Bayesian data analysis: estimating the efficacy of T'ai Chi as a case study

Bayesian inference provides a formal framework for updating knowledge by combining prior knowledge with current data. Over the past 10 years, the Bayesian paradigm has become a popular analytic tool in health research. Although the nursing literature contains examples of Bayes' theorem applications to clinical decision making, it lacks an adequate introduction to Bayesian data analysis.

Bayesian data analysis is introduced through a fully Bayesian model for determining the efficacy of tai chi as an illustrative example. The mechanics of using Bayesian models to combine prior knowledge, or data from previous studies, with observed data from a current study are discussed.

The primary outcome in the illustrative example was physical function. Three prior probability distributions (priors) were generated for physical function using data from a similar study found in the literature. Each prior was combined with the likelihood from observed data in the current study to obtain a posterior probability distribution. In each case, the posterior distribution showed that the probability that the control group is better than the tai chi treatment group was low.

Bayesian analysis is a valid technique that allows the researcher to manage varying amounts of data appropriately. As advancements in computer software continue, Bayesian techniques will become more accessible. Researchers must educate themselves on applications for Bayesian inference, as well as its methods and implications for future research.