# A Bayesian analysis of finerenone in heart failure with mildly reduced and preserved ejection fraction: a pre-specified analysis of FINEARTS-HF

Alasdair D Henderson, Kieran F Docherty, Atefeh Talebi, Toru Kondo, Mark

C Petrie, Brian L Claggett, Akshay S Desai, Muthiah Vaduganathan, John J

Atherton, Johan Bauersachs, et al.

► To cite this version:

Alasdair D Henderson, Kieran F Docherty, Atefeh Talebi, Toru Kondo, Mark C Petrie, et al. A Bayesian analysis of finerenone in heart failure with mildly reduced and preserved ejection fraction: a pre-specified analysis of FINEARTS-HF. European Heart Journal - Cardiovascular Pharmacotherapy, 2026, 10.1093/ehjcvp/pvag010. [hal-05515473](https://hal-univ-lorraine.fr/hal-05515473v1)

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1 A Bayesian analysis of finerenone in heart failure with mildly reduced and
2 preserved ejection fraction: a pre-specified analysis of FINEARTS-HF

3

4 Alasdair D Henderson¹, Kieran F Docherty¹, Atefeh Talebi¹, Toru Kondo¹,², Mark C Petrie¹,

5 Brian L Claggett³, Akshay S Desai³, Muthiah Vaduganathan³, John J Atherton⁴, Johan

6 Bauersachs⁵, Morten Schou⁶, Subodh Verma⁷, Carolyn SP Lam⁸, Bertram Pitt⁹, Michele

7 Senni¹⁰, Sanjiv J Shah¹¹, Adriaan A Voors¹², Faiez Zannad¹³, Meike Brinker¹⁴, Flaviana

8 Amarante¹⁵, Katja Rohwedder¹⁶, James Lay-Flurrie¹⁷, Scott D Solomon³, John JV McMurray¹,

9 Pardeep S Jhund¹

10

11

Affiliations

12 ¹BHF Glasgow Cardiovascular Research Centre, School of Cardiovascular and Metabolic

13 Health, University of Glasgow, Glasgow, Scotland, UK; ²Department of Cardiology, Nagoya

14 University Graduate School of Medicine, Nagoya, Japan; ³Cardiovascular Division, Brigham

15 and Women's Hospital, Harvard Medical School, Boston, Massachusetts, USA;

16 ⁴Department of Cardiology, Royal Brisbane and Women's Hospital, University of

17 Queensland Faculty of Medicine, Brisbane, Australia; ⁵Department of Cardiology and

18 Angiology, Hannover Medical School, Hannover, Germany; ⁶Department of Cardiology,

19 Herlev-Gentofte University Hospital, Hellerup, Denmark; ⁷Division of Cardiac Surgery, St.

20 Michael's Hospital, Toronto; ⁸National Heart Centre Singapore & Duke-National University
1 of Singapore, Singapore; ⁹University of Michigan, School of Medicine, Ann Arbor, Michigan,

2 USA; ¹⁰University Bicocca Milan, Italy, Papa Giovanni XXIII Hospital, Bergamo, Italy;

3 ¹¹Northwestern University Feinberg School of Medicine, Chicago, Illinois, USA; ¹²University

4 of Groningen, Groningen, Netherlands; ¹³Université de Lorraine, Inserm Clinical

5 Investigation Centre, CHU, Nancy, France. ¹⁴Bayer AG, Research & Development,

6 Pharmaceuticals, Wuppertal, Germany. ¹⁵Cardiology and Nephrology Clinical

7 Development, Bayer SA, São Paulo, Brazil. ¹⁶Global Medical Affairs, Berlin. ¹⁷Bayer plc,

8 Research & Development, Pharmaceuticals, Reading, UK

9 **Address for Correspondence:**

10 Dr Alasdair D Henderson and Prof Pardeep S Jhund

11 ¹BHF Glasgow Cardiovascular Research Centre, School of Cardiovascular and Metabolic

12 Health, University of Glasgow, Glasgow, Scotland, UK Email:

13 pardeep.jhund@glasgow.ac.uk

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15 **Word count** 3515

16

Abstract

17 **Background:** The non-steroidal mineralocorticoid receptor agonist (MRA) finerenone,

18 reduced heart failure events and cardiovascular death in patients with heart failure with

19 mildly reduced or preserved ejection fraction (HFmrEF/HFpEF) in a frequentist analysis of

20 the FINEARTS-HF trial. We applied Bayesian methods including prior information to provide

21 probabilistic estimates of efficacy and safety.

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**Objective:** To estimate the probability of different magnitudes of treatment benefit with finerenone versus placebo using Bayesian analysis of FINEARTS-HF.

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**Methods:** In this pre-specified Bayesian analysis, we estimated treatment efficacy incorporating prior information in a robust meta-analytic predictive (MAP) prior using data from two finerenone trials (FIDELIO-DKD and FIGARO-DKD) and a steroidal MRA spironolactone (TOPCAT). We compared results using vague priors and informative MAP priors. The primary outcome was cardiovascular death and total heart failure events.

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**Results:** Among 6,001 patients, Bayesian analysis with vague priors confirmed the frequentist results of a reduction in the rate of the primary outcome (RR 0.83; 95% credible interval (Crl) 0.74-0.94). Incorporating prior evidence increased the posterior probability of a ≥10% reduction in the primary event rate from 90% to 92%. The probability that finerenone reduced cardiovascular death was 80% (HR 0.93, 95% Crl: 0.79-1.10), and all-cause mortality was 85% (HR 0.94, 95% Crl: 0.83-1.06). Finerenone increased the probability of hyperkalaemia and decreased the probability of hypokalaemia.

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**Conclusion:** The non-steroidal MRA finerenone reduced the rate of cardiovascular death and total heart failure events under both frequentist and Bayesian inference methods. The

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1 probability of benefit exceeded 80% for both cardiovascular and all-cause mortality with

2 finerenone.

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4 **Trial Registration:** ClinicalTrials.gov Identifier: NCT04435626

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6 **Key words:** finerenone, mineralocorticoid receptor antagonist, heart failure with preserved

7 ejection fraction, Bayesian

8

9

Introduction

10 Randomised clinical trials are typically analysed using a frequentist approach where the

11 aim is to use the evidence gathered to reject the null hypothesis, i.e. the hypothesis that

12 there is no meaningful difference between the treatment groups. Under this framework,

13 unobservable and fixed parameters of interest from statistical models such as the

14 treatment effect (e.g. hazard ratios from a Cox proportional hazards model) are estimated.

15 We subsequently estimate the probability that we would observe a treatment effect as (or

16 more) extreme than the one observed if there was no difference between treatments and

17 accept <5% as a “significant” result.

18

19 Bayesian methods offer an alternative approach,¹⁻³ where the treatment effect is a random

20 variable to be estimated so we can make probability statements about the treatment
1 effect. As recently recognised by the Food and Drug Administration (FDA)⁴, Bayesian
2 analyses also offer the opportunity to formally incorporate prior information from previous
3 studies. Bayesian analysis can update prior knowledge with new data through application
4 of Bayes theorem. New data can update prior beliefs to provide a new estimate on a
5 research topic which considers the totality of evidence rather than analysing each new
6 study in isolation. Finally, the analyses can be used to support the primary inference in the
7 trial.

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9 The steroidal mineralocorticoid receptor antagonist (MRA) spironolactone was tested in
10 patients with heart failure with mildly reduced or preserved ejection fraction
11 (HFmrEF/HFpEF) in the TOPCAT trial (Treatment of Preserved Cardiac Function Heart
12 Failure with an Aldosterone Antagonist).⁵ Spironolactone did not reduce the primary
13 endpoint, and further analysis of the trial suggested that patients enrolled in two countries
14 may not have had heart failure and did not take randomised treatment.⁶,⁷ After excluding
15 these countries post hoc, there was a nominally significant effect of spironolactone on the
16 primary outcome.

17

18 Whether or not MRAs might benefit patients with HFmrEF/HFpEF was tested in a recent
19 trial with the non-steroidal MRA, finerenone. The FINEARTS-HF trial (FINerenone trial to
20 investigate Efficacy and sSafety superioR to placebo in paTientS with Heart Failure) was
21 designed and analysed using a frequentist approach.⁸,⁹ Finerenone significantly reduced
1 the composite primary outcome of cardiovascular death and total heart failure (HF) events

2 (rate ratio 0.84; 95% confidence interval, 0.74 to 0.95; *p* = 0.007). This analysis did not

3 incorporate prior knowledge of the effect of MRAs in HFmrEF/HFpEF from TOPCAT, or the

4 effect of finerenone in a population with chronic kidney disease and type 2 diabetes

5 (FIDELIO-DKD and FIGARO-DKD; Finerenone in Reducing Kidney Failure and Disease

6 Progression in Diabetic Kidney Disease and Finerenone in Reducing Cardiovascular

7 Mortality and Morbidity in Diabetic Kidney Disease).¹⁰,¹¹

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9 We have analysed the FINEARTS-HF trial using Bayesian methods to incorporate prior
10 knowledge from these trials with spironolactone and finerenone to estimate the probability
11 of various treatment effect sizes and summarise relative and absolute treatment effects.

12
# Methods

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## The FINEARTS-HF trial

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FINEARTS-HF (NCT04435626) was a prospective, randomised, double-blind, placebo-controlled, trial which examined the efficacy and safety of finerenone compared with placebo, in patients with HFmrEF/HFpEF. The design, baseline characteristics, and primary results are published.⁸,⁹,¹² Ethics Committees for the participating institutions approved the protocol and all patients gave written consent. Briefly, key inclusion criteria were age >40 years, symptomatic heart failure in New York Heart Association (NYHA) functional class II-IV, treatment with a diuretic for >30 days before randomization, and a left ventricular ejection fraction (LVEF) ≥40% with evidence of structural heart disease (either left atrial enlargement or left ventricular hypertrophy) measured within 12 months of screening.

Patients were also required to have elevated natriuretic peptide levels (NT-proBNP >300 pg/mL [or BNP >100 pg/mL] for patients in sinus rhythm or NT-proBNP >900 pg/mL [or BNP >300 pg/mL] for patients in atrial fibrillation), measured within 90 days in those with a recent worsening heart failure event within 90 days of randomization, or measured 30 days before randomization in those without a recent worsening heart failure event. Both ambulatory and hospitalised patients were eligible for enrolment. Patients with prior LVEF <40% with subsequent improvement to ≥40% were also eligible for enrolment provided that ongoing heart failure symptoms were present and all other inclusion criteria were satisfied.

Key exclusion criteria were eGFR <25 ml/min/1.73 m², serum/plasma potassium >5.0 mmol/L at screening or randomization, or symptomatic hypotension with mean
1 systolic blood pressure <90 mmHg at screening or randomization. The primary trial

2 outcome was the composite of cardiovascular death and total (first and recurrent) heart

3 failure events (i.e., heart failure hospitalization or urgent heart failure visit). Prespecified

4 secondary outcomes were cardiovascular death, the total number of heart failure events;

5 improvement in NYHA class from baseline to 12 months; change in the Kansas City

6 Cardiomyopathy Questionnaire (KCCQ) total symptom score (KCCQ-TSS) from baseline to

7 6, 9, and 12 months; a composite kidney endpoint (defined as a sustained decrease in

8 eGFR ≥50% relative to baseline over at least 4 weeks, or sustained eGFR decline

9 <15 ml/min/1.73 m², or initiation of dialysis or renal transplantation); and all-cause death.

10 All deaths and potential primary outcome non-fatal events were adjudicated by an

11 independent, blinded, committee. Prespecified safety analyses included serious adverse

12 events, investigator-reported hyperkalaemia and changes in laboratory parameters of

13 interest (e.g. elevations or decreases in potassium, elevations in serum creatinine, and

14 decreases in systolic blood pressure).

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16 Bayesian Priors for FINEARTS-HF

17 To allow a more direct comparison with the primary frequentist result we used a *vague*

18 prior. A vague prior provides negligible prior knowledge about the expected treatment effect

19 prior to the study and therefore conclusions are defined by the newly observed data,

20 analogous to the frequentist framework.

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1 A second set of analyses used *informative priors* estimated from previously reported
2 clinical trials in the field. We used three sources of data to derive prior distributions for the
3 efficacy of finerenone: 1) a previous study of a steroidal MRA in patients with HFpEF
4 (TOPCAT), 2) TOPCAT data from the Americas region only because of previously reported
5 regional variation in TOPCAT results,⁶ 3) the prespecified FIDELITY pooling of FIDELIO-DKD
6 and FIGARO-DKD (Finerenone in chronic kidney disease and type 2 diabetes: Combined
7 FIDELIO-DKD and FIGARO-DKD Trial programme analysis)¹³,¹⁴ (Table 1). We used these
8 results separately to define prior distributions from the reported log rate ratios,
9 downweighed by half (by doubling the variance). We defined a fourth prior which was a
10 composite TOPCAT (Americas region only), and FIDELITY results, and constructed using
11 the robust meta-analytic predictive (MAP) prior method.¹⁵ This meta-analysis of the log rate
12 ratio estimates of the previously described trials are summarised in a single distribution
13 including a component which downweighs the prior by an arbitrary 10%¹⁵ (Supplementary
14 Figure 1). This method allows for prior information to be incorporated from multiple studies
15 at once without inflating the influence of the prior over the posterior distribution or
16 selectively down weighting particular prior information because of differences with the
17 newly collected data. We performed a further sensitivity analysis by using all TOPCAT data
18 in the MAP prior estimation. We used the same methodology to derive a specific MAP prior
19 for cardiovascular death and all-cause death using previous estimates of the log hazard
20 ratio from these two sources.⁶,¹⁴

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22 Bayesian analysis of FINEARTS-HF
1 Our Bayesian analysis of FINEARTS-HF updates collective *prior* knowledge about the
treatment effect with observed data from the trial through a defined *likelihood* function.
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3 Using simulation-based methods to combine the prior and current information we derived
an updated *posterior* distribution of treatment efficacy. We followed reporting guidelines of
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Bayesian analyses (*Supplementary Table 1*).¹⁶⁻¹⁸
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7 **Statistical Analysis**

8 We analysed the same population as the primary frequentist analysis of FINEARTS-HF. The
9 primary endpoint of cardiovascular death and total (first and recurrent) heart failure events
10 and was analysed using a stratified Andersen-Gill proportional hazards model with
11 clustered standard errors by participant (LWYY) with strata defined by randomization strata
12 (region and LVEF [< 60%, ≥60%]). We used a vague prior as our primary analysis to compare
13 with the frequentist results, then used the four prior distributions described earlier (Table
14 1), each of which resulted in a posterior distribution of treatment efficacy to allow
15 comparison of the impact of different informative priors. To measure treatment effects on
16 an absolute scale we used a negative binomial likelihood, adjusted for randomization
17 strata and with an offset term for follow-up time. We used these models to estimate
18 treatment-specific predictions of the rates and their difference per 100 person-years.
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20 For secondary efficacy endpoints all time-to-first-event secondary endpoints were
21 analysed using a stratified Cox regression likelihood with the same strata as above. Total
1 heart failure events were analysed with the same LWYY as the primary composite outcome.

2 Change in NYHA was modelled with a binomial likelihood (logistic regression) with

3 adjustment for randomization strata. Change in KCCQ-TSS score from baseline to 12

4 months was modelled as a linear mixed effect model with random effects by participant,

5 an unstructured covariance matrix by treatment group, adjustment for randomization

6 strata and visit by baseline KCCQ-TSS interaction. Missing values were not explicitly

7 imputed so were assumed missing at random. Vague priors [Normal(0, 0.5)] were used for

8 all parameters in all secondary efficacy outcomes. Absolute treatment benefit for total

9 heart failure events (using a negative binomial likelihood) and cardiovascular and all-cause

10 deaths (using a Poisson likelihood) were estimated using counterfactual posterior

11 predictions as described for the primary outcome. We analysed safety outcomes with a

12 binomial likelihood and vague priors, adjusted for randomization strata.

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14 All models were fitted using Hamiltonian Markov Chains (HMC) inference through the R

15 interface to stan, brms.¹⁹,²⁰ We ran 4 chains for 4,000 iterations with a burn-in of 50% for all

16 chains for efficacy outcomes and 2,000 iterations for safety outcomes. Model convergence

17 was checked using trace plots, trace-rank plots, R-hat values and autocorrelation plots.

18 Supportive models (negative binomial for recurrent events) were summarised using the

19 marginaleffects package and tidyverse.²¹,²²

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# Results

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There were 6,001 patients validly randomised in FINEARTS-HF, 2,998 to placebo and 3,003 to finerenone. The baseline characteristics have been published previously,¹² and a condensed version is provided in *Supplementary Table 2*. Patients had a median age of 73 years, and 46% were women. Baseline characteristics were well balanced between the two treatment groups. Most patients (69%) were in NYHA functional class II, and the mean (±SD) left ventricular ejection fraction was 53±8%. The median duration of follow-up was 32 months. For the primary outcome, 624 participants experienced 1083 events in the finerenone arm compared with 1283 events among 719 participants in the placebo arm (*Supplementary Table 3*). We reproduced the frequentist maximum likelihood estimate of the primary treatment effect, expressed as a rate ratio, as 0.84 with a 95% confidence interval of 0.74 to 0.95 (p = 0.007) (*Supplementary Figure 2*).⁹

## Treatment effect estimates with a vague prior

Bayesian analysis reflecting no prior belief in the treatment efficacy (vague priors), when combined with the observed trial data, yielded a posterior estimate of the primary rate ratio of 0.83 (95% CrI: 0.74-0.94) (**Figure 1**, **Table 2**) and a posterior probability of treatment efficacy (RR<1) of 99.85%. The Bayesian models achieved good convergence (*Supplementary Figure 3-6*).
1 Bayesian posterior distributions can be evaluated at alternative critical values to the null.

2 We estimated the probability that finerenone reduced the rate of cardiovascular death and

3 total heart failure events by at least 10% (equivalent to RR<0.9) as 90%, by 15% (RR<0.85)

4 as 64% and by more than 20% (RR<0.80) as 27% (Table 2).

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6 **Treatment effect estimates with informative priors**

7 Using informative priors from a single historical trial assigned a high prior probability of

8 finding a beneficial treatment effect (Table 1), and correspondingly, the posterior

9 probability of greater treatment effects was slightly increased with these priors. The

10 probability of a relative benefit greater than 10% [Pr(RR<0.9)] when informed by TOPCAT

11 (92%), TOPCAT Americas (92%) or FIDELITY (93%) was larger than using a vague prior (90%)

12 (Table 2). Using historical results without downweighing as priors increased both the prior

13 and posterior probabilities of a treatment benefit with finerenone (Supplementary Table 4).

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15 Pooling the results from FIDELITY and TOPCAT Americas in a robust MAP prior incorporated

16 all this prior information and variation between them. This also slightly increased the

17 posterior probability of a larger treatment benefit compared to the estimate using vague

18 priors [Pr(RR<0.9)=92%] (Table 2). These findings were consistent when including TOPCAT

19 Americas or all TOPCAT in the MAP prior derivation (Supplementary Figure 7).

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1 Absolute and relative benefits of finerenone on heart failure hospitalizations and mortality
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4 To maximise the benefits of Bayesian models' flexibility and their ability to summarise quantities in clinically intuitive terms, we analysed the effect of finerenone using negative binomial and Poisson models. For the primary outcome, using vague priors and a negative binomial model likelihood, we estimated a similar rate ratio as the LWYY model (0.84, 95% CrI: 0.73-0.97). This same model can also be used to estimate the treatment effect on an absolute scale. Using this method, we estimated an event rate in the placebo arm of 23.2 events per 100 person-years (95% CrI: 21.0, 25.7) and 19.5 events with finerenone (95% CrI: 17.5, 21.8), for a rate difference of 3.7 fewer events per 100 patient-years (95% CrI: 0.7, 6.9) (Supplementary Figure 8). Similarly, for total heart failure events excluding mortality, we estimated a high probability of a benefit on the relative scale (RR, 0.82; 95% CrI: 0.73, 0.93) and on an absolute scale (rate difference, 3.2 fewer events; 95% CrI: 0.9, 5.5) (Table 2, Supplementary Figure 9).

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17 The frequentist analysis of mortality outcomes in FINEARTS-HF was unable to reject the null hypothesis of no difference in cardiovascular (HR 0.93; 95% CI: 0.78, 1.11) or all-cause mortality (HR 0.93; 95% CI: 0.83, 1.06) (Supplementary Table 3). Using a vague prior, we estimated an 80% posterior probability that the finerenone versus placebo hazard ratio for CV death was less than one (i.e. favours finerenone) and an 85% probability of treatment
1 benefit on all-cause death (Table 2). We also incorporated priors derived from FIDELITY

2 and TOPCAT-Americas to define a meta-analytic prior for each outcome (Supplementary

3 Figure 10). These prior distributions remained broad but assigned more probability to a

4 treatment benefit than harm on both CV and all-cause mortality (Supplementary Figure

5 10). The posterior probability of any treatment benefit [Pr(HR<1.0)] with finerenone

6 therefore, increased to 86% for CV death, and 88% for all-cause mortality (Table 2).

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8 Our Bayesian analysis means that we can calculate the posterior probability of varying
9 magnitudes of treatment benefits on both relative and absolute scales. **Figure 3** shows
10 these posterior probabilities, using vague priors, for four clinical endpoints and shows a
11 higher probability of benefit for endpoints including heart failure events. There was a
12 slightly higher probability of a relative benefit for total heart failure events alone, but a
13 higher probability of greater benefits on an absolute scale for the composite of
14 cardiovascular death and total heart failure events. The relatively high probability of benefit
15 for mortality endpoints declines rapidly for larger treatment benefits, especially on an
16 absolute scale.

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18 Using a vague prior for the treatment effect, we derived very similar estimates using
19 Bayesian analyses to those found in the frequentist analyses of all secondary outcomes
20 (Supplementary Figure 11, Supplementary Table 3).
# 1 Effect of finerenone on safety outcomes

Safety outcomes were also analysed in a Bayesian framework using logistic regression and vague priors, which enabled these outcomes to be summarised on both a relative and absolute (Supplementary Table 5). There was no difference in reported serious adverse events (OR 1, 95% CrI: 0.9-1.1). Finerenone increased the probability of a potassium level above 5.5 mmol/L from 7.1% in the placebo arm to 14.6% in the finerenone arm, an adjusted risk difference of 7.1% (95% CrI: 5.6-8.7), but decreased the probability of a potassium level below 3.5 mmol/L by 4.9% (95% CrI: 3.6-6.2). Finerenone increased the probability of a systolic blood pressure measurement of less than 100 mmHg (adjusted risk difference of 5.6% (95% CrI: 4.0-7.1)) and of a creatinine level of 2.5 mg/dL or more (adjusted risk difference of 1.8% (95% CrI: 0.7-2.8)).

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# 13 Discussion

In this Bayesian analysis of the FINEARTS-HF trial, we found that the probability that finerenone reduced the rate of cardiovascular death and total heart failure events was 99.85% and that the probabilities of at least 10%, 15%, and 20% relative risk reductions were 90%, 64%, and 27%, respectively, assuming no meaningful prior information.

Incorporation of prior data from the previous finerenone and spironolactone trials supported this conclusion [Pr(RR<1) = 99.90%, Pr(RR<0.9)=92%, Pr(RR<0.85)=65%, Pr(RR<0.8)=27%] respectively using a robust meta-analytic prior. For context, the updated level of evidence grading system for ESC clinical practice guidelines recommends level A
1 for "substantial evidence against the play of chance", defined as p<0.005, which
2 approximately corresponds to a posterior probability of superiority of 99.75% if minimally
3 informative priors are used.²³ We also estimated an 80% probability that finerenone
4 reduced the risk of cardiovascular death (i.e., that the hazard ratio was <1.0) and an 85%
5 probability that it reduced all-cause death using vague priors (**Central Illustration**).

6
7 Bayesian analyses can supplement frequentist approaches, which are the most commonly
8 used analyses of randomised clinical trials. 2,3,24,25 We have demonstrated several of the
9 advantages of Bayesian approaches using the results of the FINEARTS-HF trial. Without the
10 binary reliance on null hypothesis significance testing of frequentist methods, 26-29 a
11 Bayesian approach enabled us to make probabilistic statements about treatment benefit
12 at multiple clinically relevant thresholds. In addition to the frequentist analysis of
13 FINEARTS-HF, this analysis has provided additional data on the probability of various
14 relative treatment benefits, quantified the probability of a benefit on all cause death,
15 estimated absolute benefits with finerenone versus placebo, and importantly, incorporated
16 previous knowledge regarding MRAs in patients with HFmrEF/HFpEF into the results of the
17 FINEARTS-HF trial.

18
19 We were able to quantify and incorporate prior information on both the effect of finerenone
20 on cardiovascular outcomes in the FIDELIO-DKD and FIGARO-DKD trials¹⁰,¹¹ and the effect
21 of a steroidal MRA in patients with HFmrEF/HFpEF enrolled in the TOPCAT trial. 5,6 We used
1 the most agnostic and vague prior for our primary analysis and calculated a 90%
2 probability that the treatment effect was at least 10%. We have demonstrated that this
3 conclusion of treatment benefit with finerenone is consistent or enhanced across a range
4 of plausible prior beliefs. If we used the most optimistic prior based on the treatment effect
5 from the patients enrolled in the FIDELITY pooled trials, the posterior probability of a
6 treatment effect of at least 10% increased to 93%. The meta-analytic prior method
7 provides a robust framework with which to combine prior information from multiple studies
8 without exerting undue influence. With this approach, we estimated an improved posterior
9 probability of 92% for a 10% reduction in the relative rate of cardiovascular death and total
10 heart failure events.

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12 Consistent with previous trials of patients with HFmrEF/HFpEF, frequentist analysis of
13 FINEARTS-HF did not show evidence of a reduction in cardiovascular or all-cause
14 mortality.30-35 A meta-analysis of TOPCAT and FINEARTS-HF was also unable to show a
15 reduction in cardiovascular or all-cause mortality.36 We were able to expand on these
16 previous trials in the Bayesian framework by quantifying the probability that finerenone did
17 reduce the hazard of cardiovascular death (80%) and all-cause mortality (85%) using vague
18 priors. These probabilities were higher if we used informative priors from FIDELITY and
19 TOPCAT-Americas through a MAP (86% and 88% respectively). Even with this stronger prior
20 belief, the probability of a large relative treatment benefit on mortality was low, for example
21 the probability of a HR<0.9 for CV mortality was 41% and on an absolute scale the
22 probability of 1 fewer CV death per 100 person-years was <1%.
1

2 This enables clinicians and regulators to judge the strength of evidence for a treatment
3 benefit in context, instead of rejecting conclusions based on failure to meet a certain
4 statistical significance threshold. The relatively low mortality rates and higher incidence of
5 non-cardiovascular causes of death in HFmrEF/HFpEF compared to HFrEF mean that a
6 trial would need to be unfeasibly large to realistically demonstrate a mortality treatment
7 benefit under a frequentist statistical analysis plan.³⁷ Bayesian methods therefore, provide
8 a valuable pathway to better understand treatment efficacy on mortality in this patient
9 population.

10

11 A crucial unanswered question for future research is whether incorporating robust and
12 informative prior information can reduce the size of new trials in heart failure when using
13 Bayesian analyses. Combining Bayesian data analysis with adaptive trial design may
14 further improve efficiency.³⁸⁻⁴⁰ However, the desire to reduce trial sample size and cost
15 must be balanced against regulatory requirements that preserve frequentist operating
16 characteristics and overcome scepticism about subjective prior definition.⁴¹ Trials must
17 also be large enough to provide a robust evaluation of safety endpoints.

18

19 Our study has some limitations. The sources of prior information were from slightly
20 different patient populations and from steroidal and non-steroidal mineralocorticoid
21 receptor antagonists, which may affect the assumption of exchangeability between these
trials. For this reason, we excluded this information in our primary analysis and used vague priors, but we also found consistent results across a wide range of prior specifications in our secondary analyses which suggests that deriving priors from slightly different patient populations or treatments did not alter our conclusions. Secondly, we were unable to incorporate data on eplerenone into our priors as the only trial of eplerenone was conducted in patients with HFrEF⁴². In a prior meta-analysis, the treatment effect of MRAs there was significant heterogeneity in the treatment effect of MRAs in the trials of patients with HFrEF compared to HFmrEF/HFpEF³⁶ precluding inclusion in this analysis. Thirdly, we have included alternative statistical models to the primary FINEARTS-HF frequentist analysis with negative binomial and Poisson models.⁹ This allowed us to quantify absolute treatment effects, which is challenging with the semi-parametric survival models. While the specific details of prior specification and analysis strategy were not pre-registered our analysis was pre-specified.

In this Bayesian analysis of FINEARTS-HF, finerenone reduced the risk of cardiovascular death and total heart failure events. The analysis showed that there is a >80% probability that finerenone caused a small reduction in CV death and all-cause mortality.
1 Disclosures

2 The FINEARTS-HF trial was funded by Bayer AG.

3 ADH - Personal fees and travel support from Bayer AG

4 KD - His employer, the University of Glasgow, has been remunerated by AstraZeneca for his

5 work on clinical trials, and he has received speaker fees from AstraZeneca, Boehringer

6 Ingelheim, Pharmacosomos, and Translational Medicine Academy; has served on advisory

7 boards or performed consultancy for FIRE-1, Us2.ai, and Bayer AG; holds stock in Us2.ai;

8 has served on a Clinical Endpoint Committee for Bayer AG; and has received research

9 grant support (paid to his institution) from AstraZeneca, Roche, Novartis, and Boehringer

10 Ingelheim.

11 AT- none

12 TK - TK is supported by Great Britain Sasakawa Foundation, Yagi Foundation, and grant

13 20K17112 from Grant-in-Aid for Scientific Research; has received lecture fees from Abbott

14 Japan LLC, AstraZeneca K.K., Boehringer Ingelheim, Ono Pharmaceutical Co, Ltd, Kowa

15 Company, Ltd, Kyowa Kirin Co, Ltd, and Novartis Pharma K.K

16 MCP - Research grants from British Heart Foundation, NIHR, Boehringer Ingelheim, Roche,

17 SQ Innovations, AstraZeneca, Novartis, Novo Nordisk, Medtronic, Boston Scientific,

18 Medtronic, Pharmacosmos; consulting fees from Abbott, Akero, Applied Therapeutics,

19 Amgen, AnaCardio, Biosensors, Boehringer Ingelheim, Corteria, Novartis, AstraZeneca,

20 Novo Nordisk, AbbVie, Bayer, Horizon Therapeutics, Foundry, Takeda, Cardiorentis,
1 Pharmacosmos, Siemens, Eli Lilly, Vifor, New Amsterdam, Moderna, Teikoku, LIB

2 Therapeutics, 3R Lifesciences, Reprieve, FIRE 1, Corvia, Regeneron; payment from

3 Boehringer Ingelheim, Novartis, AstraZeneca, Novo Nordisk, Pharmacosmos, Eli Lilly, Vifor;

4 support for attending meetings from Boehringer Ingelheim, Novartis, AstraZeneca, Novo

5 Nordisk, Pharmacosmos, Eli Lilly, Vifor; is a data safety monitoring board or advisory board

6 member for AstraZeneca, Teikoku and Moderna

7 BLC - Dr Claggett has received personal consulting fees from Alnylam, Bristol Myers

8 Squibb, Cardior, Cardurion, Corvia, CVRx, Eli Lilly, Intellia, and Rocket; and has served on a

9 data safety monitoring board for Novo Nordisk.

10 ASD - Dr Desai has received institutional research grants (to Brigham and Women's

11 Hospital) from Abbott, Alnylam, AstraZeneca, Bayer, Novartis, and Pfizer; and has received

12 personal consulting fees from Abbott, Alnylam, AstraZeneca, Bayer, Biofourmis, Boston

13 Scientific, Medpace, Medtronic, Merck, Novartis, Parexel, Porter Health, Regeneron,

14 River2Renal, Roche, Veristat, Verily, and Zydus

15 MV - Dr Vaduganathan has received research grant support, served on advisory boards, or

16 had speaker engagements with American Regent, Amgen, AstraZeneca, Bayer AG, Baxter

17 Healthcare, BMS, Boehringer Ingelheim, Chiesi, Cytokinetics, Fresenius Medical Care,

18 Idorsia Pharmaceuticals, Lexicon Pharmaceuticals, Merck, Milestone Pharmaceuticals,

19 Novartis, Novo Nordisk, Pharmacosmos, Relypsa, Roche Diagnostics, Sanofi, and Tricog

20 Health; and participates on clinical trial committees for studies sponsored by AstraZeneca,

21 Galmed, Novartis, Bayer AG, Occlutech, and Impulse Dynamics.
1 JJA - Dr Atherton has received other support from Bayer, during the conduct of the study;

2 and has received other support from AstraZeneca, Bayer, Boehringer Ingelheim, Bristol

3 Myers Squibb, Eli Lilly, Novo Nordisk, Vifor Pharma, and Merck Sharp and Dome, outside of

4 the submitted work.

5 JB - Dr Bauersachs has received honoraria for lectures/consulting from Novartis, Vifor,

6 Bayer, Pfizer, Boehringer Ingelheim, AstraZeneca, Cardior, CVRx, Bristol Myers Squibb,

7 Amgen, Corvia, Norgine, Edwards, and Roche not related to this paper; and has received

8 research support for the department from Zoll, CVRx, Abiomed, Norgine, Roche, not

9 related to this paper.

10 MS - Dr Schou reports funding from Novo Nordisk, Novartis, AstraZeneca, and Boehringer

11 Ingelheim outside the submitted work and reports personal fees from Bayer during the

12 conduct of the study and personal fees from Alleviant, AstraZeneca, Boehringer Ingelheim,

13 Edwards Lifesciences, Janssen, Novartis, Novo Nordisk, and Rivus outside the study

14 SV - Dr Verma holds a Tier 1 Canada Research Chair in Cardiovascular Surgery; and has

15 received grants and/or research support and/or speaking honoraria from Amarin, Amgen,

16 AstraZeneca, Bayer, Boehringer Ingelheim, Canadian Medical and Surgical Knowledge

17 Translation Research Group, Eli Lilly, HLS Therapeutics, Humber River Health, Janssen,

18 Merck, Novartis, Novo Nordisk, Pfizer, PhaseBio, S&L Solutions Event Management Inc,

19 Sanofi, and Sun Pharmaceuticals; and is the President of the Canadian Medical and

20 Surgical Knowledge Translation Research Group, a federally incorporated not-for-profit

21 physician organization.
1 CSPL - Dr Lam has received research support from Novo Nordisk and Roche Diagnostics;

2 has received consulting fees from Alleviant Medical, Allysta Pharma, AnaCardio AB,

3 Applied Therapeutics, AstraZeneca, Bayer, Biomeutics, Boehringer Ingelheim, Boston

4 Scientific, Bristol Myers Squibb, CardioRenal, CPC Clinical Research, Eli Lilly, Impulse

5 Dynamics, Intellia Therapeutics, Ionis Pharmaceutical, Janssen Research & Development

6 LLC, Medscape/WebMD Global LLC, Merck, Novartis, Novo Nordisk, Prosciento Inc, Quidel

7 Corporation, Radcliffe Group Ltd., Recardio Inc, ReCor Medical, Roche Diagnostics,

8 Sanofi, Siemens Healthcare Diagnostics and, Us2.ai; and is a co-founder and nonexecutive

9 director of Us2.ai.

10 BP - Dr Pitt is a consultant for Bayer, AstraZeneca, Boehringer Ingelheim, Lexicon, Bristol

11 Myers Squibb, KBP Biosciences*, Sarfez Pharmaceuticals*, Pharmaceuticals*,

12 SQinnovations*, G3 Pharmaceuticals, Sea Star medical*, Vifor* Prointel*, and Brainstorm

13 Medical; has stock options in KBP Biosciences, Sarfez Pharmaceuticals, Pharmaceuticals,

14 SQinnovations, Sea Star medical, Vifor, Prointel, and Brainstorm Medical; and has U.S.

15 Patent 9931412-site specific delivery of eplerenone to the myocardium, and U.S. Patent

16 pending 63/045,783 Histone modulating agents for the prevention and treatment of organ

17 failure.

18 MS - Dr Senni has served on advisory boards for, as a consultant for, and has received

19 honoraria from Novartis, Abbott, Merck, MSD, Vifor, AstraZeneca, Cardurion, Novo Nordisk,

20 Bayer, and Boehringer Ingelheim.
1 SS - Dr Shah has received research grants from the NIH (U54 HL160273, X01 HL169712,

2 R01 HL140731, R01 HL149423), AHA (24SFRNPCN1291224), AstraZeneca, Corvia, and

3 Pfizer; and has received consulting fees from Abbott, Alleviant, AstraZeneca, Amgen, Aria

4 CV, Axon Therapies, Bayer, Boehringer Ingelheim, Boston Scientific, Bristol Myers Squibb,

5 Cyclerion, Cytokinetics, Edwards Lifesciences, Eidos, Imara, Impulse Dynamics, Intellia,

6 Ionis, Lilly, Merck, MyoKardia, Novartis, Novo Nordisk, Pfizer, Prothena, Regeneron, Rivus,

7 Sardocor, Shifamed, Tenax, Tenaya, and Ultromics.

8 AAV - Dr Voors' employer received consultancy fees and/or research support from

9 Adrenomed, Anacardio, AstraZeneca, Bayer AG, BMS, Boehringer Ingelheim, Corteria,

10 EliLilly, Merck, Moderna, Novartis, Novo Nordisk, Roche diagnostics, and SalubrisBio. Dr

11 Bauersachs received honoraria for lectures/consulting from Novartis, Vifor, Bayer, Pfizer,

12 Boehringer Ingelheim, AstraZeneca, Cardior, CVRx, BMS, Amgen, Corvia, Norgine,

13 Edwards, and Roche not related to this paper; and has received research support for the
department from Zoll, CVRx, Abiomed, Norgine, and Roche, not related to this paper.

15 FZ - Dr Zannad has received personal fees from 89Bio, Abbott, Acceleron, Applied

16 Therapeutics, Bayer, Betagenon, Boehringer, BMS, CVRx, Cambrian, Cardior, Cereno

17 pharmaceutical, Cellprothera, CEVA, Inventiva, KBP, Merck, NovoNordisk, Owkin, Otsuka,

18 Roche Diagnostics, Northsea, USA2; has stock options at G3Pharmaceutical; has equity in

19 Cereno, Cardiorenal, and Eshmoun Clinical research; and is the founder of Cardiovascular

20 Clinical Trialists.

21 MB, FA, KR, JL-F - employees of Bayer AG
1 SDS - Dr Solomon has received research grants from Alexion, Alnylam, AstraZeneca,

2 Bellerophon, Bayer, BMS, Boston Scientific, Cytokinetics, Edgewise, Eidos, Gossamer,

3 GSK, Ionis, Lilly, MyoKardia, NIH/NHLBI, Novartis, Novo Nordisk, Respicardia, Sanofi

4 Pasteur, Theracos, US2.Al; and has consulted for Abbott, Action, Akros, Alexion, Alnylam,

5 Amgen, Arena, AstraZeneca, Bayer, Boehringer Ingelheim, BMS, Cardior, Cardurion, Corvia,

6 Cytokinetics, Daiichi-Sankyo, GSK, Lilly, Merck, Myokardia, Novartis, Roche, Theracos,

7 Quantum Genomics, Janssen, Cardiac Dimensions, Tenaya, Sanofi-Pasteur, Dinaqor,

8 Tremeau, CellProThera, Moderna, American Regent, Sarepta, Lexicon, Anacardio, Akros,

9 and Valo.

10 JJVM - Dr McMurray has received payments through Glasgow University from work on

11 clinical trials; has received consulting and grants from Amgen, AstraZeneca, Bayer,

12 Cardurion, Cytokinetics, GSK and Novartis, British Heart Foundation, National Institute for

13 Health - National Heart, Lung, and Blood Institute (NIH-NHLBI), Boehringer Ingelheim, SQ

14 Innovations, and Catalyze Group; has received personal consultancy fees from Alnylam

15 Pharmaceuticals, Amgen, AnaCardio, AstraZeneca, Bayer, Berlin Cures, BMS, Cardurion,

16 Cytokinetics, Ionis Pharmaceuticals, Novartis, Regeneron Pharmaceuticals, and River 2

17 Renal Corp; has received personal lecture fees from Abbott, Alkem Metabolics, Astra

18 Zeneca, Blue Ocean Scientific Solutions Ltd., Boehringer Ingelheim, Canadian Medical and

19 Surgical Knowledge, Emcure Pharmaceuticals Ltd., Eris Lifesciences, European Academy

20 of CME, Hikma Pharmaceuticals, Imagica Health, Intas Pharmaceuticals, J.B. Chemicals &

21 Pharmaceuticals Ltd, Lupin Pharmaceuticals, Medscape/Heart.Org., ProAdWise

22 Communications, Radcliffe Cardiology, Sun Pharmaceuticals, The Corpus, Translation
1 Research Group, and Translational Medicine Academy; and data safety monitoring board

2 membership for WIRB-Copernicus Group Clinical Inc; and is a director of Global Clinical

3 Trial Partners Ltd.

4 PSJ - Speakers fees from AstraZeneca, Novartis, ProAdWise Communications; advisory

5 board fees from AstraZeneca, Boehringer Ingelheim, and Novartis; research funding from

6 AstraZeneca, Boehringer Ingelheim, Analog Devices Inc, Roche Diagnostics; his employer

7 the University of Glasgow has been remunerated for clinical trial work from AstraZeneca,

8 Bayer AG, Novartis, and Novo Nordisk; Director at GCTP Ltd

9 Data availability statement

10 Data will be made available to qualified scientific and medical researchers through

11 vivli.org. All requests will be reviewed by an independent scientific review panel and data

12 provided according to the conditions laid out on https://vivli.org/ourmember/bayer/.

13

14

References

15 1. Goligher EC, Heath A, Harhay MO. Bayesian statistics for clinical research. *The Lancet*.

16 2024;404:1067–1076.

17 2. Spiegelhalter DJ, Freedman LS, Parmar MKB. Bayesian Approaches to Randomized Trials.

18 *J R Stat Soc Ser A Stat Soc.* 1994;157:357–416.

19 3. Berry DA. A case for bayesianism in clinical trials. *Stat Med.* 1993;12:1377–1393.
1 4. Center for Drug Evaluation and Research. *Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products*. FDA, 2026.

3 5. Pitt B, Pfeffer MA, Assmann SF, et al. Spironolactone for Heart Failure with Preserved Ejection Fraction. *N Engl J Med*. 2014;370:1383-1392.

6 6. Pfeffer MA, Claggett B, Assmann SF, et al. Regional variation in patients and outcomes in the Treatment of Preserved Cardiac Function Heart Failure With an Aldosterone Antagonist (TOPCAT) trial. *Circulation*. 2015;131:34-42.

8 7. de Denus S, O'Meara E, Desai AS, et al. Spironolactone Metabolites in TOPCAT - New Insights into Regional Variation. *N Engl J Med*. 2017;376:1690-1692.

10 8. Vaduganathan M, Claggett BL, Lam CSP, et al. Finerenone in patients with heart failure with mildly reduced or preserved ejection fraction: Rationale and design of the FINEARTS-HF trial. *Eur J Heart Fail*. 2024;26:1324-1333.

13 9. Solomon SD, McMurray JJV, Vaduganathan M, et al. Finerenone in Heart Failure with Mildly Reduced or Preserved Ejection Fraction. *N Engl J Med*. 2024;391:1475-1485.

15 10. Pitt B, Filippatos G, Agarwal R, et al. Cardiovascular Events with Finerenone in Kidney Disease and Type 2 Diabetes. *N Engl J Med*. 2021;385:2252-2263.

17 11. Bakris GL, Agarwal R, Anker SD, et al. Effect of Finerenone on Chronic Kidney Disease Outcomes in Type 2 Diabetes. *N Engl J Med*. 2020;383:2219-2229.
1

2

3

12. Solomon SD, Ostrominski JW, Vaduganathan M, et al. Baseline characteristics of patients with heart failure with mildly reduced or preserved ejection fraction: The FINEARTS-HF trial. *Eur J Heart Fail.* 2024;26:1334–1346.

4

5

6

13. Filippatos G, Anker SD, Pitt B, et al. Finerenone and Heart Failure Outcomes by Kidney Function/Albuminuria in Chronic Kidney Disease and Diabetes. *JACC Heart Fail.* 2022;10:860–870.

7

8

9

14. Agarwal R, Filippatos G, Pitt B, et al. Cardiovascular and kidney outcomes with finerenone in patients with type 2 diabetes and chronic kidney disease: the FIDELITY pooled analysis. *Eur Heart J.* 2022;43:474–484.

10 15. Schmidli H, Gsteiger S, Roychoudhury S, O’Hagan A, Spiegelhalter D, Neuenschwander

11 B. Robust meta-analytic-predictive priors in clinical trials with historical control

12 information. *Biometrics*. 2014;70:1023–1032.

13 16. Spiegelhalter D, Myles J, Jones D, Abrams K. Bayesian methods in health technology

14 assessment: a review. *Health Technol Assess* *Winch Engl.* 2000;4.

15 17. Althouse AD, Below JE, Claggett BL, et al. Recommendations for Statistical Reporting in

16 Cardiovascular Medicine: A Special Report From the American Heart Association.

17 *Circulation*. 2021;144:e70–e91.

18 18. van de Schoot R, Depaoli S, King R, et al. Bayesian statistics and modelling. *Nat Rev*

19 *Methods Primer*. 2021;1:1–26.
1

19. Bürkner P-C. brms: An R Package for Bayesian Multilevel Models Using Stan. *J Stat*

2

Softw. 2017;80:1–28.

3

20. R Core Team. *R: A Language and Environment for Statistical Computing*. Vienna,

4

Austria: R Foundation for Statistical Computing, 2024.

5

21. Arel-Bundock V. *marginaleffects*: Predictions, Comparisons, Slopes, Marginal Means,

6

and Hypothesis Tests. 2024.

7

22. Wickham H, Averick M, Bryan J, et al. Welcome to the Tidyverse. *J Open Source Softw*.

8

2019;4:1686.

9

23. Jüni P, Antoniou S, Arbelo E, et al. 2024 Revision of the level of evidence grading system

10

for ESC clinical practice guideline recommendations I: therapy and prevention. *Eur Heart J*.

11

2025;46:1885–1894.

12

24. Brophy JM. Bayesian Analyses of Cardiovascular Trials—Bringing Added Value to the

13

Table. *Can J Cardiol.* 2021;37:1415–1427.

14

25. Berry DA. Bayesian clinical trials. *Nat Rev Drug Discov.* 2006;5:27–36.

15

26. Gelman A, Stern H. The Difference Between “Significant” and “Not Significant” is not

16

Itself Statistically Significant. *Am Stat.* 2006;60:328–331.

17

27. Greenland S, Senn SJ, Rothman KJ, et al. Statistical tests, P values, confidence

18

intervals, and power: a guide to misinterpretations. *Eur J Epidemiol.* 2016;31:337–350.
1 28. Wasserstein RL, Lazar NA. The ASA Statement on p-Values: Context, Process, and

2 Purpose. Am Stat. 2016;70:129-133.

3 29. Wasserstein RL, Schirm AL, Lazar NA. Moving to a World Beyond “p < 0.05.” Am Stat.

4 2019;73:1-19.

5 30. Anker SD, Butler J, Filippatos G, et al. Empagliflozin in Heart Failure with a Preserved

6 Ejection Fraction. N Engl J Med. 2021;385:1451-1461.

7 31. Solomon SD, McMurray JJV, Claggett B, et al. Dapagliflozin in Heart Failure with Mildly

8 Reduced or Preserved Ejection Fraction. N Engl J Med. 2022;387:1089-1098.

9 32. Solomon SD, McMurray JJV, Anand IS, et al. Angiotensin-Neprilysin Inhibition in Heart

10 Failure with Preserved Ejection Fraction. N Engl J Med. 2019;381:1609-1620.

11 33. Massie BM, Carson PE, McMurray JJ, et al. Irbesartan in Patients with Heart Failure and

12 Preserved Ejection Fraction. N Engl J Med. 2008;359:2456-2467.

13 34. Yusuf S, Pfeffer MA, Swedberg K, et al. Effects of candesartan in patients with chronic

14 heart failure and preserved left-ventricular ejection fraction: the CHARM-Preserved Trial.

15 The Lancet. 2003;362:777-781.

16 35. von Haehling S, Assmus B, Bekfani T, et al. Heart failure with preserved ejection

17 fraction: diagnosis, risk assessment, and treatment. Clin Res Cardiol. 2024;113:1287-

18 1305.
1 36. Jhund PS, Talebi A, Henderson AD, et al. Mineralocorticoid receptor antagonists in heart

2 failure: an individual patient level meta-analysis. *The Lancet*. 2024;404:1119–1131.

3 37. Kondo T, Henderson AD, Docherty KF, et al. Why Have We Not Been Able to

4 Demonstrate Reduced Mortality in Patients With HFmrEF/HFpEF? *J Am Coll Cardiol*. 2024.

5 Published online September 1, 2024. https://doi.org/10.1016/j.jacc.2024.08.033.

6 38. Ruberg SJ, Beckers F, Hemmings R, et al. Application of Bayesian approaches in drug

7 development: starting a virtuous cycle. *Nat Rev Drug Discov*. 2023;22:235–250.

8 39. Connor JT, Elm JJ, Broglio KR. Bayesian adaptive trials offer advantages in comparative

9 effectiveness trials: an example in status epilepticus. *J Clin Epidemiol*. 2013;66:S130–S137.

10

11 40. Williamson SF, Jacko P, Villar SS, Jaki T. A Bayesian adaptive design for clinical trials in

12 rare diseases. *Comput Stat Data Anal*. 2017;113:136–153.

13 41. Aberegg SK. Post Hoc Bayesian Analyses. *JAMA*. 2019;321:1631–1632.

14 42. Zannad F, McMurray JJV, Krum H, et al. Eplerenone in patients with systolic heart failure

15 and mild symptoms. *N Engl J Med*. 2011;364:11–21.

16
**Figure legends**

1

2 **Figure 1: Bayesian estimates of relative treatment benefit with finerenone under different prior distributions.** Priors from previous trials applied to FINEARTS-HF (left), estimated treatment benefit from observed data from FINEARTS-HF only (frequentist estimate) (central), Bayesian posterior estimates of the treatment effect of finerenone versus placebo on the primary composite endpoint of cardiovascular death and total heart failure events under different prior assumptions (right).

8 **Figure 2: Bayesian estimates of relative treatment benefit with finerenone under different prior distributions on mortality.** Priors from previous trials applied to FINEARTS-HF (left), estimated treatment benefit from observed data from FINEARTS-HF only (frequentist estimate) (central), Bayesian posterior estimates of the treatment effect of finerenone versus placebo on the mortality endpoints of cardiovascular death and all-cause mortality (right).

14 **Figure 3: Probability threshold curves for relative and absolute treatment benefit with finerenone.** Estimates of the posterior probability of a relative benefit (rate ratio or hazard ratio) and absolute benefit (rate difference per 100 person-years) with finerenone on four major cardiovascular clinical endpoints.
<table><caption>**Table 1:** Definition of prior distributions for the rate ratio of treatment total heart failure hospitalizations and cardiovascular death</caption><thead><tr><th>Prior</th><th>Population</th><th>Frequentist estimate</th><th>Prior distribution (log rate ratio)</th><th>Prior probability of treatment benefit (RR&lt;1.0)</th></tr></thead><tbody><tr><td>Vague</td><td>-</td><td>-</td><td>~N(0, 0.5)</td><td>50%</td></tr><tr><td>TOPCAT<sup>36</sup></td><td>HFmrEF/HFpEF</td><td>0.84 (95% CI: 0.7-1.02)</td><td>~N(-0.174, 0.19)*</td><td>82%</td></tr><tr><td>TOPCAT-Americas<sup>36</sup></td><td>HFmrEF/HFpEF</td><td>0.79 (95% CI: 0.64-0.97)</td><td>~N(-0.236, 0.21)*</td><td>87%</td></tr><tr><td>FIDELITY<sup>13</sup></td><td>Type II diabetes &amp; chronic kidney disease</td><td>0.82 (95% CI: 0.72-0.95)</td><td>~N(-0.198, 0.10)*</td><td>92%</td></tr><tr><td>Meta Analytic Predictive<sup>15</sup></td><td>Composite</td><td>-</td><td>~N(-0.188, 0.20)</td><td>81%</td></tr></tbody><tfoot><tr><td colspan="5">* Standard deviations are doubled from the published frequentist estimates to partially account for uncertainty between previous findings and new data.</td></tr></tfoot></table>

3

**Table 2:** Summary of frequentist and Bayesian posterior estimates of the effect of finerenone versus placebo for four clinical endpoints. MAP=meta-analytic prior using data from TOPCAT-Americas and FIDELITY combined. Probabilities shown are the posterior probability that the effect estimate (rate ratio, hazard ratio or rate difference) is less than the specified threshold.

4

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6

7
<table><thead><tr><th></th><th>Estimate (95% CrI)</th><th colspan="4">Posterior probability that treatment is better with finerenone versus placebo at clinically meaningful thresholds</th></tr><tr><th>Relative effects</th><th></th><th>&lt;1</th><th>&lt;0.9</th><th>&lt;0.85</th><th>&lt;0.8</th></tr></thead><tbody><tr><td colspan="6"><strong>CV death and total HF events (rate ratio)</strong></td></tr><tr><td>Frequentist</td><td>0.84 (95% CI: 0.74, 0.95)</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Vague prior</td><td>0.83 (0.74, 0.94)</td><td>99.85%</td><td>90%</td><td>64%</td><td>27%</td></tr><tr><td>TOPCAT prior</td><td>0.83 (0.74, 0.93)</td><td>99.88%</td><td>92%</td><td>65%</td><td>26%</td></tr><tr><td>TOPCAT-Americas prior</td><td>0.83 (0.74, 0.93)</td><td>99.91%</td><td>92%</td><td>67%</td><td>29%</td></tr><tr><td>FIDELITY prior</td><td>0.83 (0.74, 0.92)</td><td>&gt;99.99%</td><td>93%</td><td>67%</td><td>27%</td></tr><tr><td>Robust MAP prior</td><td>0.83 (0.74, 0.93)</td><td>99.90%</td><td>92%</td><td>65%</td><td>27%</td></tr><tr><td colspan="6"><strong>Total HF Events (rate ratio)</strong></td></tr><tr><td>Vague prior</td><td>0.82 (0.73, 0.93)</td><td>99.96%</td><td>93%</td><td>71%</td><td>33%</td></tr><tr><td colspan="6"><strong>CV Death (hazard ratio)</strong></td></tr><tr><td>Vague prior</td><td>0.93 (0.79, 1.10)</td><td>80%</td><td>36%</td><td>15%</td><td>4%</td></tr><tr><td>Robust MAP prior</td><td>0.92 (0.78, 1.07)</td><td>86%</td><td>41%</td><td>17%</td><td>5%</td></tr><tr><td colspan="6"><strong>All Cause Death (hazard ratio)</strong></td></tr><tr><td>Vague prior</td><td>0.94 (0.83, 1.06)</td><td>85%</td><td>26%</td><td>6%</td><td>&lt;1%</td></tr><tr><td>Robust MAP prior</td><td>0.93 (0.83, 1.05)</td><td>88%</td><td>29%</td><td>7%</td><td>&lt;1%</td></tr><tr><td colspan="6"><strong>Absolute effects (rates and rate reduction per 100 person-years)</strong></td></tr><tr><td>Fewer events with finerenone</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Vague priors</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="6"><strong>CV death and total HF events (rate difference)</strong></td></tr><tr><td>Placebo</td><td>23.2 (21, 25.7)</td><td></td><td></td><td></td><td></td></tr><tr><td>Finerenone</td><td>19.5 (17.5, 21.8)</td><td></td><td></td><td></td><td></td></tr><tr><td>Difference</td><td>-3.7 (-6.9, -0.7)</td><td>99.0%</td><td>96%</td><td>87%</td><td>67%</td></tr><tr><td colspan="6"><strong>Total HF Events (rate difference)</strong></td></tr><tr><td>Placebo</td><td>16.6 (14.9, 18.6)</td><td></td><td></td><td></td><td></td></tr><tr><td>Finerenone</td><td>13.5 (12, 15.1)</td><td></td><td></td><td></td><td></td></tr><tr><td>Difference</td><td>-3.2 (-5.5, -0.9)</td><td>99.7%</td><td>97%</td><td>84%</td><td>55%</td></tr><tr><td colspan="6"><strong>CV Death (rate difference)</strong></td></tr><tr><td>Placebo</td><td>3.6 (3.2, 4.1)</td><td></td><td></td><td></td><td></td></tr><tr><td>Finerenone</td><td>3.3 (3, 3.8)</td><td></td><td></td><td></td><td></td></tr><tr><td>Difference</td><td>-0.3 (-0.8, 0.3)</td><td>80%</td><td>&lt;1%</td><td>&lt;0.1%</td><td>&lt;0.1%</td></tr><tr><td colspan="6"><strong>All Cause Death (rate difference)</strong></td></tr><tr><td>Placebo</td><td>7.2 (6.6, 7.9)</td><td></td><td></td><td></td><td></td></tr><tr><td>Finerenone</td><td>6.8 (6.2, 7.4)</td><td></td><td></td><td></td><td></td></tr><tr><td>Difference</td><td>-0.5 (-1.3, 0.4)</td><td>86%</td><td>11%</td><td>&lt;0.1%</td><td>&lt;0.1%</td></tr></tbody></table>
Figure 1: Bayesian estimates of relative treatment benefit with finerenone under different prior distributions. Priors from previous trials applied to FINEARTS-HF (left), estimated treatment benefit from observed data from FINEARTS-HF only (frequentist estimate) (central), Bayesian posterior estimates of the treatment effect of finerenone versus placebo on the primary composite endpoint of cardiovascular death and total heart failure events under different prior assumptions (right).

<figure><img src="image_2.png" /></figure>

7
8
9
Figure 2: Bayesian estimates of relative treatment benefit with finerenone under different prior distributions on mortality. Priors from previous trials applied to FINEARTS-HF (left), estimated treatment benefit from observed data from FINEARTS-HF only (frequentist estimate) (central), Bayesian posterior estimates of the treatment effect of finerenone versus placebo on the mortality endpoints of cardiovascular death and all-cause mortality (right).

<figure><img src="image_3.png" /></figure>

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Figure 3: Probability threshold curves for relative and absolute treatment benefit with finerenone. Estimates of the posterior probability of a relative benefit (rate ratio or hazard ratio) and absolute benefit (rate difference per 100 person-years) with finerenone on four major cardiovascular clinical endpoints.

<figure><img src="image_4.png" /></figure>

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