Bayesian Analysis: Using Prior Information to Interpret the Results of Clinical Trials

INTRODUCTION

This JAMA Guide to Statistics and Methods discusses the Bayesian approach to integrating or updating information from previous studies with newly obtained data to yield a final quantitative summary of the information.

In a study published in JAMA, Laptook et al¹ reported the results of a clinical trial investigating the effect of hypothermia administered between 6 and 24 hours after birth on death and disability from hypoxic-ischemic encephalopathy (HIE). Hypothermia is beneficial for HIE when initiated within 6 hours of birth but administering hypothermia that soon after birth is impractical.² The study by Laptook et al¹ addressed the utility of inducing hypothermia 6 or more hours after birth because this is a more realistic time window given the logistics of providing this therapy. Performing this study was difficult because of the limited number of infants expected to be enrolled. To overcome this limitation, the investigators used a Bayesian analysis of the treatment effect to ensure that a clinically useful result would be obtained even if traditional approaches for defining statistical significance were impractical. The Bayesian approach allows for the integration or updating of prior information with newly obtained data to yield a final quantitative summary of the information. Laptook et al¹ considered several options for the representation of prior information—termed neutral, skeptical, and optimistic priors—generating different final summaries of the evidence.

PRIOR INFORMATION

What Is Prior Information?

Prior information is the evidence or beliefs about something that exist prior to or independently of the data to be analyzed. The mathematical representation of prior information (eg, of beliefs regarding the likely efficacy of hypothermia for HIE 6-24 hours after birth) must summarize both the known information and the remaining uncertainty. Some prior information is quite strong, such as data from many similar patients, and might have little remaining uncertainty or it can be weak or uninformative with substantial uncertainty.

Clinicians routinely interpret the results of a new study in the context of prior work. Are the new results consistent? How can new information be synthesized with the old? Often this synthesis is done by clinicians when they consider the totality of evidence used to treat patients or interpret research studies.

Prior information may be formally incorporated in trial analysis using Bayes theorem, which provides a mechanism for synthesizing information from multiple sources.^3,4 Clear specification of the prior information used and assumptions made need to be reported in the article or appendix to allow transparency in the analysis and reporting of outcomes.

Why Is Prior Information Important?

When large quantities of patient outcome data are available, traditional non-Bayesian (frequentist) and Bayesian approaches for quantifying observed treatment effects will yield similar results because the contribution of the observed data will outweigh that of the prior information. This is ...