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A Primer on Bayesian Analysis for Non-Statisticians

April 25, 2024

Written by Seth Walsh-Blackmore

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Bayesian analysis is becoming more common in clinical research and offers advantages over traditional frequentist methods when used appropriately. This primer can help understand Bayesian analysis better.

I’m optimistic this will be highly informative.
You are likely familiar with frequentist statistics, such as the confidence interval and the p-value. Bayesian methods are less standard in medical training but are becoming more common in clinical research. This paper offers a Bayesian crash course for providers.

A frequentist analysis only uses data from the study sample. Bayesian approaches, however, also incorporate outside information. An important term to understand is the prior distribution or “prior .”It is determined from the knowledge available before the current study. The prior influences the posterior probability or “posterior,” which means an updated probability distribution after observing new data. In other words, the type and magnitude of prior affects the results.

Basic categories of prior distributions:

  • Non-informative: Has no prior adjustment. 
  • Informative: Has an adjustment, stratified by how much information exists (vaguely, moderately, highly, etc.), which describes the weight of its adjustment as below.
  • Neutral: Adjusts for a baseline probability of an outcome but without inferring differences between groups.
  • Optimistic: Adjusts each group towards what is expected.
  • Pessimistic: Adjusts each group against what is expected.

 Example prior distributions for the probability of chronic pain when acute pain scores are > 3.

Determining the priors is called elicitation and should be done with expert consultation. When done correctly, it increases precision, especially in small samples. See example tables.

Posterior distributions represent a probability density of the true effect and derive a credible interval within which it exists. This is used analogously to a confidence interval to determine significance.

Though this example actually had probability as an outcome, the method can be used for most types of effect measures and variables. Not used in the example is the Bayes Factor, which is similar to the p-value for hypothesis testing.

How will this change my practice?
If done correctly, adding precision to a small prospective cohort or RCT is an excellent application of this method.

Source
Introduction to Bayesian Analyses for Clinical Research. Anesth Analg. 2024;138(3):530-541. doi:10.1213/ANE.0000000000006696