premise, or because I am used to read work by Harold Jeffreys. At any rate, de Finetti’s writing is clear and lively, and I look forward to studying its contents in more detail.

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