Bayesian reanalysis reinforces the potential mortality benefit of TNF-α inhibitors in COVID-19: a methodological perspective

Abstract

Dear Editor,

Five and a half years since its emergence, despite widespread vaccination efforts, COVID-19 has not disappeared due to viral evolution similar to influenza virus variants, with recurrent sporadic outbreaks occurring in many regions, cities, and countries. Consequently, intensivists worldwide continue to face severe cases, making it crucial to synthesize evidence for managing critically ill COVID-19 patients from both randomized controlled trials (RCTs) and non-RCTs accumulated over recent years. Systematic reviews with meta-analysis of similar outcomes, when pooling is feasible, represent highly valued evidence in clinical medicine, including critical care [1]. This approach is particularly valuable given the high heterogeneity among critically ill patients and recruitment challenges that often result in individual studies being underpowered to achieve statistical significance in frequentist analyses, necessitating appropriate statistical weighting through meta-analysis to achieve adequate results [2].

We read with great interest the systematic review and meta-analysis by Jánosi et al. examining TNF-α inhibitors for COVID-19 treatment [3]. The authors conducted a rigorous analysis addressing an important clinical question, demonstrating potential reduced mortality with TNF-α inhibitor treatment (odds ratio [OR] 0.67, 95% confidence interval [CI] 0.44–1.00, P = 0.052). Their comprehensive search strategy, careful study selection, and transparent reporting strengthen the validity of their findings. We commend the authors’ thorough methodology and agree with their conclusions. However, we noticed that one included study Farokhnia et al., reported zero events in both arms [4]. While this study’s weight was minimal (0.7%) in the random-effects model, the 95% confidence interval touching 1.00 creates an interpretive challenge regarding statistical significance—a limitation inherent to frequentist hypothesis testing. This borderline p-value exemplifies a common dilemma in critical care research: how to interpret and communicate findings that suggest clinical benefit but narrowly miss conventional significance thresholds.

While frequentist meta-analysis yields binary significant/non-significant decisions based on arbitrary thresholds, Bayesian approaches provide posterior distributions that directly quantify the probability of different effect sizes. This probabilistic framework is particularly advantageous with sparse data, where frequentist methods require continuity corrections that may bias results [5]. Bayesian analysis enables direct probability statements that align with clinical reasoning, avoiding the interpretive challenges of borderline p-values and providing more nuanced information for clinical decision-making [6]. Increasingly, meta-analyses in critical care medicine are adopting Bayesian approaches to address these limitations [7]. For example, Cheng et al.‘s recent publication in Critical Care on haloperidol for delirium elegantly demonstrated how Bayesian probabilities of clinically important benefit/harm facilitate clinical decision-making by providing intuitive probability statements rather than dichotomous significance tests [8]. This methodological shift reflects a growing recognition that probability distributions better capture clinical uncertainty than p-values alone.

To complement the original findings, we conducted a Bayesian reanalysis using the multinma package in R with a random-effects model (4 chains, 1000 post-warmup iterations per chain, 4000 total post-warmup draws) [9]. All parameters showed good convergence (R-hat < 1.01), indicating stable Markov chain Monte Carlo chains and reliable posterior inference. Our analysis yielded a median OR of 0.58 (95% credible interval [CrI] 0.18–1.46), substantially lower than the frequentist point estimate but with a wider range. Although the credible interval crosses 1, the posterior distribution reveals that 93% of the probability mass lies below OR = 1, strongly suggesting mortality benefit with TNF-α inhibitors (Fig. 1A). This probabilistic interpretation provides clinicians with actionable information about the likelihood of benefit. The median I² increased slightly to 20.9% under the Bayesian framework but does not affect the assessment of certainty of evidence using GRADE methodology. For clinicians who prefer absolute effect measures, we also analyzed risk differences (RD), finding a median RD of −7.31% (95% CrI − 15.34–6.66%), with the same 93% probability favoring risk reduction. The calculated number needed to treat (NNT) of 14 (1/0.0731 = 13.7, conservatively rounded) aligns closely with the original estimates and represents a clinically meaningful effect size. Even with a minimal important benefit threshold of RD = −2% (NNT = 50), the probability favoring risk reduction remains high at 88.4%. At RD = −5% (NNT = 20), which represents a substantial mortality reduction in critical care research, this probability remains at 73%. The Bayesian ‘half-eye’ plots (Fig. 1B) clearly visualize the treatment effect’s probability distribution, helping clinicians understand not just the point estimate but the full range of plausible treatment effects and their associated probabilities, potentially enabling more confident and nuanced clinical decisions [10].

The Bayesian framework’s ability to quantify treatment benefit probability—rather than simply testing null hypotheses—aligns more closely with clinical decision-making processes [11]. Clinicians naturally think in terms of probabilities (“How likely is this treatment to help my patient?“) rather than p-values. This probabilistic framework is particularly valuable when evidence suggests benefit but conventional significance is not achieved, as in the current analysis. Historically, the complexity of programming code presented a barrier to Bayesian approaches. However, with recent rapid advances in large language models and their powerful debugging capabilities, this barrier has largely been eliminated. Furthermore, even though our Bayesian approach has reinforced the impressive benefits of TNF-α inhibitors for COVID-19 treatment, we fully agree with the authors’ final conclusion that further rigorous, large-scale RCTs are still needed to provide more definitive evidence. This is especially important when exploring differential effects among specific TNF-α inhibitor agents (such as infliximab, adalimumab, etanercept, certolizumab, and golimumab), where network meta-analysis with sufficient studies would be needed to establish comparative effectiveness and appropriate clinical rankings.

In conclusion, we applaud Jánosi et al. for their important contribution to the COVID-19 treatment evidence base. Our findings reinforce the authors’ conclusion that TNF-α inhibitors show promise for COVID-19 treatment, emphasized by the high probability of mortality benefit demonstrated in our Bayesian analysis. The integration of both frequentist and Bayesian perspectives provides a more complete understanding of treatment effects, and we strongly recommend this dual approach as the standard methodology for future meta-analyses.

Fig. 1

Half-eye plots of posterior distributions from Bayesian reanalysis of TNF-α inhibitor effects on COVID-19 mortality presented as (A) odds ratio (OR) and (B) risk difference (RD). The 95% credible intervals (CrIs) are also displayed

Full size image

No datasets were generated or analysed during the current study.

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We thank Professor Yu-Kang Tu from the Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Taipei, Taiwan, for conducting the workshop that taught us how to perform Bayesian meta-analysis using the multinma package.

This research received no external funding.

Authors and Affiliations

1. Chang Gung University College of Medicine, Taoyuan City, Taiwan

   Jia-Jin Chen

2. Department of Nephrology, Linkou Chang Gung Memorial Hospital, Taoyuan City, Taiwan

   Jia-Jin Chen

3. Kidney Research Center, Linkou Chang Gung Memorial Hospital, Taoyuan City, Taiwan

   Jia-Jin Chen

4. Education Center, College of Medicine, National Cheng Kung University Hospital, National Cheng Kung University, Tainan City, Taiwan

   Pei‑Chun Lai

5. Department of Pediatrics, College of Medicine, National Cheng Kung University Hospital, National Cheng Kung University, Tainan City, Taiwan

   Pei‑Chun Lai

6. Department of Surgery, College of Medicine, National Cheng Kung University Hospital, National Cheng Kung University, No. 138, Shengli Road, Tainan City, 701, Taiwan

   Yen-Ta Huang

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1. Jia-Jin ChenView author publications

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Contributions

Methodology: YT Huang; Original draft writing: JJ Chen; Formal analysis: YT Huang; Writing—review and editing: YT Huang, CH Lai; Project administration: YT Huang.

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Correspondence to Yen-Ta Huang.

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Chen, JJ., Lai, P. & Huang, YT. Bayesian reanalysis reinforces the potential mortality benefit of TNF-α inhibitors in COVID-19: a methodological perspective. Crit Care 29, 250 (2025). https://doi.org/10.1186/s13054-025-05506-4

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• Received: 12 June 2025

• Accepted: 15 June 2025

• Published: 19 June 2025

• DOI: https://doi.org/10.1186/s13054-025-05506-4

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