A Bayesian statistics tutorial for clinical research: Prior distributions and meaningful results for small clinical samples

Abstract

Objectives: Bayesian statistics provides an effective, reliable approach for research with small clinical samples and yields clinically meaningful results that can bridge research and practice. This tutorial demonstrates how Bayesian statistics can be effectively and reliably implemented with a small, heterogeneous participant sample to promote reproducible and clinically relevant research. Methods/Results: We tested example research questions pertaining to language and clinical features in autism spectrum disorder (ASD; n = 20), a condition characterized by significant heterogeneity. We provide step-by-step instructions and visualizations detailing how to (1) identify and develop prior distributions from the literature base, (2) evaluate model convergence and reliability, and (3) compare models with different prior distributions to select the best performing model. Moreover, in step three, we demonstrate how to determine whether a sample size is sufficient for reliably interpreting model results. We also provide instructions detailing how to examine results with varied bounds of clinical interest, such as the probability that an effect will reflect at least one standard deviation change in scores on a standardized assessment. This information facilitates generalization and application of Bayesian results to a variety of clinical research questions and settings. Conclusion: The tutorial concludes with suggestions for future clinical research, ensuring the utility of our step-by-step instructions for a broad clinical audience.