Theory and practical use of Bayesian methods in interpreting clinical trial data: a narrative review

Abstract

The critical reading of scientific articles is necessary for the daily practice of evidence-based medicine. Rigorous comprehension of statistical methods is essential, as reflected by the extensive use of statistics in the biomedical literature. In contrast to the customary frequentist approach, which never uses or gives the probability of a hypothesis, Bayesian theory uses probabilities for both hypotheses and data. This statistical approach is increasingly used for analyses of clinical trial data and for applied machine learning. The aim of this review is to compare general Bayesian concepts with frequentist methods to facilitate a better understanding of Bayesian theory for readers who are not familiar with this approach. The review is intended to be used in combination with a checklist we have devised for reading reports analysed by Bayesian methods. We compare and contrast the different approaches of Bayesian vs frequentist statistical methods by considering data from a clinical trial that lends itself to this comparative approach.

A consensus checklist to help clinicians interpret clinical trial results analysed by Bayesian methods

“…The interested clinician may consult additional material further explaining the Bayesian method. 16 The presence in a given paper of all of the items in our checklist is not sufficient to guarantee that the study is statistically correct from all its aspects. To check this point, indepth comprehension of the statistical part is required, and our checklist only allows for ensuring that the required items identified are duly presented in the article.…”

“…The checklist is necessary but not sufficient for determining the quality of a Bayesian trial, which explains why we have created another document designed to help the interested reader better understand the main concepts of Bayesian methods. 16 We consider that results involving the use of Bayesian analysis that do not describe three essential items in the statistics section (prior specified, source of the prior [when the prior is informative], presentation of the point estimate and its credible interval) should be interpreted with caution.…”

“…'Comprehension' refers to the fact that a missing item may be a source of bias or omission, and the reader must search for this bias. 16 Step 4. Selection and reformulation of items by the working group…”

“…For this secondary goal, the general concepts of the Bayesian analysis are described in an accompanying publication. 16 To illustrate and clarify each item of our Bayesian interpretation checklist, we refer to a recently published trial with results analysed by Bayesian methods, the IMMERSION trial. 17…”

Interpreting the results of clinical trials, embracing uncertainty: A Bayesian approach

“…Using a Bayesian approach of inference, new trial results are considered in the context of existing information (please refer to the Appendix for an explanation of Bayes theorem in an A/B test as used in this text). It aims to update current knowledge or the prior probability of trial results gained from previous studies into a posterior probability revised by the new trial result 8‐11 . The belief in the prior probability will, and rightly so, vary among clinicians but the Bayesian approach appears intuitive to the well‐informed clinician eager to consider new trial data 12 .…”