Bayesian Reanalysis of Biomedical Research

Results

How big might the benefit be?

If the treatment works, how big might its benefit be? The curve shows the range of benefits assumed, small ones most likely. The slider sets how far that range reaches. It moves every figure worked across a range of effect sizes, and none of those worked on the postulated effect alone.

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Narrower: small benefits only Wider: large benefits too


A changed width is named beside the answer it changes, with a way back to the default.

How the answer depends on your prior, with and without the range
Desired target certainty
or
%
The prior you would have needed

Two bell curves: what the data would look like if there were no effect, and if the postulated effect were real. The red line is what this study actually observed — the closer it sits to a curve's peak, the better that hypothesis explains the result.

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These curves are built from the three priors in the legend, which describe how big the effect might be. They are the same three posteriors the interval plot draws, seen as distributions rather than as intervals.

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Vague: as if you brought no opinion at all. This row is the study's own result, restated.

Skeptical: starts by doubting the effect. This is the row to quote to a doubter.

Enthusiastic: starts by expecting the effect the trial was powered for.

The same number read as an odds ratio, relative risk, or hazard ratio gives different absolute risks, so say which the paper reported — there is no default. The control-arm risk is usually in the abstract.

These probabilities usually run higher than PEGD, and both can be right: PEGD weighs the one effect you postulated against no effect at all, while this analysis lets the effect be any size and asks how big it is. Compare PEGD with P(worthwhile), not with P(benefit).

Numbers & export

Every figure on the Main tab, grouped by the question it answers. The link carries the numbers you entered, so whoever opens it sees the same analysis.


Version 0.4.047

Please cite this page if you find it useful:

Jones PM. Bayesian Reanalysis of Biomedical Research, version 0.4.047, https://shiny.seaturtle.site/bayesian_reanalysis/ Last accessed 2026-10-14

How many patients' outcomes would have to change for this result to cross P = 0.05, the conventional line for statistical significance?


How the result comes apart
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Every patient
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What flipping outcomes does to the probability
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What each arm's true risk could be

Each curve shows how plausible each value of that arm's true risk of the outcome is, given its counts. The peak is near the observed rate, and the curve narrows as the arm gets larger. The vague line above is the probability that the experimental arm's risk is the lower of the two, so the less the curves overlap, the further that line is from 50%.

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Ratios for the experimental arm relative to the control arm
Odds ratio

                        Relative risk
                        

                        
Hazard ratio

                        

Above 1 the outcome was more common in the experimental arm and below 1 less common; which of those you want depends on the outcome, which this calculator does not know.

Bayes factor bound (Sellke–Bayarri–Berger)

                        
Minimum false positive risk

                        

It is a floor: a reader who thought a real effect less likely than not beforehand faces a higher risk than this.


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Philip M Jones
Professor
Department of Anesthesiology & Perioperative Medicine
Mayo Clinic, Jacksonville, Florida, USA
info@algonquinworks.com