Bayesian analysis of randomized controlled trials

Objective This article is an introduction to Bayesian data analysis for empirical researchers in the field of clinical psychology, focusing on applications for the study of eating disorders. We summarize the intuition and methodology of Bayesian data analysis and motivate its use for analyzing Randomized Controlled Trials (RCT). We demonstrate the strengths of the approach through the analysis of a Cognitive Behavioral Therapy RCT on the influence of a smartphone application on binge‐eating disorder (BED) and bulimia nervosa. Method We fit a multilevel Poisson regression model on outcome variable Objective Bulimic Episodes (OBE) as a function of the treatment and other covariates. OBE is a discrete count variable and the Poisson model fits well. The multilevel structure accounts for individual and time‐varying effects. Results Our analysis suggests that the smartphone application causes a reduction in the instances of OBE for patients in the initial weeks, but the effect may wear off by the end of the treatment period. Bayesian methods allow us to obtain heterogeneous treatment effects for different individuals and stages of the therapy while explicitly modeling uncertainty around these effects. Discussion We conclude that Bayesian methods are a powerful tool for incorporating data and prior information into models. They have the potential to improve analyses of RCTs in eating disorders given small sample sizes, small effect size, abundant prior information, heterogeneous participants, and experimental design. These methods are useful for empirical researchers, particularly clinical psychologists.