Bayesian Models for N-of-1 Trials.

We describe Bayesian models for data from N-of-1 trials, reviewing both the basics of Bayesian inference and applications to data from single trials and collections of trials sharing the same research questions and data structures. Bayesian inference is natural for drawing inferences from N-of-1 trials because it can incorporate external and subjective information to supplement trial data as well as give straightforward interpretations of posterior probabilities as an individual's state of knowledge about their own condition after their trial. Bayesian models are also easily augmented to incorporate specific characteristics of N-of-1 data such as trend, carryover, and autocorrelation and offer flexibility of implementation. Combining data from multiple N-of-1 trials using Bayesian multilevel models leads naturally to inferences about population and subgroup parameters such as average treatment effects and treatment effect heterogeneity and to improved inferences about individual parameters. Data from a trial comparing different diets for treating children with inflammatory bowel disease are used to illustrate the models and inferences that may be drawn. The analysis shows that certain diets were better on average at reducing pain, but that benefits were restricted to a subset of patients and that withdrawal from the study was a good marker for lack of benefit.