. 2023 Nov 8;27(1):432.

doi: 10.1186/s13054-023-04717-x.

Bayesian methods: a potential path forward for sepsis trials

George Tomlinson¹, Ali Al-Khafaji², Steven A Conrad³, Faith N F Factora⁴, Debra M Foster⁵, Claude Galphin⁶, Kyle J Gunnerson⁷, Sobia Khan⁸, Roopa Kohli-Seth⁹, Paul McCarthy¹⁰, Nikhil K Meena¹¹, Ronald G Pearl¹², Jean-Sebastien Rachoin¹³, Ronald Rains¹⁴, Michael Seneff¹⁵, Mark Tidswell¹⁶, Paul M Walker⁵, John A Kellum^{17

18}

Affiliations

¹ Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada.
² Department of Critical Care Medicine, University of Pittsburgh, 3550 Terrace Street, 600 Scaife Hall, Pittsburgh, PA, 15261, USA.
³ Departments of Medicine, Emergency Medicine, Pediatrics and Surgery, Louisiana State University Health, Shreveport, LA, USA.
⁴ Department of Intensive Care and Resuscitation, Cleveland Clinic, Cleveland, OH, USA.
⁵ Spectral Medical Inc, Toronto, ON, Canada.
⁶ Southeast Renal Research Institute, CHI Memorial Hospital, Chattanooga, TN, USA.
⁷ Departments of Emergency Medicine, Anesthesiology, and Internal Medicine, University of Michigan Medical Center, Ann Arbor, MI, USA.
⁸ Department of Medicine, Stony Brook University Hospital, Stony Brook, NY, USA.
⁹ Institute for Critical Care Medicine, Icahn School of Medicine at Mount Sinai, New York, NY, USA.
¹⁰ West Virginia University, Heart & Vascular Institute, Morgantown, WV, USA.
¹¹ Division of Pulmonary and Critical Care Medicine, University of Arkansas for Medical Sciences, Little Rock, AR, USA.
¹² Department of Anesthesiology, Perioperative and Pain Medicine, Stanford University, Stanford, CA, USA.
¹³ Cooper University Healthcare, Cooper Medical School of Rowan University, Camden, NJ, USA.
¹⁴ Pulmonary Associates, Univ of Colorado Health-Memorial Hospital, Colorado Springs, CO, USA.
¹⁵ Department of Anesthesia and Critical Care, George Washington University Hospital, Washington, DC, USA.
¹⁶ Pulmonary and Critical Care Division, Baystate Medical Center, Springfield, MA, USA.
¹⁷ Department of Critical Care Medicine, University of Pittsburgh, 3550 Terrace Street, 600 Scaife Hall, Pittsburgh, PA, 15261, USA. kellum@pitt.edu.
¹⁸ Spectral Medical Inc, Toronto, ON, Canada. kellum@pitt.edu.

PMID: 37940985
PMCID: PMC10634134
DOI: 10.1186/s13054-023-04717-x

Bayesian methods: a potential path forward for sepsis trials

George Tomlinson et al. Crit Care. 2023.

. 2023 Nov 8;27(1):432.

doi: 10.1186/s13054-023-04717-x.

Authors

Affiliations

¹ Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada.
² Department of Critical Care Medicine, University of Pittsburgh, 3550 Terrace Street, 600 Scaife Hall, Pittsburgh, PA, 15261, USA.
³ Departments of Medicine, Emergency Medicine, Pediatrics and Surgery, Louisiana State University Health, Shreveport, LA, USA.
⁴ Department of Intensive Care and Resuscitation, Cleveland Clinic, Cleveland, OH, USA.
⁵ Spectral Medical Inc, Toronto, ON, Canada.
⁶ Southeast Renal Research Institute, CHI Memorial Hospital, Chattanooga, TN, USA.
⁷ Departments of Emergency Medicine, Anesthesiology, and Internal Medicine, University of Michigan Medical Center, Ann Arbor, MI, USA.
⁸ Department of Medicine, Stony Brook University Hospital, Stony Brook, NY, USA.
⁹ Institute for Critical Care Medicine, Icahn School of Medicine at Mount Sinai, New York, NY, USA.
¹⁰ West Virginia University, Heart & Vascular Institute, Morgantown, WV, USA.
¹¹ Division of Pulmonary and Critical Care Medicine, University of Arkansas for Medical Sciences, Little Rock, AR, USA.
¹² Department of Anesthesiology, Perioperative and Pain Medicine, Stanford University, Stanford, CA, USA.
¹³ Cooper University Healthcare, Cooper Medical School of Rowan University, Camden, NJ, USA.
¹⁴ Pulmonary Associates, Univ of Colorado Health-Memorial Hospital, Colorado Springs, CO, USA.
¹⁵ Department of Anesthesia and Critical Care, George Washington University Hospital, Washington, DC, USA.
¹⁶ Pulmonary and Critical Care Division, Baystate Medical Center, Springfield, MA, USA.
¹⁷ Department of Critical Care Medicine, University of Pittsburgh, 3550 Terrace Street, 600 Scaife Hall, Pittsburgh, PA, 15261, USA. kellum@pitt.edu.
¹⁸ Spectral Medical Inc, Toronto, ON, Canada. kellum@pitt.edu.

PMID: 37940985
PMCID: PMC10634134
DOI: 10.1186/s13054-023-04717-x

Erratum in

Correction to: Bayesian methods: a potential path forward for sepsis trials.
Tomlinson G, Al-Khafaji A, Conrad SA, Factora FNF, Foster DM, Galphin C, Gunnerson KJ, Khan S, Kohli-Seth R, McCarthy P, Meena NK, Pearl RG, Rachoin JS, Rains R, Seneff M, Tidswell M, Walker PM, Kellum JA. Tomlinson G, et al. Crit Care. 2024 Jan 3;28(1):11. doi: 10.1186/s13054-023-04791-1. Crit Care. 2024. PMID: 38172963 Free PMC article. No abstract available.

Abstract

Background: Given the success of recent platform trials for COVID-19, Bayesian statistical methods have become an option for complex, heterogenous syndromes like sepsis. However, study design will require careful consideration of how statistical power varies using Bayesian methods across different choices for how historical data are incorporated through a prior distribution and how the analysis is ultimately conducted. Our objective with the current analysis is to assess how different uses of historical data through a prior distribution, and type of analysis influence results of a proposed trial that will be analyzed using Bayesian statistical methods.

Methods: We conducted a simulation study incorporating historical data from a published multicenter, randomized clinical trial in the US and Canada of polymyxin B hemadsorption for treatment of endotoxemic septic shock. Historical data come from a 179-patient subgroup of the previous trial of adult critically ill patients with septic shock, multiple organ failure and an endotoxin activity of 0.60-0.89. The trial intervention consisted of two polymyxin B hemoadsorption treatments (2 h each) completed within 24 h of enrollment.

Results: In our simulations for a new trial of 150 patients, a range of hypothetical results were observed. Across a range of baseline risks and treatment effects and four ways of including historical data, we demonstrate an increase in power with the use of clinically defensible incorporation of historical data. In one possible trial result, for example, with an observed reduction in risk of mortality from 44 to 37%, the probability of benefit is 96% with a fixed weight of 75% on prior data and 90% with a commensurate (adaptive-weighting) prior; the same data give an 80% probability of benefit if historical data are ignored.

Conclusions: Using Bayesian methods and a biologically justifiable use of historical data in a prior distribution yields a study design with higher power than a conventional design that ignores relevant historical data. Bayesian methods may be a viable option for trials in critical care medicine where beneficial treatments have been elusive.

Keywords: Endotoxemia; Endotoxin septic shock; Hemadsorption; Polymyxin-B; Septic shock; Statistical methods; Trial simulation.

PubMed Disclaimer

Conflict of interest statement

GT is a paid consultant to Spectral Medical. DMF, and JAK are employees of Spectral Medical. PMW is a member of the Board of Directors of Spectral Medical. AA-K, SAC, FNF, CG, KG, SK, RK-S, PM, NKM, RGP, J-SR, RR, MS and MT are/were investigators in the Tigris and/or EUPHRATES trials and their institutions received funding to conduct the studies.

Figures

**Fig. 1**
Potential prior distributions for the APACHE-adjusted odds ratio: a Prior from the treatable cohort b 75% weighted (25% down-weighted) prior from the treatable cohort; c 50% down-weighted prior from the treatable cohort; d uninformative prior, ignoring external evidence on treatment efficacy, a distribution that is essentially flat over the range of plausible values. Each figure shows the corresponding 95% central credible interval (CrI) and the prior probability that the odds ratio for treatment with PMX is less than 1, along with this same probability expressed as odds in favor of there being a treatment effect (i.e., a 97.0% probability of benefit is the same as an odds of benefit of 97 to 3 or 32.3 to 1)

**Fig. 2**
Power (probability of demonstrating benefit at the 95% probability threshold) versus treatment benefit (expressed as the true absolute risk reduction) with APACHE-adjusted and unadjusted analyses for four different uses of the historical data and control group risk of mortality of 40–60%

**Fig. 3**
For scenarios with a baseline risk of 50%, distributions across 2000 trials of estimated APACHE-adjusted odds ratios according to the true absolute risk reductions and colored according to whether the Bayesian analysis returns a probability of benefit larger or smaller than 95%. In each panel, each method of analysis (on the x-axis) has the same 2000 trials as input, but more of them lead to a positive finding (colored blue) when more weight is place on the historical evidence. For the planned fixed weighting of 75%, an observed adjusted OR of approximately 0.66 or lower (the threshold separating blue and gold dots) leads to a positive trial conclusion. The blue labels indicate the percentages of simulated trials where we conclude benefit (i.e., the power) for the corresponding absolute risk reduction and use of historical data

See this image and copyright information in PMC

References

1. Singer M, Deutschman CS, Seymour CW, Shankar-Hari M, Annane D, Bauer M, Bellomo R, Bernard GR, Chiche JD, Coopersmith CM, et al. The third international consensus definitions for sepsis and septic shock (Sepsis-3) JAMA. 2016;315(8):801–810. doi: 10.1001/jama.2016.0287. - DOI - PMC - PubMed
1. Seymour CW, Kennedy JN, Wang S, Chang CH, Elliott CF, Xu Z, Berry S, Clermont G, Cooper G, Gomez H, et al. Derivation, validation, and potential treatment implications of novel clinical phenotypes for sepsis. JAMA. 2019;321(20):2003–2017. doi: 10.1001/jama.2019.5791. - DOI - PMC - PubMed
1. Yarnell CJ, Abrams D, Baldwin MR, Brodie D, Fan E, Ferguson ND, Hua M, Madahar P, McAuley DF, Munshi L, et al. Clinical trials in critical care: can a Bayesian approach enhance clinical and scientific decision making? Lancet Respir Med. 2021;9(2):207–216. doi: 10.1016/S2213-2600(20)30471-9. - DOI - PMC - PubMed
1. Annane D. Improving clinical trials in the critically ill: unique challenge–sepsis. Crit Care Med. 2009;37(1 Suppl):S117–128. doi: 10.1097/CCM.0b013e318192078b. - DOI - PubMed
1. Racine A, Grieve AP, Flühler H, Smith AF. Bayesian methods in practice: experiences in the pharmaceutical industry. Appl Stat. 1986;35:93–150. doi: 10.2307/2347264. - DOI

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Bayesian methods: a potential path forward for sepsis trials

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Bayesian methods: a potential path forward for sepsis trials

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Erratum in

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Conflict of interest statement

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