Bayesian Modeling Method for an Observational Data Analysis.

Many hypothesis testing and statistical inferential methods learned through clinical epidemiologic studies are based on the so-called “frequentist approach”, which relies on Fisher's and Neyman-Pearson's theories established in the mid-20th century for application in clinical studies. In recent years, however, Bayesian methods are increasingly frequently recognized as being more convenient than frequentist methods for application in many different areas and are being implemented in a variety of clinical studies (1,2). While the use of Bayesian methods has established their essential role in clinical trials, it is pleasing to find that Iwata et al. (3) used this approach to analyze observational and retrospectively collected data with a small sample size. Since our convention to rely on the p value remains controversial (4), as an alternative method, the interval estimation method of the effect size, such as the 95% credible intervals (CrIs) of relative risk or the hazard ratio that can be quantified by the Bayesian method, is considered to be a more important measurement to evaluate the causal effect than before. Considering the broad-range applicability of Bayesian method in simple two-group comparison, such as in the study conducted by Iwata et al. (3), to a variety of clinical datasets, it is vital to review the characteristics of Bayesian modeling method, especially for use in clinical data analyses.

Regarding how the Bayesian modeling differs from the frequentist approach, there are two notable differences. First, the Bayesian method uses prior knowledge as initial input. For instance, if there is a published study with an identical outcome to a new study, the published estimate provides the “initial guess” for the results of an ongoing study. Second, the effect size, e.g., the relative reduction in the risk of death among patients receiving a particular treatment, is obtained as the distribution, which is referred to as the posterior distribution. Tails of posterior distribution give the uncertainty bound, referred to as the 95% CrI, which is the Bayesian method analogue of 95% confidence intervals. Implementing the Bayesian analysis may be the biggest hazard for clinicians, as a computational analysis employing the Markov Chain Monte Carlo (MCMC) method is usually required. However, it should be noted that the utility of statistical packages for MCMC remains a challenge for clinicians as they must study it via short courses [or sometimes even from free online MOOC materials (5)], but once the implementation has been facilitated, the technique remains a strong weapon for data analyses. Recently, a statistical research support system has been launched in Japan, offering statistical consultation advice by hospital statisticians at all university hospitals, as has been previously described by Iwata at al. (3). If clinicians do not belong to university sectors, then establishing an adjunct relationship at a higher education institute would enable them to better utilize the consultation service.

Regarding why the Bayesian method is useful for clinical studies, statistical analyses can remain meaningful even when the available number of patients is limited. In the frequentist approach, with a p>0.05, small sample studies have frequently been judged simply as underpowered. However, as shown by Iwata et al. (3), the probability that one group is superior to the other can be shown using the Bayesian method. In addition, the number of incurable disease patients or critically ill patients being extremely limited is a common problem with the frequentist approach, but such a dataset can be used in an exploratory manner to verify the proof of concept (POC) that may be hypothesized from experimental studies. Furthermore, the Bayesian method has an advantage from an ethical perspective: using previously available information, researchers can justify a reduction in the required sample size. In addition, even when the posterior distribution of an analysis indicates that the effect size is not substantial, that distribution can be used to predict future clinical study results.

An important note is that the results from Bayesian analyses are sometimes quantitatively inconclusive, although researchers may draw practical conclusions based on their additional judgement (e.g. biological plausibility and experimental findings). The results of Bayesian analyses are presented as the posterior distribution, always accompanied by uncertainty bounds. This method with small sample size should thus be regarded as not for offering a conclusive finding to create new evidence but rather for defining the appropriate range of uncertainty, e.g., to supply a “possible” new statistical association between treatment and outcome.

There is no doubt that Bayesian modeling method can utilize data resources more effectively than a frequentist approach. As clearly outlined by Iwata et al. (3), underpowered studies with p＞0.05 can still be regarded as insightful contributory pieces that will help reduce uncertainty. While the use of the Bayesian method for academically designing clinical trials has been well explored by biostatisticians, the key players in the widespread practical use of this method for analyzing observational data should be physicians and not biostatisticians. With assistance from clinical epidemiologists and/or hospital statisticians, readers are encouraged to conduct similar observational studies, even with very small samples. That would fulfill the accountability of clinicians to continuously offer important feedback for society by evaluating the optimal bedside practices.

The author states that he has no Conflict of Interest (COI).