Frequentist Methods Research Articles

THE SPECTRAL APPROACH TO LINEAR RATIONAL EXPECTATIONS MODELS

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite-dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the models in the context of nonuniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties.

Radiofrequency treatments for lumbar facet joint syndrome: a systematic review and network meta-analysis.

Lumbar facet joint syndrome (FJS) is a common cause of chronic low back pain (LBP). Radiofrequency treatments are commonly used to treat chronic LBP-related FJS that is refractory to conservative treatment, although evidence supporting this treatment is controversial. We explored the therapeutic effects of radiofrequency on FJS using a network meta-analysis (NMA). A comprehensive systematic search of multiple databases was conducted to identify randomized controlled trials (RCTs) that compared radiofrequency with other treatments (sham procedures, facet joint corticosteroid injection, and conservative treatment) for FJS. We searched PubMed, Embase, Web of Science, the Cochrane Database, and handsearching. The primary outcomes were pain score and Oswestry Disability Index (ODI). Statistical analysis included conventional pairwise meta-analysis and NMA using the frequentist method. The treatments were ranked using surface under the cumulative ranking curve (SUCRA) values. The search yielded 25 RCTs (1969 patients) and a mixed quality regarding the risk of bias, with most studies exhibiting a low risk of bias for most domains. Endoscopic neurotomy consistently ranked highest in terms of pain reduction and ODI score improvement at 1, 3, 6, and 12 months. At 1 and 6 months, endoscopic neurotomy had the highest SUCRA value for pain reduction (0.833 and 0.860, respectively), followed by medial branch thermal radiofrequency. This NMA demonstrates that endoscopic neurotomy is the most effective treatment for lumbar FJS, providing superior and sustained pain relief and functional improvement compared with other treatments. Further, high-quality RCTs are needed to confirm these findings and address the existing limitations. CRD42024524657.

Concentration of a Sparse Bayesian Model With Horseshoe Prior in Estimating High‐Dimensional Precision Matrix

ABSTRACTPrecision matrices are crucial in many fields such as social networks, neuroscience and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off‐diagonal position of the precision matrix indicates conditional independence between nodes. In high‐dimensional settings where the dimension of the precision matrix exceeds the sample size and the matrix is sparse, methods like graphical Lasso, graphical SCAD and CLIME are popular for estimating GGMs. While frequentist methods are well‐studied, Bayesian approaches for (unstructured) sparse precision matrices are less explored. The graphical horseshoe estimate, applying the global‐local horseshoe prior, shows superior empirical performance, but theoretical work for sparse precision matrix estimations using shrinkage priors is limited. This paper addresses these gaps by providing concentration results for the tempered posterior with the fully specified horseshoe prior in high‐dimensional settings. Moreover, we also provide novel theoretical results for model misspecification, offering a general oracle inequality for the posterior. A concise set of simulations is performed to validate our theoretical findings.

Effect of obesity and NAFLD on leukocyte telomere length and hTERT gene MNS16A VNTR variant

It is known that telomere length (TL) (evaluated with T/S ratio) is shortened in the presence of obesity. In this study, we aimed to investigate how obesity in adolescents and non-alcoholic liver disease (NAFLD) within the obese group affect TL and the clinical significance of the human telomerase reverse transcriptase (hTERT) gene MNS16A VNTR variant in terms of NAFLD. Adolescents with exogenous obesity and healthy controls (aged 10–19 years) who applied to our adolescent outpatient clinic between May-October 2023 were included in this study. We performed upper abdominal ultrasonography to investigate the presence of NAFLD in adolescents with obesity and divided into two groups: those without hepatosteatosis (obese NAFLD (-)) and those with hepatosteatosis (obese NAFLD (+)). We recorded body weight, height, waist circumference, and blood pressure measurements and measured the T/S ratio (telomere sequence copy number/gene single copy number) by the Quantitative Polymerase Chain Reaction method. The groups were compared using frequentist and Bayesian methods. Eighty-three obese adolescents [63 NAFLD(+) 20 NAFLD(-)] and 69 lean controls were included in the study. Pairwise comparisons revealed that T/S ratio was significantly lower in the obese NAFLD (-) group than the obese NAFLD (+) and the control group (p = 0.025, p = 0.007, respectively). T/S ratio was lower in the LL allele group than in the other alleles (p = 0.022) and slightly higher in the obese group with metabolic syndrome compared to the obese group without metabolic syndrome (p = 0.072). hTERT-MNS16A-VNTR gene variant LL allele had a negative correlation with T/S ratio among the obese adolescent group. Patients with LL alleles had higher ALT, GGT, HOMA-IR, and ALT/AST. Diastolic blood pressure had a significant correlation with the T/S ratio. The T/S ratio was shorter in the obese adolescent group compared to healthy ones but was higher in the NAFLD (+) obese compared to the NAFLD (-) obese. ALT level and ALT/AST ratio were higher, T/S ratio was lower in the hTERT MNS16A VNTR variant LL allele group among obese adolescents. In addition, there was a significant correlation between the T/S ratio and diastolic blood pressure in obese adolescents.

Interval-Valued Random Matrices

This paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices. This framework is designed to address the complexities of real-world data, offering enhanced statistical modeling techniques particularly suited for large and complex datasets where traditional methods may be inadequate. We develop both frequentist and Bayesian methods for the statistical inference of interval-valued random matrices, providing a comprehensive analytical framework. We conduct extensive simulations to compare the performance of these methods, demonstrating that Bayesian estimators outperform maximum likelihood estimators under the Frobenius norm loss function. The practical utility of our approach is further illustrated through an application to climatology and temperature data, highlighting the advantages of interval-valued random matrices in real-world scenarios.

Empirical Inferences Under Bayesian Framework to Identify Cellwise Outliers

Outliers are typically identified using frequentist methods. The data are classified as “outliers” or “not outliers” based on a test statistic that measures the magnitude of the difference between a value and the majority part of the data. The threshold for a data value to be an outlier is typically defined by the user. However, a subjective choice of the threshold increases the uncertainty associated with outlier status for each data value. A cellwise outlier detection algorithm named FuzzyHRT is used to automate the editing process in repeated surveys. This algorithm uses Bienaymé–Chebyshev’s inequality and fuzzy logic to detect four different types of outliers resulting from format inconsistencies, historical, tail, and relational anomalies. However, fuzzy logic is not suited for probabilistic reasoning behind the identification of anomalous cells. Bayesian methods are well suited for quantifying the uncertainty associated with the identification of outliers. Although, as suggested by the literature, there exist well-developed Bayesian methods for record-level outlier detection, Bayesian methods for identifying outliers within individual records (i.e., at the cell level) remain unexplored. This paper presents two approaches from the Bayesian perspective to study the uncertainty associated with identifying outliers. A Bayesian bootstrap approach is explored to study the uncertainty associated with the output scores from the FuzzyHRT algorithm. Empirical likelihoods in a Bayesian setting are also considered for probabilistic reasoning behind the identification of anomalous cells. NASS survey data for livestock and major crop yield (such as corn) are considered for comparing the performances of the two proposed approaches with recent cellwise outlier methods.

Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

AbstractThis study uses two frequentist approaches and the Bayesian method of estimation using progressively first‐failure type‐II censored data to estimate process capability index (PCI), , for the Wilson–Hilferty (WH) distribution. A competitive maximum product of spacing (MPS) method for estimation of is proposed in the frequentist method as an alternative to conventional likelihood (LK)‐based estimation. We have also taken into account the PS function in the Bayesian setup as an alternative to the conventional LK function, and both LK and PS‐based Bayesian estimates are given for . Further, the Bayes estimates are evaluated by applying Tierney–Kadane (TK) approximation method and Markov chain Monte Carlo (MCMC) method with the help of both LK and PS functions and Jeffrey's prior. Additionally, the approximate confidence intervals based on the suggested frequentist techniques as well as the Bayes highest posterior density (HPD) credible intervals are built for the index . In addition, two bootstrap confidence intervals are obtained. In the simulation exercise, the performance of the Bayes and traditional estimates of is assessed in terms of their mean squared errors, and the average width and coverage probabilities of the CIs and HPD intervals are compared. An actual data set from the electronic industries is reanalyzed in order to show the efficacy of the proposed index and estimation methodology.

A tutorial on Bayesian structural equation modelling: Principles and applications.

This paper explores the utilisation of Bayesian structural equation modelling (BSEM) in psychology, highlighting its advantages over frequentist methods for handling complex models and small sample sizes. Basic concepts and fundamental issues relevant to BSEM are introduced, such as prior setting, model convergence, and model fit evaluation and so on. The paper also provides illustrative examples of commonly employed BSEMs, including confirmatory factor analysis (CFA) models, mediation models and multigroup CFA models, accompanied by empirical data and computer codes to facilitate implementation. Our goal is to provide researchers with novel ideas for empirical research and equip them to overcome challenges inherent to traditional methods. As BSEM continues to gain traction in various fields, we anticipate its development will feature improved methods, techniques and reporting standards.

Bayesian statistical concepts with examples from rodent toxicology studies.

The theory and practice of statistics comprises two main schools of thought: frequentist statistics and Bayesian statistics. Frequentist methods are most commonly used to analyze animal-based laboratory data, while Bayesian statistical methods have been implemented less widely and may be relatively unfamiliar to practitioners in experimental science. This paper provides a high-level overview of Bayesian statistics and how they compare with frequentist methods. Using examples in rodent toxicity research, we argue that Bayesian methods have much to offer laboratory animal researchers. We advocate for increased attention to and adoption of Bayesian methods in laboratory animal research. Bayesian statistical theory, methods, software, and education have advanced significantly in the last 30 years, making these tools more accessible than ever.

Enhancing work zone crash severity analysis: The role of synthetic minority oversampling technique in balancing minority categories

Road work zones are becoming increasingly common due to the aging infrastructure and the need for capacity enhancement. They present significant safety risks due to narrow lanes, uneven traffic flow, lower speed, and reduced visibility. It is particularly important to understand the role of human behavioral factors in WZ crash injury severity due to difficulty navigating such areas. Furthermore, the crash injury data available is mostly imbalanced, primarily due to the lower incidence of high-cost fatal and severe injuries, and can benefit from the use of emerging analysis techniques. This research study examines a unique dataset comprising 7,855 WZ crashes in Tennessee from 2018 to 2022 as a case study to provide useful insight into the behavioral factors associated with injury severity and how they change after adjusting for the underrepresented fatal and serious injuries within the dataset. The study applies frequentist methods and a machine learning technique enhanced with the Synthetic Minority Oversampling Technique (SMOTE), addressing the data imbalance (relatively fewer fatal and serious injuries) for useful inferences and predictions. The study results indicate that aggressive driving, overspeeding, and drunk driving significantly elevate injury severity. Additionally, after balancing the minority categories of crash injury severity levels, the importance of contributing factors changes. The study offers engineers and data analysts a framework for analyzing imbalanced data, a prevalent issue in crash injury severity analysis. By exploring key behavioral factors responsible for injury severity in WZ crashes, the study provides useful insight and valuable information to traffic safety engineers, transportation agencies, and policymakers to implement enhanced safety measures in WZ design and management, ultimately aiming to mitigate injury severity and to improve overall safety for road users.

A Network Meta-Analysis of Randomized Controlled Trials on the Comparative Efficacy of Stem Cells Therapy for Diabetic Foot Ulcer Healing

Stem cell therapy in diabetic foot ulcer has emerged as a promising treatment option to promote ulcer healing. This network meta-analysis was undertaken to evaluate how they compete with each other and their ranking with respect to chances of ulcer healing. A systematic search strategy to retrieve data from five databases, were used to identify potential studies. Randomized controlled trial or clinical controlled trial, published in English, using any type of stem cells as intervention in individuals aged over 18 years diagnosed with diabetic foot ulcers were included. This network meta-analysis was performed using frequentist method using R version 4.2.1. Eighteen clinical trials were included in the study which included 13 interventions. The study found that most of the stem cells were significantly promoting ulcer healing chances with human viable wound matrix (hVWM) [RR 2.91; CI: 1.28, 6.64], peripheral blood mononuclear cells (PBMNC) [RR 2.35; CI: 1.21, 4.55], bone marrow mesenchymal stem cells (BMMSCs) [RR 2.20; CI: 1.34, 3.60], were top three stem cell options among all. P score also suggested the same. Risk of bias study suggested that there was “some concern or “high risk’’ among majority of studies. It is evident from this study that bone marrow mononuclear cells were found to be most effective in wound healing in cases of diabetic foot ulcer in that order. Though there was no significant difference between these and more studies were required to ascertain whether they differ in term of efficacy for the clinical outcome of ulcer healing.

Evaluation of the Fill-it-up-design to use historical control data in randomized clinical trials with two arm parallel group design

PurposeIn the context of clinical research, there is an increasing need for new study designs that help to incorporate already available data. With the help of historical controls, the existing information can be utilized to support the new study design, but of course, inclusion also carries the risk of bias in the study results.MethodsTo combine historical and randomized controls we investigate the Fill-it-up-design, which in the first step checks the comparability of the historical and randomized controls performing an equivalence pre-test. If equivalence is confirmed, the historical control data will be included in the new RCT. If equivalence cannot be confirmed, the historical controls will not be considered at all and the randomization of the original study will be extended. We are investigating the performance of this study design in terms of type I error rate and power.ResultsWe demonstrate how many patients need to be recruited in each of the two steps in the Fill-it-up-design and show that the family wise error rate of the design is kept at 5%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}. The maximum sample size of the Fill-it-up-design is larger than that of the single-stage design without historical controls and increases as the heterogeneity between the historical controls and the concurrent controls increases.ConclusionThe two-stage Fill-it-up-design represents a frequentist method for including historical control data for various study designs. As the maximum sample size of the design is larger, a robust prior belief is essential for its use. The design should therefore be seen as a way out in exceptional situations where a hybrid design is considered necessary.

Effects of transcranial direct current stimulation on cognition in MCI with Alzheimer's disease risk factors using Bayesian analysis

Despite the growing interest in precision medicine-based therapies for Alzheimer's disease (AD), little research has been conducted on how individual AD risk factors influence changes in cognitive function following transcranial direct current stimulation (tDCS). This study evaluates the cognitive effects of sequential tDCS on 63 mild cognitive impairment (MCI) patients, considering AD risk factors such as amyloid-beta deposition, APOE ε4, BDNF polymorphism, and sex. Using both frequentist and Bayesian methods, we assessed the interaction of tDCS with these risk factors on cognitive performance. Notably, we found that amyloid-beta deposition significantly interacted with tDCS in improving executive function, specifically Stroop Word-Color scores, with strong Bayesian support for this finding. Memory enhancements were differentially influenced by BDNF Met carrier status. However, sex and APOE ε4 status did not show significant effects. Our results highlight the importance of individual AD risk factors in modulating cognitive outcomes from tDCS, suggesting that precision medicine may offer more effective tDCS treatments tailored to individual risk profiles in early AD stages.

Bayesian Methods for Quality Tolerance Limit (QTL) Monitoring.

In alignment with the ICH guideline for Good Clinical Practice [ICH E6(R2)], quality tolerance limit (QTL) monitoring has become a standard component of risk-based monitoring of clinical trials by sponsor companies. Parameters that are candidates for QTL monitoring are critical to participant safety and quality of trial results. Breaching the QTL of a given parameter could indicate systematic issues with the trial that could impact participant safety or compromise the reliability of trial results. Methods for QTL monitoring should detect potential QTL breaches as early as possible while limiting the rate of false alarms. Early detection allows for the implementation of remedial actions that can prevent a QTL breach at the end of the trial. We demonstrate that statistically based methods that account for the expected value and variability of the data generating process outperform simple methods based on fixed thresholds with respect to important operating characteristics. We also propose a Bayesian method for QTL monitoring and an extension that allows for the incorporation of partial information, demonstrating its potential to outperform frequentist methods originating from the statistical process control literature.

Extended fiducial inference: toward an automated process of statistical inference

Abstract While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set—‘inferring the uncertainty of model parameters on the basis of observations’—has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. Extended Fiducial inference involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. Extended Fiducial inference also provides an innovative framework for semisupervised learning.

The second data release from the European Pulsar Timing Array V. Search for continuous gravitational wave signals

We present the results of a search for continuous gravitational wave signals (CGWs) in the second data release (DR2) of the European Pulsar Timing Array (EPTA) collaboration. The most significant candidate event from this search has a gravitational wave frequency of 4-5 nHz. Such a signal could be generated by a supermassive black hole binary (SMBHB) in the local Universe. We present the results of a follow-up analysis of this candidate using both Bayesian and frequentist methods. The Bayesian analysis gives a Bayes factor of 4 in favour of the presence of the CGW over a common uncorrelated noise process. In contrast, the frequentist analysis estimates the p-value of the candidate to be $< 1<!PCT!>$, also assuming the presence of common uncorrelated red noise. However, comparing a model that includes both a CGW and a gravitational wave background (GWB) to a GWB only, the Bayes factor in favour of the CGW model is only $0.7$. Therefore, we cannot conclusively determine the origin of the observed feature, nor can we rule it out as a CGW source. We present results of simulations that demonstrate that data containing a weak gravitational wave background can be misinterpreted as data including a CGW and vice versa, providing two plausible explanations for the EPTA DR2 data. Further investigations combining data from all PTA collaborations will be needed to reveal the true origin of this feature.

Bayesian estimation of the prevalence of antimicrobial resistance: a mathematical modelling study.

Estimates of the prevalence of antimicrobial resistance (AMR) underpin effective antimicrobial stewardship, infection prevention and control, and optimal deployment of antimicrobial agents. Typically, the prevalence of AMR is determined from real-world antimicrobial susceptibility data that are time delimited, sparse, and often biased, potentially resulting in harmful and wasteful decision-making. Frequentist methods are resource intensive because they rely on large datasets. To determine whether a Bayesian approach could present a more reliable and more resource-efficient way to estimate population prevalence of AMR than traditional frequentist methods. Retrospectively collected, open-source, real-world pseudonymized healthcare data were used to develop a Bayesian approach for estimating the prevalence of AMR by combination with prior AMR information from a contextualized review of literature. Iterative random sampling and cross-validation were used to assess the predictive accuracy and potential resource efficiency of the Bayesian approach compared with a standard frequentist approach. Bayesian estimation of AMR prevalence made fewer extreme estimation errors than a frequentist estimation approach [n = 74 (6.4%) versus n = 136 (11.8%)] and required fewer observed antimicrobial susceptibility results per pathogen on average [mean = 28.8 (SD = 22.1) versus mean = 34.4 (SD = 30.1)] to avoid any extreme estimation errors in 50 iterations of the cross-validation. The Bayesian approach was maximally effective and efficient for drug-pathogen combinations where the actual prevalence of resistance was not close to 0% or 100%. Bayesian estimation of the prevalence of AMR could provide a simple, resource-efficient approach to better inform population infection management where uncertainty about AMR prevalence is high.

A Bayesian semi-parametric scalar-on-function regression with measurement error using instrumental variables.

Wearable devices such as the ActiGraph are now commonly used in research to monitor or track physical activity. This trend corresponds with the growing need to assess the relationships between physical activity and health outcomes, such as obesity, accurately. Device-based physical activity measures are best treated as functions when assessing their associations with scalar-valued outcomes such as body mass index. Scalar-on-function regression (SoFR) is a suitable regression model in this setting. Most estimation approaches in SoFR assume that the measurement error in functional covariates is white noise. Violating this assumption can lead to underestimating model parameters. There are limited approaches to correcting measurement errors for frequentist methods and none for Bayesian methods in this area. We present a non-parametric Bayesian measurement error-corrected SoFR model that relaxes all the constraining assumptions often involved with these models. Our estimation relies on an instrumental variable allowing a time-varying biasing factor, a significant departure from the current generalized method of moment (GMM) approach. Our proposed method also permits model-based grouping of the functional covariate following measurement error correction. This grouping of the measurement error-corrected functional covariate allows additional ease of interpretation of how the different groups differ. Our method is easy to implement, and we demonstrate its finite sample properties in extensive simulations. Finally, we applied our method to data from the National Health and Examination Survey to assess the relationship between wearable device-based measures of physical activity and body mass index in adults in the United States.

Comparative host transcriptomics as a tool to identify candidate biomarkers for immune reactions in leprosy using meta-analysis.

Background Leprosy is no longer considered an imprecation, as an effective multidrug therapy regimen is available worldwide for its cure. However, its diverse clinical manifestations sometimes involve acute inflammatory reactions. These complications result in irreversible nerve damage, neuritis and anatomical deformities that emerge before, during the treatment or after the completion of treatment. Reversal reaction (Type-I) and erythema nodosum leprosum (Type-II) are the leprosy reactions generally seen in patients with lepromatous and borderline forms of leprosy. At present, there is no accurate diagnostic test available to detect these leprosy reactions. Objectives To identify potential biomarkers indicative of Type-I and Type-II leprosy reactions that could help in their early diagnosis. Methods and Results Host-transcriptomics investigations have been utilised in this study to decipher a correlation between host-gene expression-based biomarkers and exacerbation of leprosy reactions. We present a comparative analysis of publicly available host transcriptomics datasets (from Gene Expression Omnibus) related to leprosy reactions. Individual datasets were analysed and integration of results was carried out using meta-analysis. Common differentially expressed genes (DEGs) were identified using the frequentist and Bayesian ratio association test methods. We have identified several genes - ADAMTS5, ADAMTS9, IFITM2, IFITM3, KIRREL, ANK3, CD1E, CTSF, DOCK9 and KRT73 to name a few - which can serve as potential biomarkers for Type-II reaction. Similarly, ACP5, APOC1, CCL17, S100B, SLC11A1 among others may likely serve as biomarkers for Type-I reaction. Limitations The number of datasets related to leprosy reactions found after the systematic search is less (n = 4) and may limit the accuracy of identified biomarker genes. This could be resolved by including more studies in the data analysis. Conclusion We provide a comprehensive list of gene candidates which could be prioritised further in research focusing on immune reactions in leprosy, as they are likely important in understanding its complexities and could be useful in its early diagnosis.

Extracorporeal cardiopulmonary resuscitation versus standard treatment for refractory out-of-hospital cardiac arrest: a Bayesian meta-analysis

BackgroundThe outcomes of several randomized trials on extracorporeal cardiopulmonary resuscitation (ECPR) in patients with refractory out-of-hospital cardiac arrest were examined using frequentist methods, resulting in a dichotomous interpretation of results based on p-values rather than in the probability of clinically relevant treatment effects. To determine such a probability of a clinically relevant ECPR-based treatment effect on neurological outcomes, the authors of these trials performed a Bayesian meta-analysis of the totality of randomized ECPR evidence.MethodsA systematic search was applied to three electronic databases. Randomized trials that compared ECPR-based treatment with conventional CPR for refractory out-of-hospital cardiac arrest were included. The study was preregistered in INPLASY (INPLASY2023120060). The primary Bayesian hierarchical meta-analysis estimated the difference in 6-month neurologically favorable survival in patients with all rhythms, and a secondary analysis assessed this difference in patients with shockable rhythms (Bayesian hierarchical random-effects model). Primary Bayesian analyses were performed under vague priors. Outcomes were formulated as estimated median relative risks, mean absolute risk differences, and numbers needed to treat with corresponding 95% credible intervals (CrIs). The posterior probabilities of various clinically relevant absolute risk difference thresholds were estimated.ResultsThree randomized trials were included in the analysis (ECPR, n = 209 patients; conventional CPR, n = 211 patients). The estimated median relative risk of ECPR for 6-month neurologically favorable survival was 1.47 (95%CrI 0.73–3.32) with a mean absolute risk difference of 8.7% (− 5.0; 42.7%) in patients with all rhythms, and the median relative risk was 1.54 (95%CrI 0.79–3.71) with a mean absolute risk difference of 10.8% (95%CrI − 4.2; 73.9%) in patients with shockable rhythms. The posterior probabilities of an absolute risk difference > 0% and > 5% were 91.0% and 71.1% in patients with all rhythms and 92.4% and 75.8% in patients with shockable rhythms, respectively.ConclusionThe current Bayesian meta-analysis found a 71.1% and 75.8% posterior probability of a clinically relevant ECPR-based treatment effect on 6-month neurologically favorable survival in patients with all rhythms and shockable rhythms. These results must be interpreted within the context of the reported credible intervals and varying designs of the randomized trials.RegistrationINPLASY (INPLASY2023120060, December 14th, 2023, https://doi.org/10.37766/inplasy2023.12.0060).