A Bayesian analysis integrating expert beliefs to better understand how new evidence ought to update what we believe: a use case of chiropractic care and acute lumbar disc herniation with early surgery.

Background: A Bayesian approach may be useful in the study of possible treatment-related rare serious adverse events, particularly when there are strongly held opinions in the absence of good quality previous data. We demonstrate the application of a Bayesian analysis by integrating expert opinions with population-based epidemiologic data to investigate the association between chiropractic care and acute lumbar disc herniation (LDH) with early surgery.

Methods: Experts' opinions were used to derive probability distributions of the incidence rate ratio (IRR) for acute LDH requiring early surgery associated with chiropractic care. A 'community of priors' (enthusiastic, neutral, and skeptical) was built by dividing the experts into three groups according to their perceived mean prior IRR. The likelihood was formed from the results of a population-based epidemiologic study comparing the relative incidence of acute LDH with early surgery after chiropractic care versus primary medical care, with sensitive and specific outcome case definitions and surgery occurring within 8- and 12-week time windows after acute LDH. The robustness of results to the community of priors and specific versus sensitive case definitions was assessed.

Results: The most enthusiastic 25% of experts had a prior IRR of 0.42 (95% credible interval [CrI], 0.03 to 1.27), while the most skeptical 25% of experts had a prior IRR of 1.66 (95% CrI, 0.55 to 4.25). The Bayesian posterior estimates across priors and outcome definitions ranged from an IRR of 0.39 (95% CrI, 0.21 to 0.68) to an IRR of 1.40 (95% CrI, 0.52 to 2.55). With a sensitive definition of the outcome, the analysis produced results that confirmed prior enthusiasts' beliefs and that were precise enough to shift prior beliefs of skeptics. With a specific definition of the outcome, the results were not strong enough to overcome prior skepticism.

Conclusion: A Bayesian analysis integrating expert beliefs highlighted the value of eliciting informative priors to better understand how new evidence ought to update prior existing beliefs. Clinical epidemiologists are encouraged to integrate informative and expert opinions representing the end-user community of priors in Bayesian analyses, particularly when there are strongly held opinions in the absence of definitive scientific evidence.