Bayesian Statistics: A Walkthrough with a Simulated Dental Dataset.

Abstract

When a clinician sees a patient with a complication, they often go through a Bayesian style of logic, most likely without even knowing it. They assess whether they have seen the complication before, provide an intervention based on historical knowledge of what leads to improvement, and then later assess how the intervention is performed. This process, which is routine in clinical practice, can be mathematically extended into an alternative way of performing statistical analyses to assess clinical research. However, this process is contrary to the most common statistical methods used in dental research: frequentist statistics. Though powerful, frequentist methods come with advantages and disadvantages. Bayesian statistics are an alternative method, one that mirrors how we as researchers think and process new information. In this primer, a walkthrough of Bayesian statistics is performed by constructing priors, defining the likelihood, and using the posterior result to draw conclusions on parameters of interest. The motivating example for this walkthrough was a Bayesian analog to logistic regression, fit using a simulated dental-related dataset of 50 patients who received a dental implant-classified as either within or outside normal limits-from practitioners who did or did not receive a training course in implant placement. The results of the Bayesian and traditional frequentist logistic regression models were compared, resulting in very similar conclusions regarding which parameters seemed to be strongly associated with the outcome.