Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery. A Bayesian post-hoc analysis of the NIVAS trial

Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery. 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A Bayesian post-hoc analysis of the NIVAS trial Arthur Naudet-Lasserre, Joris Pensier, Audrey de Jong, Mathieu Capdevila, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7702781/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Dec, 2025 Read the published version in Critical Care → Version 1 posted 10 You are reading this latest preprint version Abstract Background Clinicians’ decision-making regarding the use of noninvasive ventilation (NIV) after abdominal surgery requires evaluating the probability of clinically meaningful benefit. The Bayesian framework may help caregivers interpret the findings of a randomized controlled trial (NIVAS) assessing curative NIV after abdominal surgery by incorporating their own beliefs and providing better estimates of treatment effects. This study aimed to use a Bayesian framework to estimate posterior probabilities of NIV effect under various prior assumptions, reflecting diverse clinicians’ beliefs. Method A prospectively registered, post-hoc Bayesian reanalysis of the NIVAS multicenter trial was conducted. The study included 293 patients with acute respiratory failure following abdominal surgery who were randomly assigned to receive either conventional oxygen therapy or NIV. Four statistical priors were defined: minimally informative, skeptical, enthusiastic, and pessimistic, reflecting a range of clinical beliefs. The primary outcome was day-7 reintubation. Secondary outcomes included day-30 mortality. Effect sizes were presented as odds ratios (OR) and absolute risk reduction (ARR) with 95% credible intervals (CrI). Results The minimally informative prior resulted in a posterior median OR for day-7 reintubation of 0.59 (95% CrI 0.37 to 0.95) in favor of NIV. Under the pessimistic prior, the posterior median OR was 0.64 (95% CrI 0.40 to 1.00). The posterior probability of NIV being superior to oxygen therapy varied from 96 to 99% when considering various priors from pessimistic to enthusiastic. The probability of benefit beyond an ARR ≥ 5% ranged from 77 to 93%. Regarding day-30 mortality, the posterior median OR was 0.63 (95% CrI 0.32 to 1.31) under minimally informative prior and 0.79 (95% CrI 0.48 to 1.29) under the skeptical prior. The probability of NIV superiority ranged from 82 to 90%. Conclusion This pre-registered Bayesian analysis indicates that NIV consistently reduces day-7 reintubation, with a high probability of achieving a clinically meaningful effect, even under pessimistic prior beliefs. These results provide compelling evidence for its broad use to treat respiratory failure after abdominal surgery. There was a high probability of mortality reduction with NIV, though the effect magnitude was imprecise. Acute respiratory failure noninvasive ventilation abdominal surgery Figures Figure 1 Figure 2 Figure 3 BACKGROUND Abdominal surgery, particularly of the upper abdomen, impairs respiratory mechanics through diaphragmatic dysfunction ( 1 ) and lung volume restriction. This leads to atelectasis, decreased functional residual capacity, and ventilation-perfusion mismatch, predisposing patients to acute respiratory failure (ARF) ( 2 , 3 ). While invasive mechanical ventilation has traditionally been the treatment for ARF ( 4 ), it has been associated with increased morbidity, mortality, and healthcare costs ( 5 , 6 ). Noninvasive respiratory supports have emerged as an alternative to avoid reintubation ( 7 – 9 ). A multicenter, randomized controlled trial (RCT), NIVAS ( 10 ), concluded that noninvasive ventilation (NIV) was superior to standard oxygen therapy for preventing day-7 reintubation, with a p-value of 0.03. However, traditional p-values provide limited clinical guidance ( 11 ) as they ignore prior knowledge about treatment effectiveness and yield only binary "significant" or "non-significant" results. NIV is often perceived as unpleasant ( 12 ) for patients, time-consuming for caregivers, and costly ( 13 ). Additionally, it remains a symptomatic treatment with the risk of delaying reintubation. Despite international guidelines ( 14 ) supporting its application in treating postoperative ARF ( 15 ), its widespread adoption remains limited due to diverging clinical opinions. Bayesian analysis provides a probabilistic framework that updates prior knowledge with new data ( 16 , 17 ). In this context of divergent clinicians’ beliefs, submitting the data to different priors ( 18 ) could help with the comprehensive examination and adequate propagation of guidelines ( 19 ). Moreover, Bayesian analysis also offers probability estimates of treatment effectiveness rather than binary outcomes, supporting more intuitive clinical interpretation ( 20 ). We aimed to reanalyze the NIVAS trial within a Bayesian framework, assuming various priors that reflect a range of clinician dispositions toward postoperative curative NIV, from enthusiastic support to pessimism. Our findings could either reinforce enthusiasm for NIV or suggest more selective application. METHODS Study design and ethical statement We performed a post-hoc Bayesian analysis of the NIVAS trial (Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery, NCT01971892 (10)). The NIVAS trial was an open-label multicenter randomized controlled trial that evaluated the efficacy of NIV versus standard oxygen therapy in preventing day-7 reintubation in patients with ARF following abdominal surgery. The study protocol was registered online before the acquisition of data (https://osf.io/6am3s). Approval for data reuse was obtained from the Scientific and Ethics Committee of Montpellier University Hospital (2025-04-256). The dataset was de-identified before transfer and information of patients was not required. Study population The eligible population is thoroughly defined in the original publication (10) In brief, the study population consisted of patients over 18 years of age who experienced ARF within 7 days of undergoing abdominal surgery under general anesthesia. ARF was defined as a partial oxygen pressure <60 mm Hg when breathing room air or <80 mm Hg when breathing 15 L/min of oxygen, or a peripheral oxygen saturation (SpO₂) ≤90% when breathing room air, plus either a respiratory rate higher than 30/min or clinical signs indicating intense respiratory muscle work and/or labored breathing. Patients were randomly assigned to receive either oxygen therapy to maintain a SpO₂ of at least 94% or NIV for at least six hours within the first 24 hours. Statistical analysis The primary endpoint was day-7 reintubation, and secondary endpoints were day-30 reintubation, day-30 and day-90 mortality, day-7 and day-30 healthcare-associated infections, day-7 and day-30 pneumonia, intensive care unit (ICU) and hospital length of stay to day 30. In Bayesian statistics, “priors” represent our knowledge, beliefs, or reasonable assumptions about treatment effects before seeing the data. The prior mean parameter of our regression model represents the expected treatment effect (as log OR), while the standard deviation (SD) quantifies the degree of uncertainty around this expectation. To assess the feasibility of literature-informed priors, we conducted a systematic literature review identifying all studies published before the NIVAS trial that compared NIV versus oxygen therapy and reported day-7 reintubation (see eMethod 1). This search identified five relevant studies: two RCTs (21,22) and three observational studies (23–25) as depicted in eFigure 1 and eTable 1. The two RCTs addressed substantially different populations, with reintubation rates in the oxygen groups of 33% and 10%, as compared to the 65% reintubation rate expected in the NIVAS sample size calculation. While a previous meta-analysis of these trials reported a significant benefit (risk ratio 0.25 [95% CI: 0.08, 0.83]), differences in the studied population precluded using these data for prior specification. The three observational studies examined populations more comparable to the NIVAS trial, with control group reintubation rates from 48% to 64%. However, these retrospective studies carried a serious to critical risk of bias, making them unsuitable for quantitative prior construction (see eFigure 2). While these data suggested modest evidence in favor of NIV, it was still considered a relative contraindication after abdominal surgery (26). To reflect diverging opinions, we therefore used a minimally informative prior as a reference (16) with a mean set to the absence of effect (log(OR) = 0), and a wide uncertainty (SD = 10). The resulting credible intervals (CrI) closely approximate frequentist confidence intervals. The skeptical prior was centered on the absence of effect (log OR = 0), but with moderate confidence that extreme benefits or harms are unlikely. This prior is equivalent to a 95% probability that the OR falls between 0.5 and 2 (normal distribution: mean = 0, SD = 0.355) (20). We then defined enthusiastic and pessimistic priors based on the NIVAS protocol sample size assumptions, which anticipated an event rate of 65% in the standard oxygen therapy group and 40% in the NIV group (expected OR of 0.35, log OR = -1.02). Thus, the enthusiastic prior follows a normal distribution (mean = -1.02, SD = 0.99) and the pessimistic prior was its symmetric about zero (mean = 1.02, SD = 0.99). The SD of 0.99 was calculated to ensure that each informative prior allowed a 15% probability of treatment inferiority (P(log OR > 0) = 0.15 for the enthusiastic prior), representing moderate strength of belief while preserving uncertainty (20). Table 1 and Figure 1A summarize prior specification. Table 1 . Characteristics of priors for day-7 reintubation Prior Belief Assumed Median of Logarithm of OR Assumed SD of Logarithm of OR P (OR <1) Rationale for Specifying Distribution Characteristics Prior Evidence Equivalent Minimally informative 0 10 50% Similar to conducting a frequentist analysis Skeptical 0 0.355 50% 95% of the probability mass is under the assumption of an OR lying between 0.5 and 2. Equivalent to an RCT enrolling 126 patient finding 0% RR Enthusiastic -1.02 0.99 85% NIVAS was powered to detect a 25% RD from 65% in oxygen group to 40% in NIV group representing an OR of 0.36, log OR of -1.02 Equivalent to a previous RCT enrolling 18 patients finding 25% RR Pessimistic 1.02 0.99 15% Symmetric about zero of the Enthusiastic, OR of 1/0.36 = 2.8 log OR =1.02. With sd estimated to allow 15% chance of benefit from NIV. Equivalent to a previous RCT enrolling 18 patients finding 25%¨Increased risk Abbreviations: OR, odds ratio; SD, Standard Deviation; P, probability. For other outcomes, pre-existing knowledge was unavailable; therefore, only the minimally informative and the skeptical priors were employed. Additionally, sensitivity analyses using informative priors on baseline risk are detailed in eMethod 2. We used a Bayesian logistic regression model: P(β|Data) ∝ P(Data|β) · P(β), where β represents the logarithm of the odds ratio (OR) for treatment effect. The following metrics were reported: (a) median OR, absolute risk reduction (ARR), and posterior distribution (b) Posterior 95% CrI according to the highest density method (c) probability of effect size beyond 10%, 5% and 2% of ARR. This choice of threshold with corresponding numbers needed to treat provides intuitive guidance for bedside decision-making beyond traditional statistical significance. A multivariate model was fitted to assess the risk of reintubation with greater precision. This model included the adjustment variables from the original NIVAS trial analysis (chronic obstructive pulmonary disease, ischemic heart disease, chronic heart failure, and body mass index > 30) as well as more recently identified risk factors (27) (presence of postoperative sepsis). We also included the stratification variables used in the randomization process (age, surgical site, and presence of epidural anesthesia). All analyses were performed using R statistical software (version 4.2.1), with the “brms” package (28) implementing No-U-Turn Sampler adaptive Hamiltonian Monte Carlo (4 chains, 1,000 burn-in iterations, 4,000 saved iterations per chain). The complete code for the analysis is available at https://github.com/pollux74/bayesian_reanalysis_NIVAS.git. Role of the funding source There was no funding source for this study. RESULTS All 293 patients from the intention-to-treat analysis described in the primary report were included in the subsequent analysis. Detailed patient characteristics are described in the primary report (10). Primary outcome: day-7 reintubation As shown in Table 1 and Figure 1B, under the minimally informative prior, NIV reduced the incidence of the primary outcome, with a posterior median OR for day-7 reintubation of 0.59 (95% CrI 0.37 to 0.95), corresponding to an ARR of 12.5% (95% CrI 1.2% to 23.3%). The probability that NIV was superior to standard oxygen therapy was 98%, and the probability of achieving an ARR ≥ 5% was 90%. Under the enthusiastic prior, the posterior median OR was 0.57 (95% CrI 0.36 to 0.91) corresponding to an ARR of 13.1% (95% CrI 2.4% to 23.6%). The pessimistic prior yielded a posterior median OR of 0.64 (95% CrI 0.40 to 1.00) corresponding to an ARR of 10.5% (95% CrI -0.1% to 21.2%). The skeptical prior produced the most conservative estimates, with a posterior median OR of 0.70 (95% CrI 0.47 to 1.05) corresponding to an ARR of 8.5% (95% CrI -1.0% to 17.7%). As shown in Table 2 and Figure 2, the choice of prior had minimal influence on the results, with the probability of benefit from NIV ranging from 96% to 99% and the probability of an ARR ≥ 5% ranging from 77% to 93%. After adjusting for stratification variables and prognostic factors, the treatment effect strengthened: posterior median OR of 0.50 (95% CrI 0.28 to 0.88) and ARR 13.1% (95% CrI 2.5% to 23.5%) under the minimally informative prior (see eTable 2 and eFigure 3). The probability of benefit from NIV ranged from 97% to 99% and the probability of achieving an ARR ≥ 5% from 78% to 94% across the four priors. As shown in eTable 2 and eFigures 4 to 6, applying priors to the intercept had negligible influence on effect size estimation, yielding similar estimates (see eTable 3). Table 2. Posterior probabilities and effect estimate for primary and secondary endpoints under each prior assumption Prior Belief Posterior Median OR (95% CrI) P(OR < 1) Posterior Median ARR, % (95% CrI) P(ARR ≥2%) NNT = 50 P(ARR ≥5%) NNT = 20 P(ARR ≥10%) NNT = 10 Day-7 reintubation Minimally informative 0.59 (0.37 to 0.95) 98% 12.5% (1.2% to 23.3%) 96% 90% 67% Enthusiastic 0.57 (0.36 to 0.91) 99% 13.1% (2.4% to 23.6%) 98% 93% 71% Pessimistic 0.64 (0.40 to 1.00) 97% 10.5% (-0.1% to 21.2%) 94% 85% 54% Skeptical 0.70 (0.47 to 1.05) 96% 8.5% (-1.0% to 17.7%) 91% 77% 37% Day-30 mortality Minimally informative 0.63 (0.32 to 1.31) 90% 5.0% (-2.4% to 12.7%) 78% 50% 10% Skeptical 0.79 (0.48 to 1.29) 82% 2.5% (-3.3% to 7.8%) 57% 18% 1% Day-7 healthcare-Associated infection Minimally informative 0.51 (0.30 to 0.90) 99% 12.1% (2.4% to 21.6%) 98% 93% 67% Skeptical 0.66 (0.44 to 1.01) 97% 7.6% (-0.2% to 15.0%) 92% 74% 27% Day-7 pneumonia Minimally informative 0.39 (0.20 to 0.75) 100% 11.9% (3.7% to 20.4%) 99% 95% 67% Skeptical 0.61 (0.38 to 0.97) 98% 6.6% (0.3% to 13.1%) 92% 69% 15% Abbreviations: OR, odds ratio; CrI, Credible interval; P, probability; ARR, absolute risk reduction; NNT = Number Needed to Treat (of patients to avoid one event). Secondary outcomes For day-30 mortality, the minimally informative prior resulted in a posterior median OR of 0.63 corresponding to an ARR of 5.0% (95% CrI -2.4% to 12.7%), as shown in Table 2 and Figure 3. This analysis showed a 90% probability that NIV reduces day-30 mortality compared to standard care, with a 50% probability of achieving a clinically meaningful ARR ≥ 5%. The skeptical prior resulted in a posterior median OR of 0.79 (95% CrI 0.48 to 1.29) and a corresponding median ARR of 2.5% (95% CrI -3.3% to 7.8%). In the multivariate analysis, adjustment for covariates yielded larger effect estimates favouring NIV, with a posterior median OR of 0.47 (95% CrI 0.18 to 1.19) corresponding to an ARR of 5.1% (95% CrI -1.1% to 11.4%) under the minimally informative prior. This adjustment increased the probability of benefit from NIV to 95% and resulted in a 51% probability of achieving an ARR ≥ 5% (see eTable 4 and eFigure 7). Regarding day-90 mortality, the minimally informative prior resulted in a posterior median OR of 0.64 (95% CrI 0.34-1.13), while the skeptical prior yielded an OR of 0.78 (95% CrI 0.49-1.22) as shown in eTable5 and eFigure 8. The probability that NIV reduces day-90 mortality compared to standard care ranged from 87 % to 93 %. For day-7 healthcare-associated infections and day-7 pneumonia, both priors indicated a high probability of benefit from NIV, as shown in Table 2 and eFigures 9 and 10. The probability of benefit from NIV ranged from 97% to 99% for day-7 healthcare-associated infections with a 74% to 93% probability of an effect beyond 5% of ARR. For day-7 pneumonia, probability of benefit ranged from 98% to 100% with a 69% to 95% probability of an effect beyond 5% of ARR. Results for day-30 healthcare-associated infections, pneumonia, reintubation, are described in eTable 5 and eFigures 11 to 13 and results for ICU and hospital length of stay are described in eTable 6. Posteriors estimates in each pre-defined sub-groups are described in eFigure 14. Bayesian model validity was confirmed through chain convergence assessment using inspection of traceplots and autocorrelograms for all analyses (see eFigures 15-27). DISCUSSION In this prospectively registered, post-hoc Bayesian analysis of the NIVAS multicenter trial evaluating non-invasive ventilation (NIV) for treating acute respiratory failure (ARF) following abdominal surgery, we found a high probability that NIV reduces the day-7 reintubation rate, even when considering clinically relevant thresholds. This result was consistent across a range of diverging priors, reflecting varying clinicians’ opinions from pessimistic to enthusiastic. Additionally, we observed a high probability that NIV decreases secondary outcomes, including day-30 and day-90 mortality, day-7 pneumonia and healthcare-associated infections. Beyond the original study, our Bayesian analysis provides enhanced understanding of the findings. First, we used a rigorous approach including a systematic literature review and bias evaluation of studies published before the trial. This approach contextualizes our findings within the existing evidence base and enables rigorous prior specification for Bayesian analysis. The use of a skeptical prior, which better reflects the typical distribution of treatment effects, and pessimistic priors, which hypothesize oxygen superiority, challenged the original results and enhanced the robustness of our findings. Incorporating priors that constrain extreme effect sizes therefore reinforces results’ credibility. Second, presenting full posterior distributions rather than point estimates with confidence intervals provides clinicians with comprehensive information about the range of plausible treatment effects and their relative likelihoods, enabling more informed clinical decision-making. Third, while reintubation and mortality are clinically relevant, we calculated probabilities of treatment effects beyond certain thresholds to help caregivers better understand effect magnitude. This approach quantifies the uncertainty around clinically meaningful effect sizes. With a baseline mortality risk of 20%, a 2% absolute reduction in mortality represents a substantial clinical benefit. Therefore, a 78% probability of an ARR ≥ 2% suggests a clinically significant benefit for mortality reduction with NIV, a well-established therapeutic intervention. Considering the lack of new randomized controlled trials since the NIVAS trial, this study is a valuable addition to the existing literature. A large randomized trial involving 4,808 patients across 70 centers worldwide comparing CPAP to standard treatment showed no significant improvement in composite outcomes (29), but used NIV to prevent ARF rather than for treatment. These contrasting results align with the recent network meta-analysis by Pettenuzzo et al. (30), where NIV was found to reduce the risk of reintubation. However, the effect was only achieved when applied as a treatment for ARF, or when used in high-risk patients. Among high-risk patients, those who suffer from obesity represent a priority target where NIV is effective for preventing (7) or treating ARF (6). This reinforces the NIVAS findings that NIV should be reserved for patients with established ARF rather than for an unselected population (7), or when used for prevention in high-risk patients. These divergent findings across similar interventions illustrate why probabilistic approaches to evidence interpretation merit consideration. The current Bayesian analysis emerges within the context of increased criticism (18) regarding the overreliance on p-values and null hypothesis significance testing (NHST), which often reduces complex findings to binary outcomes based on arbitrary thresholds. Given the substantial resources required for randomized controlled trials, maximizing interpretive value from existing data becomes paramount. Bayesian reanalysis has proven valuable in critical care, providing nuanced interpretations that complement traditional analyses. Goligher et al. demonstrated this approach in their EOLIA trial reanalysis (31), providing a nuanced interpretation of the results in the context of a high risk-reward ratio (mortality benefit in patients with severe ARDS). Conversely, Zampieri et al. (32) used Bayesian methods to challenge optimistic interpretations in their STARRT-AKI re-analysis by showing a low probability of reduced mortality. Here, despite confirming and strengthening the original results, the current analysis calls into question the likelihood of large effect sizes. Our study has several limitations. First, we inherit the limitations of the original trial including the lower-than-expected rate of reintubation, limited power to detect mortality effects, and lack of blinding for the somewhat subjective primary endpoint (i.e., day-7 reintubation). Second, this post-hoc analysis carries inherent risks of data-dependent findings. Despite the analysis plan having been registered before data acquisition, it is acknowledged that the report is of an exploratory nature. To mitigate this risk, we limited our analysis to pre-specified outcomes from the original trial and employed a conservative skeptical prior. Third, our method for defining informative priors may be criticized. Although we conducted a systematic review to evaluate prior knowledge, we decided not to use these studies to construct quantitative Bayesian priors because the two RCTs addressed significantly less severe populations, and the three observational studies had a high risk of bias. We therefore used assumptions from the NIVAS trial’s sample size calculation. Nonetheless, sample size calculations often involve subjective assumptions and economic/feasibility considerations. However, these assumptions must be credible to initiate a multicenter RCT. To mitigate this risk, we used a minimally informative prior as reference and employed informative priors representing more extreme clinical opinions that might exist in the medical community. We encountered a common situation where uncertain data quality raised questions about the feasibility and relevance of data-driven priors. Furthermore, no universally rigorous method exists for defining priors, and because they can influence results and conclusions, this remains an ongoing challenge. CONCLUSION In this prospectively registered, post-hoc analysis of the NIVAS trial, NIV consistently reduced the day-7 reintubation rate across various prior distributions, including a pessimistic prior re-flecting a reluctant clinician’s perspective, providing compelling evidence for its use. There was a high probability of mortality reduction with NIV, though the effect magnitude was impre-cise. Declarations Ethics approval and consent to participate Approval for data reuse was obtained from the Scientific and Ethics Committee of Montpellier University Hospital (number 2025-04-256) Consent for publication Not applicable Availability of data and materials Data will be available to researchers upon reasonable request immediately following publication. Proposals should be directed to the corresponding author. The R code is available at https://github.com/pollux74/bayesian_reanalysis_NIVAS.git. Conflicts of Interest NM reports receiving consulting fees from Adene, Nomics, Sanofi, Bruxless, ID Solution, Archean Technologies, MSD, BMS, AB science and SimeoxSJ reports receiving consulting fees from Drager, Medtronic, Baxter, Fresenius-Xenios, Mindray, and Fisher & Paykel. ADJ reports receiving consulting fees from Medtronic, Dräger, Viatris and Fisher & Paykel. No conflicts of interest are reported for other authors. Funding This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors. Author’s contributions ANL, JP, NM, SJ, and ADJ contributed to conception and design of the study, to the acquisition of the data, to the analysis and interpretation of the data, to drafting the submitted article, and to provide final approval of the version to be published. 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Extracorporeal Membrane Oxygenation for Severe Acute Respiratory Distress Syndrome and Posterior Probability of Mortality Benefit in a Post Hoc Bayesian Analysis of a Randomized Clinical Trial. JAMA. 2018;320(21):2251–9. Zampieri FG, Machado FR, Biondi RS, Freitas FGR, Veiga VC, Figueiredo RC, et al. Association between Type of Fluid Received Prior to Enrollment, Type of Admission, and Effect of Balanced Crystalloid in Critically Ill Adults: A Secondary Exploratory Analysis of the BaSICS Clinical Trial. Am J Respir Crit Care Med. 2022 June;15(12):1419–28. Additional Declarations Competing interest reported. NM reports receiving consulting fees from Adene, Nomics, Sanofi, Bruxless, ID Solution, Ar-chean Technologies, MSD, BMS, AB science and SimeoxSJ reports receiving consulting fees from Drager, Medtronic, Baxter, Fresenius-Xenios, Mindray, and Fisher & Paykel. ADJ reports receiving consulting fees from Medtronic, Dräger, Viatris and Fisher & Paykel. No conflicts of interest are reported for other authors. Supplementary Files 20250924BayesianNIVASSupplementalamended.docx Cite Share Download PDF Status: Published Journal Publication published 10 Dec, 2025 Read the published version in Critical Care → Version 1 posted Editorial decision: Revision requested 20 Oct, 2025 Reviewers agreed at journal 15 Oct, 2025 Reviews received at journal 14 Oct, 2025 Reviewers agreed at journal 12 Oct, 2025 Reviews received at journal 09 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers invited by journal 07 Oct, 2025 Editor assigned by journal 06 Oct, 2025 Submission checks completed at journal 06 Oct, 2025 First submitted to journal 24 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7702781","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":531334835,"identity":"0d066aba-dd01-4e42-94fc-abb0464c10cc","order_by":0,"name":"Arthur Naudet-Lasserre","email":"data:image/png;base64,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","orcid":"","institution":"Regional University Hospital of Montpellier, University of Montpellier","correspondingAuthor":true,"prefix":"","firstName":"Arthur","middleName":"","lastName":"Naudet-Lasserre","suffix":""},{"id":531334836,"identity":"b356815c-ee8a-44b6-960c-7fb89f9b428f","order_by":1,"name":"Joris Pensier","email":"","orcid":"","institution":"Regional University Hospital of Montpellier, University of Montpellier","correspondingAuthor":false,"prefix":"","firstName":"Joris","middleName":"","lastName":"Pensier","suffix":""},{"id":531334837,"identity":"43b081c0-4e2b-4f2e-9684-a921c12e2d75","order_by":2,"name":"Audrey de Jong","email":"","orcid":"","institution":"Regional University Hospital of Montpellier, University of Montpellier","correspondingAuthor":false,"prefix":"","firstName":"Audrey","middleName":"","lastName":"de Jong","suffix":""},{"id":531334838,"identity":"9d2d9d5b-2fbf-4b54-940d-3b6c1f475c1f","order_by":3,"name":"Mathieu Capdevila","email":"","orcid":"","institution":"Regional University Hospital of Montpellier, University of Montpellier","correspondingAuthor":false,"prefix":"","firstName":"Mathieu","middleName":"","lastName":"Capdevila","suffix":""},{"id":531334839,"identity":"fc08c22a-7680-4208-b15c-7f0a4849a345","order_by":4,"name":"Samir Jaber","email":"","orcid":"","institution":"Regional University Hospital of Montpellier, University of 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08:42:22","extension":"html","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":104213,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7702781/v1/03849e4995b96a31e89fe705.html"},{"id":93914924,"identity":"0d599ba4-10b8-4b9e-8d4d-aa1d799554fd","added_by":"auto","created_at":"2025-10-20 08:42:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":34066,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePrior probability distributions for day-7 reintubation. \u003c/strong\u003e(A) and posterior ARR distributions (B) according to the minimally informative prior. Panel A represents the probability density distribution of each priors on the log-OR scale. Panel B, the teal area depicts the probability of oxygen therapy being superior (ARR \u0026lt; 0%). The green area represents the probability of NIV providing low benefit (ARR 0-2%). The yellow area shows moderate benefit (ARR 2-5%), the orange area of ARR 5-10%, and the red area strong benefit (ARR ≥ 10%).\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7702781/v1/f617aa106e9dfd06be294017.png"},{"id":93914926,"identity":"cfad06d4-5eba-41aa-80c8-bad50a209aa8","added_by":"auto","created_at":"2025-10-20 08:42:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":23670,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePosterior probability distributions for OR and ARR comparing NIV versus oxy-gen on day-7 reintubation according to each prior\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7702781/v1/c9c131640759f5bc02c89267.png"},{"id":93914927,"identity":"4ee6b320-ec9e-49c3-9e6d-a9017bd94f68","added_by":"auto","created_at":"2025-10-20 08:42:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":16451,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePosterior probability distributions for OR and ARR comparing NIV versus oxy-gen on day-30 mortality according to each prior\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7702781/v1/bb3d38ff5f07cb1e25a8b5a2.png"},{"id":98244734,"identity":"3e2435be-d87a-4c15-a44b-53a1997c3ef8","added_by":"auto","created_at":"2025-12-15 16:14:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1143403,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7702781/v1/67cb1684-9006-4bbb-a87f-33028836b691.pdf"},{"id":93914934,"identity":"a68dc35e-0d39-4021-91d7-cfd441cb97bd","added_by":"auto","created_at":"2025-10-20 08:42:22","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":8487625,"visible":true,"origin":"","legend":"","description":"","filename":"20250924BayesianNIVASSupplementalamended.docx","url":"https://assets-eu.researchsquare.com/files/rs-7702781/v1/266bf7c5acbe724e40acb59d.docx"}],"financialInterests":"Competing interest reported. NM reports receiving consulting fees from Adene, Nomics, Sanofi, Bruxless, ID Solution, Ar-chean Technologies, MSD, BMS, AB science and SimeoxSJ reports receiving consulting fees from Drager, Medtronic, Baxter, Fresenius-Xenios, Mindray, and Fisher \u0026 Paykel. ADJ reports receiving consulting fees from Medtronic, Dräger, Viatris and Fisher \u0026 Paykel. No conflicts of interest are reported for other authors.","formattedTitle":"Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery. A Bayesian post-hoc analysis of the NIVAS trial","fulltext":[{"header":"BACKGROUND","content":"\u003cp\u003eAbdominal surgery, particularly of the upper abdomen, impairs respiratory mechanics through diaphragmatic dysfunction (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) and lung volume restriction. This leads to atelectasis, decreased functional residual capacity, and ventilation-perfusion mismatch, predisposing patients to acute respiratory failure (ARF) (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). While invasive mechanical ventilation has traditionally been the treatment for ARF (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e), it has been associated with increased morbidity, mortality, and healthcare costs (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Noninvasive respiratory supports have emerged as an alternative to avoid reintubation (\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA multicenter, randomized controlled trial (RCT), NIVAS (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e), concluded that noninvasive ventilation (NIV) was superior to standard oxygen therapy for preventing day-7 reintubation, with a p-value of 0.03. However, traditional p-values provide limited clinical guidance (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e) as they ignore prior knowledge about treatment effectiveness and yield only binary \"significant\" or \"non-significant\" results. NIV is often perceived as unpleasant (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e) for patients, time-consuming for caregivers, and costly (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e). Additionally, it remains a symptomatic treatment with the risk of delaying reintubation. Despite international guidelines (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e) supporting its application in treating postoperative ARF (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e), its widespread adoption remains limited due to diverging clinical opinions.\u003c/p\u003e\u003cp\u003eBayesian analysis provides a probabilistic framework that updates prior knowledge with new data (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e). In this context of divergent clinicians\u0026rsquo; beliefs, submitting the data to different priors (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e) could help with the comprehensive examination and adequate propagation of guidelines (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e). Moreover, Bayesian analysis also offers probability estimates of treatment effectiveness rather than binary outcomes, supporting more intuitive clinical interpretation (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eWe aimed to reanalyze the NIVAS trial within a Bayesian framework, assuming various priors that reflect a range of clinician dispositions toward postoperative curative NIV, from enthusiastic support to pessimism. Our findings could either reinforce enthusiasm for NIV or suggest more selective application.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e\u003cstrong\u003eStudy design and ethical statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe performed a post-hoc Bayesian analysis of the NIVAS trial (Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery, NCT01971892 (10)). The NIVAS trial was an open-label multicenter randomized controlled trial that evaluated the efficacy of NIV versus standard oxygen therapy in preventing day-7 reintubation in patients with ARF following abdominal surgery. The study protocol was registered online before the acquisition of data (https://osf.io/6am3s). Approval for data reuse was obtained from the Scientific and Ethics Committee of Montpellier University Hospital (2025-04-256). The dataset was de-identified before transfer and information of patients was not required.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStudy population\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe eligible population is thoroughly defined in the original publication (10) In brief, the study population consisted of patients over 18 years of age who experienced ARF within 7 days of undergoing abdominal surgery under general anesthesia. ARF was defined as a partial oxygen pressure \u0026lt;60 mm Hg when breathing room air or \u0026lt;80 mm Hg when breathing 15 L/min of oxygen, or a peripheral oxygen saturation (SpO₂) \u0026le;90% when breathing room air, plus either a respiratory rate higher than 30/min or clinical signs indicating intense respiratory muscle work and/or labored breathing. Patients were randomly assigned to receive either oxygen therapy to maintain a SpO₂ of at least 94% or NIV for at least six hours within the first 24 hours.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStatistical analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe primary endpoint was day-7 reintubation, and secondary endpoints were day-30 reintubation, day-30 and day-90 mortality, day-7 and day-30 healthcare-associated infections, day-7 and day-30 pneumonia, intensive care unit (ICU) and hospital length of stay to day 30.\u003c/p\u003e\n\u003cp\u003eIn Bayesian statistics, \u0026ldquo;priors\u0026rdquo; represent our knowledge, beliefs, or reasonable assumptions about treatment effects before seeing the data. The prior mean parameter of our regression model represents the expected treatment effect (as log OR), while the standard deviation (SD) quantifies the degree of uncertainty around this expectation. To assess the feasibility of literature-informed priors, we conducted a systematic literature review identifying all studies published before the NIVAS trial that compared NIV versus oxygen therapy and reported day-7 reintubation (see eMethod 1). This search identified five relevant studies: two RCTs (21,22) and three observational studies (23\u0026ndash;25) as depicted in eFigure 1 and eTable 1.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe two RCTs addressed substantially different populations, with reintubation rates in the oxygen groups of 33% and 10%, as compared to the 65% reintubation rate expected in the NIVAS sample size calculation. While a previous meta-analysis of these trials reported a significant benefit (risk ratio 0.25 [95% CI: 0.08, 0.83]), differences in the studied population precluded using these data for prior specification. The three observational studies examined populations more comparable to the NIVAS trial, with control group reintubation rates from 48% to 64%. However, these retrospective studies carried a serious to critical risk of bias, making them unsuitable for quantitative prior construction (see eFigure 2). While these data suggested modest evidence in favor of NIV, it was still considered a relative contraindication after abdominal surgery (26).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo reflect diverging opinions, we therefore used a minimally informative prior as a reference (16) with a mean set to the absence of effect (log(OR) = 0), and a wide uncertainty (SD = 10). The resulting credible intervals (CrI) closely approximate frequentist confidence intervals. \u0026nbsp;The skeptical prior was centered on the absence of effect (log OR = 0), but with moderate confidence that extreme benefits or harms are unlikely. This prior is equivalent to a 95% probability that the OR falls between 0.5 and 2 (normal distribution: mean = 0, SD = 0.355) (20). We then defined enthusiastic and pessimistic priors based on the NIVAS protocol sample size assumptions, which anticipated an event rate of 65% in the standard oxygen therapy group and 40% in the NIV group (expected OR of 0.35, log OR = -1.02). Thus, the enthusiastic prior follows a normal distribution (mean = -1.02, SD = 0.99) and the pessimistic prior was its symmetric about zero (mean = 1.02, SD = 0.99). The SD of 0.99 was calculated to ensure that each informative prior allowed a 15% probability of treatment inferiority (P(log OR \u0026gt; 0) = 0.15 for the enthusiastic prior), representing moderate strength of belief while preserving uncertainty (20). \u0026nbsp;Table 1 and Figure 1A summarize prior specification. \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003cstrong\u003e. Characteristics of priors for day-7 reintubation\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"651\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePrior Belief\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 98px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eAssumed Median of Logarithm of OR\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eAssumed SD of Logarithm of OR\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 67px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eP (OR \u0026lt;1)\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eRationale for Specifying Distribution Characteristics\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePrior Evidence Equivalent\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eMinimally informative\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e50%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 198px;\"\u003e\n \u003cp\u003eSimilar to conducting a frequentist analysis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eSkeptical\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.355\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e50%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 198px;\"\u003e\n \u003cp\u003e95% of the probability mass is under the assumption of an OR lying between 0.5 and 2.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003eEquivalent to an RCT enrolling 126 patient finding 0% RR\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eEnthusiastic\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e-1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e85%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 198px;\"\u003e\n \u003cp\u003eNIVAS was powered to detect a 25% RD from 65% in oxygen group to 40% in NIV group representing an OR of 0.36, log OR of -1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003eEquivalent to a previous RCT enrolling 18 patients finding 25% RR\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 113px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePessimistic\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 198px;\"\u003e\n \u003cp\u003eSymmetric about zero of the Enthusiastic, OR of 1/0.36 = 2.8 log OR =1.02. With sd estimated to allow 15% chance of benefit from NIV.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003eEquivalent to a previous RCT enrolling 18 patients finding 25%\u0026uml;Increased risk\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 78px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 35px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 56px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 5px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 1px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 63px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 18px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 191px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd style=\"width: 111px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eAbbreviations: OR, odds ratio; SD, Standard Deviation; P, probability.\u003c/p\u003e\n\u003cp\u003eFor other outcomes, pre-existing knowledge was unavailable; therefore, only the minimally informative and the skeptical priors were employed. Additionally, sensitivity analyses using informative priors on baseline risk are detailed in eMethod 2.\u003c/p\u003e\n\u003cp\u003eWe used a Bayesian logistic regression model: P(\u0026beta;|Data)\u0026nbsp;\u0026prop;\u0026nbsp;P(Data|\u0026beta;) \u0026middot; P(\u0026beta;), where \u0026beta; represents the logarithm of the odds ratio (OR) for treatment effect. The following metrics were reported: (a) median OR, absolute risk reduction (ARR), and posterior distribution (b) Posterior 95% CrI according to the highest density method (c) probability of effect size beyond 10%, 5% and 2% of ARR. This choice of threshold with corresponding numbers needed to treat provides intuitive guidance for bedside decision-making beyond traditional statistical significance.\u003c/p\u003e\n\u003cp\u003eA multivariate model was fitted to assess the risk of reintubation with greater precision. This model included the adjustment variables from the original NIVAS trial analysis (chronic obstructive pulmonary disease, ischemic heart disease, chronic heart failure, and body mass index \u0026gt; 30) as well as more recently identified risk factors (27) (presence of postoperative sepsis). We also included the stratification variables used in the randomization process (age, surgical site, and presence of epidural anesthesia).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAll analyses were performed using R statistical software (version 4.2.1), with the \u0026ldquo;brms\u0026rdquo; package (28) implementing No-U-Turn Sampler adaptive Hamiltonian Monte Carlo (4 chains, 1,000 burn-in iterations, 4,000 saved iterations per chain). The complete code for the analysis is available at https://github.com/pollux74/bayesian_reanalysis_NIVAS.git.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRole of the funding source\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere was no funding source for this study.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eAll 293 patients from the intention-to-treat analysis described in the primary report were included in the subsequent analysis. Detailed patient characteristics are described in the primary report (10).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePrimary outcome: day-7 reintubation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAs shown in Table 1 and Figure 1B, under the minimally informative prior, NIV reduced the incidence of the primary outcome, with a posterior median OR for day-7 reintubation of 0.59 (95% CrI 0.37 to 0.95), corresponding to an ARR of 12.5% (95% CrI 1.2% to 23.3%). The probability that NIV was superior to standard oxygen therapy was 98%, and the probability of achieving an ARR \u0026ge; 5% was 90%. Under the enthusiastic prior, the posterior median OR was 0.57 (95% CrI 0.36 to 0.91) corresponding to an ARR of 13.1% (95% CrI 2.4% to 23.6%). The pessimistic prior yielded a posterior median OR of 0.64 (95% CrI 0.40 to 1.00) corresponding to an ARR of 10.5% (95% CrI -0.1% to 21.2%). The skeptical prior produced the most conservative estimates, with a posterior median OR of 0.70 (95% CrI 0.47 to 1.05) corresponding to an ARR of 8.5% (95% CrI -1.0% to 17.7%). As shown in Table 2 and Figure 2, the choice of prior had minimal influence on the results, with the probability of benefit from NIV ranging from 96% to 99% and the probability of an ARR \u0026ge; 5% ranging from 77% to 93%. \u0026nbsp;After adjusting for stratification variables and prognostic factors, the treatment effect strengthened: posterior median OR of 0.50 (95% CrI 0.28 to 0.88) and ARR 13.1% (95% CrI 2.5% to 23.5%) under the minimally informative prior (see eTable 2 and eFigure 3). The probability of benefit from NIV ranged from 97% to 99% and the probability of achieving an ARR \u0026ge; 5% from 78% to 94% across the four priors. As shown in eTable 2 and eFigures 4 to 6, applying priors to the intercept had negligible influence on effect size estimation, yielding similar estimates (see eTable 3).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;Table 2. Posterior probabilities and effect estimate for primary and secondary endpoints under each prior assumption\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"660\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePrior\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eBelief\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePosterior Median OR (95% CrI)\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eP(OR \u0026lt; 1)\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePosterior Median ARR, % (95% CrI)\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eP(ARR \u0026ge;2%)\u003cbr\u003e\u0026nbsp;NNT = 50\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eP(ARR \u0026ge;5%)\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eNNT = 20\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; P(ARR \u0026ge;10%)\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eNNT = 10\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"7\" valign=\"top\" style=\"width: 660px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eDay-7 reintubation\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eMinimally informative\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.59 (0.37 to 0.95)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e98%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e12.5% (1.2% to 23.3%)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e96%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e90%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e67%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eEnthusiastic\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.57 (0.36 to 0.91)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e99%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e13.1% (2.4% to 23.6%)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e98%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e93%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e71%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003ePessimistic\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.64 (0.40 to 1.00)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e97%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e10.5% (-0.1% to 21.2%)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e94%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e85%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e54%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eSkeptical\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.70 (0.47 to 1.05)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e96%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e8.5% (-1.0% to 17.7%)\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e91%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e77%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e37%\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"7\" valign=\"top\" style=\"width: 660px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eDay-30 mortality\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eMinimally informative\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.63 (0.32 to 1.31)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e90%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e5.0% (-2.4% to 12.7%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e78%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e50%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e10%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eSkeptical\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.79 (0.48 to 1.29)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e82%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e2.5% (-3.3% to 7.8%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e57%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e18%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e1%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"7\" valign=\"top\" style=\"width: 660px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eDay-7 healthcare-Associated infection\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eMinimally informative\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.51 (0.30 to 0.90)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e99%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e12.1% (2.4% to 21.6%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e98%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e93%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e67%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eSkeptical\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.66 (0.44 to 1.01)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e97%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e7.6% (-0.2% to 15.0%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e92%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e74%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e27%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"7\" valign=\"top\" style=\"width: 660px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eDay-7 pneumonia\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eMinimally informative\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.39 (0.20 to 0.75)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e100%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e11.9% (3.7% to 20.4%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e99%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e95%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e67%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 75px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eSkeptical\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 144px;\"\u003e\n \u003cp\u003e0.61 (0.38 to 0.97)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e98%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 106px;\"\u003e\n \u003cp\u003e6.6% (0.3% to 13.1%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e92%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e69%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 86px;\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eAbbreviations: OR, odds ratio; CrI, Credible interval; P, probability; ARR, absolute risk reduction; NNT = Number Needed to Treat (of patients to avoid one event).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSecondary outcomes\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor day-30 mortality, the minimally informative prior resulted in a posterior median OR of 0.63 corresponding to an ARR of 5.0% (95% CrI -2.4% to 12.7%), as shown in Table 2 and Figure 3. This analysis showed a 90% probability that NIV reduces day-30 mortality compared to standard care, with a 50% probability of achieving a clinically meaningful ARR \u0026ge; 5%. The skeptical prior resulted in a posterior median OR of 0.79 (95% CrI 0.48 to 1.29) and a corresponding median ARR of 2.5% (95% CrI -3.3% to 7.8%). In the multivariate analysis, adjustment for covariates yielded larger effect estimates favouring NIV, with a posterior median OR of 0.47 (95% CrI 0.18 to 1.19) corresponding to an ARR of 5.1% (95% CrI -1.1% to 11.4%) under the minimally informative prior. This adjustment increased the probability of benefit from NIV to 95% and resulted in a 51% probability of achieving an ARR \u0026ge; 5% (see eTable 4 and eFigure 7).\u003c/p\u003e\n\u003cp\u003eRegarding day-90 mortality, the minimally informative prior resulted in a posterior median OR of 0.64 (95% CrI 0.34-1.13), while the skeptical prior yielded an OR of 0.78 (95% CrI 0.49-1.22) as shown in eTable5 and eFigure 8. The probability that NIV reduces day-90 mortality compared to standard care ranged from 87 % to 93 %.\u003c/p\u003e\n\u003cp\u003eFor day-7 healthcare-associated infections and day-7 pneumonia, both priors indicated a high probability of benefit from NIV, as shown in Table 2 and eFigures 9 and 10. The probability of benefit from NIV ranged from 97% to 99% for day-7 healthcare-associated infections with a 74% to 93% probability of an effect beyond 5% of ARR. For day-7 pneumonia, probability of benefit ranged from 98% to 100% with a 69% to 95% probability of an effect beyond 5% of ARR.\u003c/p\u003e\n\u003cp\u003eResults for day-30 healthcare-associated infections, pneumonia, reintubation, are described in eTable 5 and eFigures 11 to 13 and results for ICU and hospital length of stay are described in eTable 6. Posteriors estimates in each pre-defined sub-groups are described in eFigure 14.\u003c/p\u003e\n\u003cp\u003eBayesian model validity was confirmed through chain convergence assessment using inspection of traceplots and autocorrelograms for all analyses (see eFigures 15-27).\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eIn this prospectively registered, post-hoc Bayesian analysis of the NIVAS multicenter trial evaluating non-invasive ventilation (NIV) for treating acute respiratory failure (ARF) following abdominal surgery, we found a high probability that NIV reduces the day-7 reintubation rate, even when considering clinically relevant thresholds. This result was consistent across a range of diverging priors, reflecting varying clinicians\u0026rsquo; opinions from pessimistic to enthusiastic. Additionally, we observed a high probability that NIV decreases secondary outcomes, including day-30 and day-90 mortality, day-7 pneumonia and healthcare-associated infections.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBeyond the original study, our Bayesian analysis provides enhanced understanding of the findings. First, we used a rigorous approach including a systematic literature review and bias evaluation of studies published before the trial. This approach contextualizes our findings within the existing evidence base and enables rigorous prior specification for Bayesian analysis. The use of a skeptical prior, which better reflects the typical distribution of treatment effects, and pessimistic priors, which hypothesize oxygen superiority, challenged the original results and enhanced the robustness of our findings. Incorporating priors that constrain extreme effect sizes therefore reinforces results\u0026rsquo; credibility. Second, presenting full posterior distributions rather than point estimates with confidence intervals provides clinicians with comprehensive information about the range of plausible treatment effects and their relative likelihoods, enabling more informed clinical decision-making. Third, while reintubation and mortality are clinically relevant, we calculated probabilities of treatment effects beyond certain thresholds to help caregivers better understand effect magnitude. This approach quantifies the uncertainty around clinically meaningful effect sizes. With a baseline mortality risk of 20%, a 2% absolute reduction in mortality represents a substantial clinical benefit. Therefore, a 78% probability of an ARR \u0026ge; 2% suggests a clinically significant benefit for mortality reduction with NIV, a well-established therapeutic intervention.\u003c/p\u003e\n\u003cp\u003eConsidering the lack of new randomized controlled trials since the NIVAS trial, this study is a valuable addition to the existing literature. A large randomized trial involving 4,808 patients across 70 centers worldwide comparing CPAP to standard treatment showed no significant improvement in composite outcomes (29), but used NIV to prevent ARF rather than for treatment. \u0026nbsp;These contrasting results align with the recent network meta-analysis by Pettenuzzo et al. (30), where NIV was found to reduce the risk of reintubation. However, the effect was only achieved when applied as a treatment for ARF, or when used in high-risk patients. Among high-risk patients, those who suffer from obesity represent a priority target where NIV is effective for preventing (7) or treating ARF (6). This reinforces the NIVAS findings that NIV should be reserved for patients with established ARF rather than for an unselected population (7), or when used for prevention in high-risk patients. These divergent findings across similar interventions illustrate why probabilistic approaches to evidence interpretation merit consideration.\u003c/p\u003e\n\u003cp\u003eThe current Bayesian analysis emerges within the context of increased criticism (18) regarding the overreliance on p-values and null hypothesis significance testing (NHST), which often reduces complex findings to binary outcomes based on arbitrary thresholds. Given the substantial resources required for randomized controlled trials, maximizing interpretive value from existing data becomes paramount. Bayesian reanalysis has proven valuable in critical care, providing nuanced interpretations that complement traditional analyses. Goligher et al. demonstrated this approach in their EOLIA trial reanalysis (31), providing a nuanced interpretation of the results in the context of a high risk-reward ratio (mortality benefit in patients with severe ARDS). Conversely, Zampieri et al. (32) used Bayesian methods to challenge optimistic interpretations in their STARRT-AKI re-analysis by showing a low probability of reduced mortality. Here, despite confirming and strengthening the original results, the current analysis calls into question the likelihood of large effect sizes.\u003c/p\u003e\n\u003cp\u003eOur study has several limitations. First, we inherit the limitations of the original trial including the lower-than-expected rate of reintubation, limited power to detect mortality effects, and lack of blinding for the somewhat subjective primary endpoint (i.e., day-7 reintubation). Second, this post-hoc analysis carries inherent risks of data-dependent findings. Despite the analysis plan having been registered before data acquisition, it is acknowledged that the report is of an exploratory nature. To mitigate this risk, we limited our analysis to pre-specified outcomes from the original trial and employed a conservative skeptical prior. Third, our method for defining informative priors may be criticized. Although we conducted a systematic review to evaluate prior knowledge, we decided not to use these studies to construct quantitative Bayesian priors because the two RCTs addressed significantly less severe populations, and the three observational studies had a high risk of bias. We therefore used assumptions from the NIVAS trial\u0026rsquo;s sample size calculation. Nonetheless, sample size calculations often involve subjective assumptions and economic/feasibility considerations. However, these assumptions must be credible to initiate a multicenter RCT. To mitigate this risk, we used a minimally informative prior as reference and employed informative priors representing more extreme clinical opinions that might exist in the medical community. We encountered a common situation where uncertain data quality raised questions about the feasibility and relevance of data-driven priors. Furthermore, no universally rigorous method exists for defining priors, and because they can influence results and conclusions, this remains an ongoing challenge.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eIn this prospectively registered, post-hoc analysis of the NIVAS trial, NIV consistently reduced the day-7 reintubation rate across various prior distributions, including a pessimistic prior re-flecting a reluctant clinician’s perspective, providing compelling evidence for its use. There was a high probability of mortality reduction with NIV, though the effect magnitude was impre-cise. \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u0026nbsp;\u003c/strong\u003e Approval for data reuse was obtained from the Scientific and Ethics Committee of Montpellier University Hospital (number 2025-04-256)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u0026nbsp;\u003c/strong\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u0026nbsp;\u003c/strong\u003eData will be available to researchers upon reasonable request immediately following publication. Proposals should be directed to the corresponding author. The R code is available at https://github.com/pollux74/bayesian_reanalysis_NIVAS.git.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest\u0026nbsp;\u003c/strong\u003eNM reports receiving consulting fees from Adene, Nomics, Sanofi, Bruxless, ID Solution, Archean Technologies, MSD, BMS, AB science and SimeoxSJ reports receiving consulting fees from Drager, Medtronic, Baxter, Fresenius-Xenios, Mindray, and Fisher \u0026amp; Paykel. ADJ reports receiving consulting fees from Medtronic, Dr\u0026auml;ger, Viatris and Fisher \u0026amp; Paykel.\u0026nbsp;No conflicts of interest are reported for other authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u0026nbsp;\u003c/strong\u003eThis research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor\u0026rsquo;s contributions\u0026nbsp;\u003c/strong\u003eANL, JP, NM, SJ, and ADJ contributed to conception and design of the study, to the acquisition of the data, to the analysis and interpretation of the data, to drafting the submitted article, and to provide final approval of the version to be published. MC contributed to the interpretation of the data, to drafting the submitted article, and to provide final approval of the version to be published.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgment\u0026nbsp;\u003c/strong\u003eNone\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDureuil B, Cantineau JP, Desmonts JM, EFFECTS OF UPPER OR, LOWER ABDOMINAL SURGERY ON DIAPHRAGMATIC FUNCTION. Br J Anaesth. 1987;59(10):1230\u0026ndash;5.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJaber S, Delay JM, Chanques G, Sebbane M, Jacquet E, Souche B, et al. Outcomes of patients with acute respiratory failure after abdominal surgery treated with noninvasive positive pressure ventilation. Chest. 2005;128(4):2688\u0026ndash;95.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLAS VEGAS investigators. Epidemiology, practice of ventilation and outcome for patients at increased risk of postoperative pulmonary complications: LAS VEGAS - an observational study in 29 countries. Eur J Anaesthesiol. 2017;34(8):492\u0026ndash;507.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJaber S, Antonelli M. Preventive or curative postoperative noninvasive ventilation after thoracic surgery: still a grey zone? Intensive Care Med. 2014;40(2):280\u0026ndash;3.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXie Z, Liu J, Yang Z, Tang L, Wang S, Du Y, et al. Risk Factors for Post-operative Planned Reintubation in Patients After General Anesthesia: A Systematic Review and Meta-Analysis. Front Med. 2022;9:839070.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJaber S, Pensier J, Futier E, Paugam-Burtz C, Seguin P, Ferrandiere M, et al. 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Effect of non-invasive ventilation after extubation in critically ill patients with obesity in France: a multicentre, unblinded, pragmatic randomised clinical trial. The Lancet Respiratory Medicine. 2023 June 1;11(6):530\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJaber S, Lescot T, Futier E, Paugam-Burtz C, Seguin P, Ferrandiere M, et al. Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery: A Randomized Clinical Trial. JAMA. 2016;315(13):1345\u0026ndash;53.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOutline of a. Theory of Statistical Estimation Based on the Classical Theory of Probability. STATISTICAL ESTIMATION.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePearse R, Ranieri M, Abbott T, Pakats ML, Piervincenzi E, Patel A, et al. 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Available from: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.cochranelibrary.com/central/doi/10.1002/central/CN-00450659/full\u003c/span\u003e\u003cspan address=\"https://www.cochranelibrary.com/central/doi/10.1002/central/CN-00450659/full\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSquadrone V, Coha M, Cerutti E. Piedmont Intensive Care Units Network. Continuous positive airway pressure for treatment of postoperative hypoxemia: a randomized controlled trial. JAMA. 2005;293(5):589\u0026ndash;95.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eConti G, Cavaliere F, Costa R. Noninvasive positive-pressure ventilation with different interfaces in patients with respiratory failure after abdominal surgery: a matched-control study. Respir Care. 2007;52(11):1463\u0026ndash;71.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNarita M, Tanizawa K, Chin K, Ikai I, Handa T, Oga T, et al. Noninvasive ventilation improves the outcome of pulmonary complications after liver resection. Intern Med. 2010;49(15):1501\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMichelet P, D\u0026rsquo;Journo XB, Seinaye F, Forel JM, Papazian L, Thomas P. Non-invasive ventilation for treatment of postoperative respiratory failure after oesophagectomy. Br J Surg. 2009;96(1):54\u0026ndash;60.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKelly CR, Higgins AR, Chandra S. Videos in clinical medicine. Noninvasive positive-pressure ventilation. N Engl J Med. 2015 June;4(23):e30.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDe Jong A, Capdevila M, Aarab Y, Cros M, Pensier J, Lakbar I, et al. 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JAMA. 2018;320(21):2251\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZampieri FG, Machado FR, Biondi RS, Freitas FGR, Veiga VC, Figueiredo RC, et al. Association between Type of Fluid Received Prior to Enrollment, Type of Admission, and Effect of Balanced Crystalloid in Critically Ill Adults: A Secondary Exploratory Analysis of the BaSICS Clinical Trial. Am J Respir Crit Care Med. 2022 June;15(12):1419\u0026ndash;28.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"critical-care","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cric","sideBox":"Learn more about [Critical Care](http://ccforum.biomedcentral.com/)","snPcode":"13054","submissionUrl":"https://submission.nature.com/new-submission/13054/3","title":"Critical Care","twitterHandle":"@Crit_Care","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Acute respiratory failure, noninvasive ventilation, abdominal surgery","lastPublishedDoi":"10.21203/rs.3.rs-7702781/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7702781/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cb\u003eBackground\u003c/b\u003e\u003c/p\u003e\u003cp\u003eClinicians\u0026rsquo; decision-making regarding the use of noninvasive ventilation (NIV) after abdominal surgery requires evaluating the probability of clinically meaningful benefit. The Bayesian framework may help caregivers interpret the findings of a randomized controlled trial (NIVAS) assessing curative NIV after abdominal surgery by incorporating their own beliefs and providing better estimates of treatment effects. This study aimed to use a Bayesian framework to estimate posterior probabilities of NIV effect under various prior assumptions, reflecting diverse clinicians\u0026rsquo; beliefs.\u003c/p\u003e\u003cp\u003e\u003cb\u003eMethod\u003c/b\u003e\u003c/p\u003e\u003cp\u003eA prospectively registered, post-hoc Bayesian reanalysis of the NIVAS multicenter trial was conducted. The study included 293 patients with acute respiratory failure following abdominal surgery who were randomly assigned to receive either conventional oxygen therapy or NIV. Four statistical priors were defined: minimally informative, skeptical, enthusiastic, and pessimistic, reflecting a range of clinical beliefs. The primary outcome was day-7 reintubation. Secondary outcomes included day-30 mortality. Effect sizes were presented as odds ratios (OR) and absolute risk reduction (ARR) with 95% credible intervals (CrI).\u003c/p\u003e\u003cp\u003e\u003cb\u003eResults\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe minimally informative prior resulted in a posterior median OR for day-7 reintubation of 0.59 (95% CrI 0.37 to 0.95) in favor of NIV. Under the pessimistic prior, the posterior median OR was 0.64 (95% CrI 0.40 to 1.00). The posterior probability of NIV being superior to oxygen therapy varied from 96 to 99% when considering various priors from pessimistic to enthusiastic. The probability of benefit beyond an ARR\u0026thinsp;\u0026ge;\u0026thinsp;5% ranged from 77 to 93%. Regarding day-30 mortality, the posterior median OR was 0.63 (95% CrI 0.32 to 1.31) under minimally informative prior and 0.79 (95% CrI 0.48 to 1.29) under the skeptical prior. The probability of NIV superiority ranged from 82 to 90%.\u003c/p\u003e\u003cp\u003e\u003cb\u003eConclusion\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThis pre-registered Bayesian analysis indicates that NIV consistently reduces day-7 reintubation, with a high probability of achieving a clinically meaningful effect, even under pessimistic prior beliefs. These results provide compelling evidence for its broad use to treat respiratory failure after abdominal surgery. There was a high probability of mortality reduction with NIV, though the effect magnitude was imprecise.\u003c/p\u003e","manuscriptTitle":"Effect of Noninvasive Ventilation on Tracheal Reintubation Among Patients With Hypoxemic Respiratory Failure Following Abdominal Surgery. A Bayesian post-hoc analysis of the NIVAS trial","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-20 08:42:17","doi":"10.21203/rs.3.rs-7702781/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-20T11:12:06+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"119815574536656014963319655100274095160","date":"2025-10-15T21:49:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-14T10:42:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"68600765435814956033951697969238817798","date":"2025-10-12T17:55:00+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-10T02:08:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"51078045023225339476563896138996109863","date":"2025-10-09T23:17:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-07T16:15:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-06T09:54:19+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-06T09:53:14+00:00","index":"","fulltext":""},{"type":"submitted","content":"Critical Care","date":"2025-09-24T10:46:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"critical-care","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cric","sideBox":"Learn more about [Critical Care](http://ccforum.biomedcentral.com/)","snPcode":"13054","submissionUrl":"https://submission.nature.com/new-submission/13054/3","title":"Critical Care","twitterHandle":"@Crit_Care","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"eea7b12c-20db-42f7-aff7-733a01423898","owner":[],"postedDate":"October 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-15T16:08:42+00:00","versionOfRecord":{"articleIdentity":"rs-7702781","link":"https://doi.org/10.1186/s13054-025-05795-9","journal":{"identity":"critical-care","isVorOnly":false,"title":"Critical Care"},"publishedOn":"2025-12-10 15:58:59","publishedOnDateReadable":"December 10th, 2025"},"versionCreatedAt":"2025-10-20 08:42:17","video":"","vorDoi":"10.1186/s13054-025-05795-9","vorDoiUrl":"https://doi.org/10.1186/s13054-025-05795-9","workflowStages":[]},"version":"v1","identity":"rs-7702781","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7702781","identity":"rs-7702781","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}