Bayesian vs Frequentist Statistics: A Clinician’s Guide (Lessons from the TIGRIS Trial)

We briefly touched on Bayesian statistics in our latest podcast episode (https://youtu.be/cGu1QEmMRmQ?si=OR6AjFcu60_2Q-F8). In this post, we’ll build on that discussion and unpack some of the key concepts—before exploring how the TIGRIS trial applied (and stretched) these ideas.

Frequentist vs Bayesian: A Different Way of Asking the Question

At its core, the biggest difference between frequentist and Bayesian statistics lies in the question being asked.

In a conventional frequentist framework, the question is:

What is the probability of observing these results (or more extreme), assuming the null hypothesis is true?

If this probability (the p-value) is less than 5%—the conventional Type I error threshold—we reject the null hypothesis.

While statistically rigorous, this approach is not particularly intuitive. It answers a somewhat indirect question that clinicians rarely ask in practice.

In contrast, the Bayesian approach asks:

What is the probability that a given hypothesis is true, given the observed data?

This is far more aligned with how clinicians think and make decisions.

Priors and Posteriors: The Core of Bayesian Thinking

A defining feature of Bayesian analysis is the use of priors.

We begin with a prior probability distribution, based on existing knowledge (previous studies, clinical experience, or assumptions).
We then collect new data from a study or trial.
Finally, we combine these to generate an updated posterior probability.

If this feels familiar, it should. Clinicians use this reasoning every day.

Consider diagnostic testing:

You start with a pre-test probability
You interpret the test result
You arrive at a post-test probability

That is Bayesian thinking in practice.

Types of Priors

Several types of priors are commonly encountered:

Informative vs Non-informative priors

Informative priors incorporate existing data and meaningfully influence the results.
Non-informative priors make minimal assumptions, allowing the trial data to dominate the posterior.

Optimistic vs pessimistic priors

Optimistic priors assume a beneficial effect of the intervention.
Pessimistic priors assume little or no benefit (or even harm).

These are essentially directional forms of informative priors.

What Did the TIGRIS Trial Do Differently?

The TIGRIS trial (https://www.thelancet.com/journals/lanres/article/PIIS2213-2600(26)00047-0/fulltext) used a Bayesian framework—but with an important twist.

Rather than simply using prior data to inform the prior distribution, the investigators went a step further. They incorporated patients from a post hoc “treatable subgroup” (https://pmc.ncbi.nlm.nih.gov/articles/PMC6280819/)of the EUPHRATES trial (those with endotoxin activity levels between 0.60–0.89) directly into their analytical framework.

In effect, TIGRIS was positioned not as a completely independent trial, but as a continuation of this subgroup.

A “Continuation” Model

The investigators justified this approach by:

Closely matching inclusion and exclusion criteria between TIGRIS and the EUPHRATES subgroup
Arguing that the populations were sufficiently exchangeable

However, they acknowledged potential differences:

Changes in care over time
Residual differences in patient characteristics

To account for this, they down-weighted the EUPHRATES data to 75%, rather than treating it as fully equivalent. They also conducted sensitivity analyses with varying weights.

Why This Matters: Sensitivity to Assumptions

This approach has important implications.

For the 28-day mortality outcome, the posterior probability drops below 95% when the weight assigned to the EUPHRATES subgroup falls to 72% or lower.
In contrast, 90-day mortality results appear more robust—but this outcome was reportedly added later, at the request of the FDA.

Equally important is what was not done:

The analysis did not explore a range of alternative priors (e.g., non-informative, weakly informative, or pessimistic priors)
Instead, it relied heavily on the EUPHRATES subgroup—effectively an optimistic prior

Interpreting TIGRIS: A Balanced View

The TIGRIS approach sits at the edge of conventional trial design.

On one hand:

It reflects a pragmatic approach and an efficient use of existing data- especially when recruiting patients with a specific endotype or phenotype, which can be challenging
It aligns with Bayesian principles of cumulative learning

On the other:

It blurs the boundary between independent trials
It places substantial weight on a post hoc subgroup
It makes results sensitive to assumptions about how much to trust prior data

A broader exploration of priors would have strengthened interpretability and confidence in the findings.

Final Thoughts

Bayesian methods offer a powerful and intuitive framework for clinical research. But as TIGRIS illustrates, how priors are constructed and used can meaningfully shape conclusions.

Understanding these nuances is essential—not just for statisticians, but for clinicians interpreting the evidence.