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Can Bayesian analysis clarify the interpretation of clinical trial results?
In a post hoc Bayesian analysis of the recent EOLIA (Extracorporeal Membrane Oxygenation [ECMO] to Rescue Lung Injury in Severe ARDS) trial, the posterior probability of mortality benefit (relative risk <1) ranged between 88% and 99% given a range of prior assumptions reflecting varying degrees of skepticism and enthusiasm regarding previous evidence for the benefit of ECMO. Probabilities varied according to the definition of minimum clinically important mortality benefit; for example, the posterior probability of relative risk less than 0.67 ranged between 0% and 48% given the same range of prior assumptions.
Information about the posterior probability of treatment effect provided by Bayesian analysis may help clarify the interpretation of clinical trial findings.
Bayesian analysis of clinical trial data may provide useful information to aid in study interpretation, especially when trial evidence suggests that the benefits of an intervention are uncertain, such as in a trial that evaluated early extracorporeal membrane oxygenation (ECMO) for severe acute respiratory distress syndrome (ARDS).
To demonstrate the potential utility of Bayesian analyses by estimating the posterior probability, under various assumptions, that early ECMO was associated with reduced mortality in patients with very severe ARDS in a randomized clinical trial (RCT).
Design and Evidence
A post hoc Bayesian analysis of data from an RCT (ECMO to Rescue Lung Injury in Severe ARDS [EOLIA]) that included 249 patients with very severe ARDS who had been randomized to receive early ECMO (n = 124; mortality at 60 days, 35%) vs initial conventional lung-protective ventilation with the option for rescue ECMO (n = 125, mortality at 60 days, 46%). The trial was designed to detect an absolute risk reduction (ARR) of 20%, relative risk (RR) of 0.67. Statistical prior distributions were specified to represent varying levels of preexisting enthusiasm or skepticism for ECMO and by Bayesian meta-analysis of previously published studies (with downweighting to account for differences and quality between studies). The RR, credible interval (CrI), ARR, and probability of clinically important mortality benefit (varying from RR less than 1 to RR less than 0.67 and ARR from 2% or more to 20% or more) were estimated with Bayesian modeling.
Combining a minimally informative prior distribution with the findings of the EOLIA trial, the posterior probability of RR less than 1 for mortality at 60 days after randomization was 96% (RR, 0.78 [95% CrI, 0.56-1.04]); the posterior probability of RR less than 0.67 was 18%, the probability of ARR of 2% or more was 92%, and the probability of ARR of 20% or more was 2%. With a moderately enthusiastic prior, equivalent to information from a trial of 264 patients with an RR of 0.78, the estimated RR was 0.78 (95% CrI, 0.63-0.96), the probability of RR less than 1 was 99%, the probability of RR less than 0.67 was 8%, the probability of ARR of 2% or more was 97%, and the probability of ARR of 20% or more was 0%. With a strongly skeptical prior, equivalent to information from a trial of 264 patients with an RR of 1.0, the estimated RR was 0.88 (95% CrI, 0.71-1.09), the probability of RR less than 1 was 88%, the probability of RR less than 0.67 was 0%, the probability of ARR of 2% or more was 78%, and the probability of ARR of 20% or more was 0%. If the prior was informed by previous studies, the estimated RR was 0.71 (95% CrI, 0.55-0.94), the probability of RR less than 1 was 99%, the probability of RR less than 0.67 was 48%, the probability of ARR of 2% or more was 98%, and the probability of ARR of 20% or more was 4%.
Conclusions and Relevance
Post hoc Bayesian analysis of data from a randomized clinical trial of early extracorporeal membrane oxygenation compared with conventional lung-protective ventilation with the option for rescue extracorporeal membrane oxygenation among patients with very severe acute respiratory distress syndrome provides information about the posterior probability of mortality benefit under a broad set of assumptions that may help inform interpretation of the study findings.
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Corresponding Author: Ewan C. Goligher, MD, PhD, Toronto General Hospital, 585 University Ave, Peter Munk Bldg, 11th Floor, Room 192, Toronto, ON M5G 2N2, Canada (firstname.lastname@example.org).
Accepted for Publication: September 26, 2018.
Published Online: October 22, 2018. doi:10.1001/jama.2018.14276
Correction: This article was corrected on November 14, 2018, to correct a degree in the author byline and to add a conflict of interest disclosure that was inadvertently omitted. It was corrected on June 11, 2019, to provide the prior probabilities for RR <0.67 in Table 1 and update an absolute risk reduction value in Table 3.
Author Contributions: Dr Goligher had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Drs Tomlinson and Goligher conducted and are responsible for the data analysis.
Concept and design: Goligher, Tomlinson, Wijeysundera, Jüni, Brodie, Slutsky, Combes.
Acquisition, analysis, or interpretation of data: All authors.
Drafting of the manuscript: Goligher.
Critical revision of the manuscript for important intellectual content: All authors.
Statistical analysis: Goligher, Tomlinson, Hajage.
Administrative, technical, or material support: Slutsky, Combes.
Conflict of Interest Disclosures: Dr Goligher reports receiving travel reimbursement and speaking honoraria from Getinge outside the submitted work. Dr Jüni reports being a tier 1 Canada research chair in clinical epidemiology of chronic diseases. Dr Brodie reports serving as the cochair of the trial steering committee for the VENT-AVOID trial sponsored by ALung Technologies; serving on the medical advisory board for Baxter; and previously serving on the medical advisory boards of ALung Technologies and Kadence (Johnson & Johnson), with all compensation for these activities paid to Columbia University. Dr Slutsky reports serving as a paid consultant for Maquet Critical Care, Baxter, and Novalung/Xenios. Dr Combes reports receiving study grant support from Maquet, lecture fees from Maquet and Baxter, and consulting fees from Hemovent, outside the submitted work. No other disclosures were reported.
Funding/Support: This work is supported by a new investigator award from the Canadian Institutes of Health Research (Drs Fan and Wijeysundera) and a merit award from the department of anesthesia at the University of Toronto (Dr Wijeysundera).
Role of the Funder/Sponsor: The funders had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.
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