Bayesian and Frequentist Comparison for Epidemiologists: A Non Mathematical Application on Logistic Regressions

Background: Statistical frequentist techniques are sometimes misinterpreted or misused, while Bayesian techniques seem to present several practical advantages, such as accommodating small sample sizes, unobserved variables along with measurement errors and incorporating information from previous studies. The primary objective of this study was to evaluate the association between waterpipe dependence and chronic obstructive pulmonary disease (COPD), by comparing frequentist and Bayesian methods’ results. Methods: It is a multicenter case-control study, comparing a group of COPD patients with a control group. COPD diagnosis was held after clinical and paraclinical testing, while a standardized questionnaire was used to evaluate smoking history. Both frequentist and Bayesian analyses were performed. Results: Although carried out on the same dataset, the results quantitatively differed between the frequentist and Bayesian analysis. Whenever the frequentist results were clear cut such as in case of cigarette smoking association with COPD, performing the MCMC method helped to increase the accuracy of the results, but did not change the direction of hypothesis acceptance, except in doubtful cases. When the frequentist p-value was ≤0.100, such as in case of smoking more than 15 waterpipe-years, the MCMC method improved deciding between the null and alternative hypothesis. Conclusion: The Bayesian approach may have advantages over the frequentist one, particularly in case of a low power of the frequentist analysis, due to low sample size or sparse data; the use of informative priors might be particularly useful in narrowing credible interval and precising the choice between the null and alternative hypothesis. In case of borderline frequentist results, the MCMC method may be more conservative, particularly without priors. However, in case of large sample sizes, using frequentist methods is preferred.