Highlights
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This study presents a Bayesian re-analysis of the STRESS trial, which evaluated prophylactic methylprednisolone versus placebo in 1,200 infants undergoing heart surgery with cardiopulmonary bypass.
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The Bayesian approach found a 92% posterior probability that methylprednisolone provides benefit (odds ratio < 1) and only a 8% probability of harm, with a mean odds ratio of 0.87 favoring methylprednisolone.
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The absolute risk difference for death, transplant, or major complications was approximately–2% (95% CI–3%, +1%) for methylprednisolone compared to placebo, indicating a modest but clinically relevant reduction in adverse outcomes.
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Sensitivity analyses using a range of prior beliefs and strengths consistently favored methylprednisolone, with 8 out of 9 scenarios showing ≥80% probability of benefit and ≥1% absolute risk reduction.
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The findings suggest that prophylactic methylprednisolone is likely beneficial and unlikely to cause harm, supporting its continued use despite previous “negative” frequentist trial results.
ABSTRACT
Background
Prophylactic steroids are often used to reduce the systemic inflammatory response to cardiopulmonary bypass in infants undergoing heart surgery. The STRESS trial found that the odds of a worse outcome did not differ between infants randomized to methylprednisolone (n = 599) versus placebo (n = 601) (adjusted odds ratio [OR], 0.86; P =.14). However, secondary analyses showed possible benefits with methylprednisolone. To investigate further using a different probabilistic approach, we re-analyzed the STRESS trial using Bayesian analytics.
Methods
We used a covariate-adjusted proportional odds model using the original STRESS trial primary endpoint, a ranked composite of death, transplant, major complication and post op length of stay. We performed Markov Chain Monte Carlo simulations to assess the probability of benefit (OR < 1) versus harm (OR > 1). Primary analysis assumed a neutral probability of benefit versus harm with weak prior belief strength (nearly noninformative prior distribution). To illustrate magnitude of effect, we calculated predicted risk of death, transplant or major complications for methylprednisolone and placebo. Sensitivity analyses evaluated pessimistic (5%-30% prior likelihood of benefit), neutral and optimistic (70%-95%) prior beliefs, and controlled strength of prior belief as weak (30% variance), moderate (15%) and strong (5%). A secondary analysis derived empirical priors using data from four previous steroid trials.
Results
The posterior probability of any benefit from methylprednisolone was 92% and probability of harm was 8%. Composite death or major complication occurred in 18.8% of subjects with an absolute risk difference of −2% (95% CI −3%, +1%) for methylprednisolone. Each of 9 sensitivity analyses demonstrated greater probability of benefit than harm in the methylprednisolone group with 8 of 9 demonstrating >80% probability of benefit and ≥1% absolute difference in risk of death, transplant or major complications. In secondary analysis deriving priors from previous steroid trials, results were consistent with a 95% posterior probability of benefit.
Conclusion
Our Bayesian re-analysis of the STRESS trial, using a range of prior beliefs, demonstrated a high probability that perioperative methylprednisolone reduces the risk of death or major complications in infants undergoing cardiopulmonary bypass compared with placebo. This more in-depth analysis expands the initial clinical evaluation of methylprednisolone provided by the STRESS trial.
Trial Registration
Clinicaltrials.gov: NCT03229538 ( https://clinicaltrials.gov/study/NCT03229538 ).
Background
Perioperative glucocorticoids are commonly administered to infants undergoing cardiac surgery to mitigate the systemic inflammation caused by cardiopulmonary bypass. This postbypass systemic inflammatory response contributes to postoperative morbidity and mortality. However, early pediatric trials and adult trials evaluating safety and efficacy of perioperative glucocorticoids have yielded conflicting results. ,,,,,,,,, The STeroids to REduce Systemic Inflammation after infant heart Surgery (STRESS) Trial randomized 1200 infants (under 1 year of age) undergoing heart surgery with cardiopulmonary bypass to receive either perioperative methylprednisolone or placebo. , In a covariate-adjusted analysis of the primary endpoint (a ranked composite), the likelihood of a worse outcome did not differ significantly between the methylprednisolone and placebo groups (adjusted odds ratio, 0.86; 95% confidence interval [CI], 0.71 to 1.05; P =.14). However, secondary analyses, including an unadjusted analysis of the primary outcome and a win ratio analysis, favored the methylprednisolone group, suggesting potential benefits.
Bayesian analysis offers a unique perspective in evaluating clinical trial data. Unlike frequentist statistical designs which are centered around hypothesis testing and a predetermined threshold (eg, P <.05) to accept or reject the hypothesis, Bayesian analyses evaluate the probability of benefit based on a prior degree of belief in the occurrence of such benefit. This approach allows for incorporating prior knowledge to assess the probability of benefit under different hypotheses and with varying degrees of confidence in the prior knowledge. Bayesian analysis is particularly valuable in rare diseases, including most pediatric conditions, where underpowering is common, and where underpowered studies could be discarded despite offering important information. For example, investigators used Bayesian analysis to re-evaluate the Therapeutic Hypothermia after In-Hospital Cardiac Arrest in Children (THAPCA) Trial. Although the original THAPCA analysis did not meet its primary endpoint, Bayesian re-analysis demonstrated a high probability that the intervention offered benefit with a very low likelihood of harm.
We sought to apply Bayesian analysis, including incorporating a range of potential “prior beliefs,” to re-assess the outcomes of the STRESS trial. Our primary objective was to determine the probability of benefit versus harm associated with prophylactic methylprednisolone in order to better guide clinical decision-making.
Methods
The STRESS Trial was a multicenter double-blind, randomized, controlled “trial within a registry.” Study design and results have been previously reported. , Briefly, 1263 infants (under 1 year of age) undergoing heart surgery with cardiopulmonary bypass at 24 centers in the United States were randomized to methylprednisolone (30mg/kg administered into the CPB pump prime) versus placebo. Trial outcomes were collected from the Society of Thoracic Surgeons Congenital Heart Surgery Database. The primary outcome was a hierarchically ranked composite endpoint with components ranked commensurate with their perceived clinical significance. Individual components included operative mortality, heart transplant, or any of 13 individual major complications. Outcomes in the composite endpoint were ranked into 97 levels of clinical prioritization as follows: operative death was ranked as 97 (worst outcome); heart transplantation during hospitalization as 96; permanent dialysis, tracheostomy, or neurologic deficit at discharge as 95; postoperative mechanical circulatory support or unplanned cardiac reoperation (exclusive of reoperation for bleeding) as 94; reoperation for bleeding, unplanned delayed sternal closure, or postoperative unplanned interventional cardiac catheterization as 93; postoperative cardiac arrest, multisystem organ failure, kidney failure with temporary dialysis, or postoperative mechanical ventilator support for more than 7 days as 92; and postoperative length of hospital stay of 91 days or longer as 91. Patients with none of these postoperative complications were assigned ranked outcomes according to postoperative length of hospital stay (1 to 90 days). The distribution of the ranked outcome components of the primary endpoint were compared between the trial groups with the use of a proportional-odds logistic-regression model for ordered categorical data with prespecified covariates adjustment for age, weight, prematurity status, and the 2020 STS–European Association for Cardio-Thoracic Surgery (STAT) Mortality Category ; in addition, adjustment was made for the random effect of enrollment site.
Parameter estimation
Bayesian analysis requires assigning prior distributions to model parameters reflecting prior knowledge or belief about them. Because our prior information was limited, our goal for our primary analysis was to select a prior distribution that would allow inferences to be driven by the study data as opposed to strong prior beliefs. In keeping with this goal, we specified that the logarithm of the odds ratio would follow a normal distribution with mean = 0 and SD = 3. Other model parameters besides the odds ratio were assigned noninformative prior distributions. To assess whether results were sensitive to the choice of prior, we performed sensitivity analyses re-fitting the model using a range of priors chosen to reflect different possible beliefs about the odds ratio’s direction and magnitude, as suggested by Wijeysundera et al and Zampieri et al. , Moreover, following Harhay et al, we considered priors based on combinations of three possible “best guesses” for the unknown odds ratio, ranging from optimistic (best guess = 0.80; suggesting benefit from methylprednisolone) to pessimistic (best guess = 1.25; suggesting harm from methylprednisolone), and three choices for the strength of belief in this best guess, ranging from weak to strong prior belief (see Table 1 and Supplementary Methods for details). As a additional sensitivity analysis, we derived an empirical prior for the treatment effect using mortality data from four previous randomized trials of corticosteroids in cardiac surgery—the DECS trial (n = 4,494 adult subjects), SIRS trial (n = 7,507 adult subjects), DECISION trial (n = 394 infants) and a neonatal steroid trial performed by Graham and colleagues (n = 190 neonates). Parameter estimation was performed using Markov Chain Monte Carlo (MCMC) sampling as implemented in the R software package brms. Posterior summaries are based on 10,000 MCMC samples drawn after a burn-in of 10,000 iterations. Convergence of the MCMC procedure was confirmed through evaluation of trace plots, autocorrelation plots, and effective sample size.
Table 1
Priors assigned to the odds ratio (OR) in Bayesian re-analysis of STRESS trial
| Prior belief | Belief strength |
Prior parameters
(on log scale)* |
Interpretation |
|---|---|---|---|
| Neutral | Weak |
Mean = log(1)
SD = 3 |
No reason to believe methylprednisolone will improve or worsen patient outcome overall. Nearly noninformative prior |
| Moderate |
Mean = log(1)
SD = 0.355 |
No strong reason to believe methylprednisolone will improve or worsen patient outcome overall. 95% prior probability OR is between 0.5 and 2. | |
| Strong |
Mean = log(1)
SD = 0.205 |
Believe methylprednisolone will improve patient outcome overall, but acknowledge harm is possible. 95% prior probability OR is between 1/1.5 and 1.5. | |
| Pessimistic | Weak |
Mean = log(1.25)
SD = 0.425 |
Believe methylprednisolone will worsen patient outcome, but acknowledge improvement is possible. Chosen SD allows 30% prior probability OR < 1. |
| Moderate |
Mean = log(1.25)
SD = 0.215 |
Believe methylprednisolone will worsen patient outcome overall, but acknowledge some improvement is possible. Chosen SD allows 15% prior probability OR < 1. | |
| Strong |
Mean = log(1.25)
SD = 0.135 |
Believe methylprednisolone will worsen patient outcome overall, and that improvement is doubtful. Chosen SD allows 5% prior probability OR < 1. | |
| Optimistic | Weak |
Mean = log(1/1.25)
SD = 0.425 |
Believe methylprednisolone will improve patient outcome overall, but acknowledge harm is possible. Chosen SD allows 30% prior probability OR > 1. |
| Moderate |
Mean = log(1/1.25)
SD = 0.215 |
Believe methylprednisolone will improve patient outcome overall, but acknowledge some harm is possible. Chosen SD allows 15% prior probability OR > 1. | |
| Strong |
Mean = log(1/1.25)
SD = 0.135 |
Believe methylprednisolone will improve patient outcome overall and that any harm is unlikely. Chosen SD allows 5% prior probability OR > 1. |
Prior and text interpretations are adapted from Harhay et al. and Zampieri et al. The primary outcome was based on neutral prior belief with weak belief strength.
*Each prior is a normal distribution and is assigned to the natural logarithm of odds ratio. The normal distribution’s mean and SD determine its center and spread, respectively. Higher SD values imply greater prior uncertainty about the odds ratio.
Statistical analysis
A detailed description of the statistical approach is provided in the Supplementary Methods. Briefly, we performed a Bayesian re-analysis of the STRESS trial’s primary outcome using statistical methods aligned with the original main results presentation. To match the trial’s original analysis, we used data from the same cohort of randomized subjects who received study drug (methylprednisolone or placebo) and were included in the modified intention-to-treat population (n = 599 methylprednisolone, n = 601 placebo). To further align with the original analysis, we used a proportional odds (also known as cumulative logits) and adjusted for the same set of prespecified covariates, including age, weight, prematurity status, the 2020 STS–European Association for Cardio-Thoracic Surgery (STAT) Mortality Category, and randomizing site. The proportional odds model is an extension of binary logistic regression to accommodate ordered outcomes with more than two categories. The model’s dependent (outcome) variable was an ordered categorical variable representing the patient’s ranked outcome category (1=best, 97=worst). The treatment effect of methylprednisolone versus placebo was expressed as an odds ratio with an odds ratio <1 favoring methylprednisolone and an odds ratio >1 favoring placebo. Additionally, to help interpret the odds ratio’s magnitude, we transformed parameter estimates from the fitted proportional odds model to the scale of probabilities and used this transformation to calculate the difference in the model-predicted probability of death, transplant or major complications for methylprednisolone minus placebo, denoted as “risk difference.” This transformed treatment effect parameter was not estimated in the original results presentation but was included here to make analysis results more clinically interpretable. For sensitivity analysis, we derived an empirical prior for the treatment effect using mortality data from previous randomized trials of corticosteroids in cardiac surgery. ,,, A Bayesian hierarchical meta-analysis with a random treatment effect was fit, using a Truncated Normal (0, 5) prior on the standard deviation of treatment effects to allow for substantial heterogeneity. The resulting distribution for the treatment effect in a new trial (ie, STRESS) was used as a prior in a re-analysis. Additional details are provided in the Supplementary Methods. Finally, we completed a tipping point analysis to explore the threshold at which a strongly pessimistic prior belief would overturn the conclusion that methylprednisolone offers benefit. Specifically, we evaluated priors centered at an odds ratio (OR) of 1.25 (suggesting harm) and varied the strength of belief.
Results
For the primary outcome, as in the original trial, 1200 trial participants were evaluated (599 patients in the methylprednisolone group and 601 in the placebo group). The cumulative number of endpoint events was lower in the methylprednisolone group than in the placebo group for all successive endpoint categories ( Table 2 ).
Table 2
Cumulative endpoint event rates
| Primary cumulative endpoint groupings |
Methylprednisolone
N = 599 |
Placebo
N = 601 |
|---|---|---|
| Rank = 97 | 12/599 (2.0%) | 17/601 (2.8%) |
| Rank ≥ 96 | 15/599 (2.5%) | 24/601 (4.0%) |
| Rank ≥ 95 | 19/599 (3.2%) | 32/601 (5.3%) |
| Rank ≥ 94 | 63/599 (10.5%) | 68/601 (11.3%) |
| Rank ≥ 93 | 75/599 (12.5%) | 98/601 (16.3%) |
| Rank ≥ 92 | 99/599 (16.5%) | 120/601 (20.0%) |
| Rank ≥ 91 | 103/599 (17.2%) | 122/601 (20.3%) |
97- Operative Mortality; 96- Heart Transplant; 95- Renal failure with permanent dialysis, neurologic deficit persistent at discharge, or respiratory failure requiring tracheostomy; 94- Postoperative mechanical circulatory support or unplanned cardiac reoperation (exclusive of reoperation for bleeding); 93- Reoperation for bleeding, unplanned delayed sternal closure, or post op unplanned interventional cardiac catheterization; 92—Post op cardiac arrest, multisystem organ failure, renal failure with temporary dialysis, or prolonged ventilator support (> 7 days); 91- Post operative length of stay > 90 days; 1-90—post op length of stay in days.
In primary risk-adjusted Bayesian analysis (under the neutral prior belief, weak belief strength), the posterior probability of any benefit (OR < 1.0) from methylprednisolone was 92% and the probability of any harm (OR > 1.0) was 8%. The methylprednisolone group had a mean odds ratio of 0.87 denoting a 13% mean reduction in the odds of a worse outcome ( Table 3 , Figure 1 ). The composite of death or major complication occurred in 17.2% of subjects randomized to methylprednisolone and 20.3% of those randomized to placebo (adjusted odds ratio 0.83; 95% CI, 0.61 to 1.13). In primary risk-adjusted Bayesian analysis, the posterior distribution indicated a 2% lower risk of death, transplant or major complication with methylprednisolone ( Table 4 , Figure 1 ).
Table 3
Posterior summary of odds ratio (OR)
|
Prior
belief |
Belief
strength |
Estimate
(95% CI) |
Prob of
OR < 0.8 |
Prob of
OR < 0.9 |
Prob of
OR < 1 |
Prob of
OR > 1 |
Prob of
OR > 1.1 |
Prob of
OR > 1.2 |
|---|---|---|---|---|---|---|---|---|
| Neutral | Weak | 0.87 (0.71, 1.06) | 0.22 | 0.65 | 0.92 | 0.08 | 0.01 | <0.01 |
| Moderate | 0.88 (0.72, 1.06) | 0.18 | 0.62 | 0.91 | 0.09 | 0.01 | <0.01 | |
| Strong | 0.89 (0.74, 1.07) | 0.13 | 0.55 | 0.90 | 0.10 | 0.01 | <0.01 | |
| Pessimistic | Weak | 0.89 (0.73, 1.07) | 0.16 | 0.57 | 0.89 | 0.11 | 0.01 | <0.01 |
| Moderate | 0.93 (0.77, 1.11) | 0.06 | 0.38 | 0.80 | 0.20 | 0.03 | <0.01 | |
| Strong | 0.99 (0.84, 1.16) | <0.01 | 0.12 | 0.57 | 0.43 | 0.09 | 0.01 | |
| Optimistic | Weak | 0.87 (0.71, 1.04) | 0.22 | 0.67 | 0.93 | 0.07 | 0.01 | <0.01 |
| Moderate | 0.86 (0.71, 1.02) | 0.25 | 0.72 | 0.96 | 0.04 | <0.01 | <0.01 | |
| Strong | 0.84 (0.72, 0.99) | 0.27 | 0.80 | 0.98 | 0.02 | <0.01 | <0.01 |
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