Bayesian Therapy: A Good Treatment for Potentially Underpowered Trials?

Cristian Tebé, Natàlia Pallarès, Francesc Escrihuela, Sean W X Ong, Isabel Oriol, Sara Grillo, Miquel Pujol, Jose M Miró, Steven Y C Tong and Jordi Carratalà

Biostatistics Support and Research Unit

Germans Trias i Pujol Research Institute and Hospital (IGTP)
Badalona

June 25, 2026

INTRODUCTION

Staphylococcus aureus

  • Staphylococcus aureus is a leading cause of both hospital-acquired and community-onset bacteremia.

  • It’s one of the most serious common bloodstream infections (fatality rate of 15%-30%).

  • Empirical treatment often includes an antibiotic active against MRSA, such as vancomycin or daptomycin, until antimicrobial susceptibility results are available.

  • Combination antibiotic therapy has been proposed as a potential approach to enhance treatment efficacy.

Fosfomycin

  • Fosfomycin is broad-spectrum, bactericidal, and shows promise against drug-resistant bacteria in experimental models.

  • Fosfomycin has a different mechanism of action than vancomycin or daptomycin.

  • A synergistic effect was expected, leading to a rapid bactericidal response.

BACSARM trial 2013-2017

  • Evaluated fosfomycin’s role in combination therapy for MRSA bacteremia.

  • Terminated before reaching its planned sample size, which may have limited its statistical power to detect differences in clinical outcomes.

  • Daptomycin plus fosfomycin provided a 12% higher rate of treatment success than daptomycin alone.

SAFO trial 2019-2022

  • Evaluated fosfomycin’s role in combination therapy for MSSA bacteremia.

  • Terminated before reaching its planned sample size, which may have limited their statistical power to detect differences in clinical outcomes.

  • Cloxacillin plus fosfomycin provided a 5.3% higher rate of treatment success than cloxacillin alone.

## Why were the original trials inconclusive?

  • Both trials ended before reaching their planned sample sizes.

  • Point estimates favoured fosfomycin, but confidence intervals were wide.

  • Lack of statistical significance did not demonstrate absence of benefit.

  • The central problem was limited precision rather than necessarily absence of effect.

BACSARM + SAFO -> BACSAFO

  • We performed a pooled post hoc analysis of individual participant data from the BACSARM and SAFO trials.

  • Applying complementary Bayesian and frequentist analytical approaches to refine the assessment of fosfomycin efficacy and safety.

METHODS

Data

BACSARM:

  • Adult patients with MRSA bacteremia
  • Randomized 1:1 to receive daptomycin vs daptomycin + fosfomycin.
  • Intention to treat: 81 vs 74 participants.

SAFO:

  • Adult patients with MSSA bacteremia
  • Randomized 1:1 to receive cloxacillin vs cloxacillin + fosfomycin.
  • Intention to treat: 110 vs 104 participants.

All patients from the intention-to-treat populations were included.

Outcomes


  • Treatment success at 8 weeks from randomization:

    Alive, without signs of relapse, and improvement in clinical signs and symptoms.

  • Secondary outcomes: persistent bacteremia, adverse events leading to treatment discontinuation and all cause mortality.

  • Subgroup analysis: Age, MSSA vs MRSA, site of acquisition, complicated bacteremia.



The study was registered at ClinicalTrials.gov (NCT06695832).

Why an individual-participant-data analysis?

Advantages:

  • Harmonised outcome definition.
  • Consistent subgroup definitions.
  • Preservation of within-trial randomization.
  • Modelling of trial and hospital structure.
  • Improved precision

What pooling cannot solve:

  • Differences in background antibiotics.
  • Differences between MRSA and MSSA populations.
  • Missing outcomes.
  • Clinical heterogeneity.
  • Premature trial termination.

BACSARM participants+SAFO participants ⟶One-stage individual-participant-data model

One-stage statistical model


\[Y_{ih} \sim \text{Binomial}(1,p_{ih})\] \[log(p_{ih})=\alpha_0 + u_h + \beta T_{ih} \]

  • \(h\) is the hospital.
  • \(\alpha_0\) is the hospital-specific baseline risk.
  • \(u_h \sim N(0,\tau^2)\)
  • \(exp(\beta)\) is the treatment risk ratio.

One model, two inferential frameworks



Frequentist Bayesian
Data Data + prior
Estimate + 95% CI Posterior median + 95% CrI
Hypothesis test against RR=1 P(RR>1 )
Compatibility with the null model Probability of benefit or harm

Statistical Analysis: Bayesian

Hierarchical Bayesian log-binomial model

\[Y_{ih} \sim \text{Binomial}(1,p_{ih})\]

\[log(p_{ih})=\beta_0 + u_h + \beta T_{ih} \rightarrow RR_{treatment}=\exp(\beta) \] \(i\) stands for participant and \(u_h \sim N(0,\tau^2)\) is the hospital-specific random intercept.


Minimally informative prior centered on no treatment effect

\[\beta \sim N(0,5^2)\] \[\text{95% RR prior interval:}\] \[\text{0.00006 to 18,000}\]

Statistical Analysis: Bayesian

Prior sensitivity analyses

Pessimistic: \(\beta \sim N(-0.22,0.15^2)\) \(\text{Prior median RR=0.8}\) \(\text{95% prior interval: 0.60 to 1.08}\)

Skeptical: \(\beta \sim N(0,0.25^2)\) \(\text{Prior median RR=1.0}\) \(\text{95% prior interval: 0.61 to 1.63}\)

Optimistic: \(\beta \sim N(0.18,0.15^2)\) \(\text{Prior median RR=1.2}\) \(\text{95% prior interval: 0.89 to 1.61}\)

Statistical Analysis: frequentist

Hierarchical log-binomial model

\[Y_{ih} \sim \text{Binomial}(1,p_{ih})\]

\[log(p_{ih})=\beta_0 + u_h + \beta T_{ih} \rightarrow RR=\exp(\beta) \] \(i\) stands for participant and \(u_h \sim N(0,\tau^2)\) is the hospital-specific random intercept.



Software



All analyses were performed using R software (v.4.4.1).

Relevant packages:

flowchart, tydiverse, ggplot2, gtsummary, rstanarm and lme4.

RESULTS

Flowchart and baseline characteristics

Table 1. Baseline Characteristics
Characteristic Combination
N = 1781
Monotherapy
N = 1911
Age

    Median (Q1, Q3) 67 (56, 77) 70 (57, 79)
Sex

    Men 117 (66%) 137 (72%)
    Women 61 (34%) 54 (28%)
Charlson

    Median (Q1, Q3) 4.00 (2.00, 5.00) 4.00 (2.00, 6.00)
Community-acquired 50 (28%) 41 (21%)
MRSA/MSSA

    MRSA 74 (42%) 81 (42%)
    MSSA 104 (58%) 110 (58%)
Complicated bacteriemia 33 (20%) 61 (33%)
1 n (%)

Primary outcome

Table 2. Clinical success at week 8
RR 95% CrI P(RR>1|data)
Bayesian 1.10 (0.97–1.26) 91.8%
RR 95% CI p-value
Frequentist 1.11 (0.97–1.27) 0.112

Primary outcome


Table 3. Clinical success at week 8

Group Incidence ARD 95% CrI NNT
Combination 129/178 (72.5%) 7.1% (-2% to 17%) ~14
Monotherapy 125/191 (65.5%)
ARD: Absolute Risk Difference (Combination minus Monotherapy).
NNT: Number needed to treat.


The point estimate corresponds to an NNT of approximately 14. However, the 95% credible interval includes no effect and spans both benefit and harm: its upper limit corresponds to an NNT of approximately 6, whereas its lower limit corresponds to one additional failure per approximately 50 patients treated.

Primary outcome: sensitivity analysis


Table 4. Clinical success at week 8

Characteristic RR 95% CrI P(RR>1|data)
Pessimistic N(-0.22, 0.15^2) 1.04 (0.92 – 1.17) 75.8%
Skeptical N(0, 0.25^2) 1.09 (0.96 – 1.25) 91.7%
Optimistic N(0.18, 0.15^2) 1.12 (1.00 – 1.27) 97.2%

Primary outcome: subgroup


(*) The frequentist approach yielded similar results.

Secondary outcome

Table 4.1 Microbiological outcomes
Outcome RR 95% CrI Prb(RR<1) RR 95% CI p-value
Persistent bacteremia at day 3 0.19 (0.07 – 0.41) 100% 0.16 (0.03–.86) 0.033
Persistent bacteremia at day 7 0.22 (0.03 – 0.84) 98.9% 0.22 (0.05–.95) 0.042


Table 4.2 Mortality/AEs outcomes
Outcome RR 95% CrI Prb(RR<1) RR 95% CI p-value
Mortality at day 14 1.16 (0.56 – 2.35) 34.2% 1.08 (0.61–1.94) 0.783
Mortality at day 30 1.07 (0.60 – 1.88) 40.6% 1.20 (0.66–2.20) 0.548
Mortality at day 60 0.81 (0.50 – 1.27) 81.7% 0.80 (0.51–1.25) 0.329
Adverse events leading to treatment discontinuation 1.97 (1.04 – 3.92) 98.0%* 2.03 (1.13–3.63) 0.017
Adverse events: Gastrointestinal disturbances, Heart failure, Liver injury.
* P(RR>1∣data)

Adverse Events Leading to Treatment Discontinuation

Adverse Event Combination Monotherapy ARD NNH/NNT
Gastrointestinal disturbances 7 (3.93%) 1 (0.52%) +3.41% NNH = 29
Acute heart failure 5 (2.81%) 1 (0.52%) +2.29% NNH ≈ 44
Hypokalemia (<3 mmol/L) 3 (1.69%) 1 (0.52%) +1.16% NNH ≈ 86
Acute liver injury 4 (2.25%) 0 (0.00%) +2.25% NNH = 45
Acute kidney failure 0 (0.00%) 3 (1.57%) -1.57% NNT = 64
Creatinine phosphokinase increase (>10-fold) 1 (0.56%) 1 (0.52%) +0.04% Negligible
Hypocalcemia (<2.0 mmol/L) 1 (0.56%) 0 (0.00%) +0.56% NNH ≈ 178
Othera 3 (1.69%) 6 (3.14%) -1.46% NNT ≈ 69
TOTAL 24 (13.48%) 13 (6.81%) +6.68% NNH = 15
Absolute Risk Difference (Combination minus Monotherapy)

Other: Combination = hepatic metastases, multiple organ dysfunction syndrome, pneumonia; Monotherapy = rectosigmoid cancer, acute coronary syndrome, skin rash, COVID-19, pneumonia, respiratory failure

DISCUSSION

Clinical discussion

  • Fosfomycin may enhance treatment success at 8 weeks compared to monotherapy.

  • Higher incidence of adverse events leading to treatment discontinuation.

  • Subgroup analyses suggested potentially greater benefit in patients with MRSA bacteremia, and those with nosocomial acquisition.

  • Heterogeneity in study design—including variations in dosing, duration, and fosfomycin administration protocols—may introduce variability in the observed effects.

Methodological discussion

  • Pooling individual patient data from multiple trials increases precision and may provide more informative estimates of clinical effects.

  • In this study, Bayesian and frequentist approaches gave similar results.

  • The Bayesian and frequentist methods provided complementary insights into treatment effects.

  • The posterior probability distribution provided additional insight, supporting a more detailed clinical interpretation.

Final message

  • Adjunctive fosfomycin may improve early bacterial clearance and treatment success in Staphylococcus aureus bacteremia but at the cost of increased toxicity.

  • Pooling individual participant data improved precision but did not eliminate the uncertainty caused by premature trial termination.

  • Bayesian analysis allowed that remaining uncertainty to be expressed as clinically interpretable probabilities of benefit and harm, even in the absence of frequentist statistical significance.

BIBLIOGRAPHY

  • Tong SYC, Fowler VG, Skalla L, Holland TL. Management of Staphylococcus aureus Bacteremia: A Review. JAMA. 2025;334(9):798–808.

  • Pujol M, Miró JM, Shaw E, Aguado JM, San-Juan R et al; MRSA Bacteremia (BACSARM) Trial Investigators. Daptomycin Plus Fosfomycin Versus Daptomycin Alone for Methicillin-resistant Staphylococcus aureus Bacteremia and Endocarditis: A Randomized Clinical Trial. Clin Infect Dis. 2021 May 4;72(9):1517-1525.

  • Grillo S, Pujol M, Miró JM, López-Contreras J, Gorane E et al; SAFO study group. Cloxacillin plus fosfomycin versus cloxacillin alone for methicillin-susceptible Staphylococcus aureus bacteremia: a randomized trial. Nat Med. 2023 Oct;29(10):2518-2525.

  • Escrihuela-Vidal F, Ong SWX, Oriol I, Grillo S, Pujol M et al. Adjunctive Fosfomycin for the Treatment of Staphylococcus aureus Bacteremia: A Pooled Post-hoc Analysis of Individual Participant Data from Two Randomized Trials. Clin Infect Dis. 2025 Jul 16:ciaf387.

Moltes gràcies!

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