Unifying the analysis of continuous and categorical measures of weight loss and incorporating group effect: a secondary re-analysis of a large cluster randomized clinical trial using Bayesian approach

Abstract

Background: Although frequentist paradigm has been the predominant approach to clinical studies for decades, some limitations associated with the frequentist null hypothesis significance testing have been recognized. Bayesian approaches can provide additional insights into data interpretation and inference by deriving posterior distributions of model parameters reflecting the clinical interest. In this article, we sought to demonstrate how Bayesian approaches can improve the data interpretation by reanalyzing the Rural Engagement in Primary Care for Optimizing Weight Reduction (REPOWER).

Methods: REPOWER is a cluster randomized clinical trial comparing three care delivery models: in-clinic individual visits, in-clinic group visits, and phone-based group visits. The primary endpoint was weight loss at 24 months and the secondary endpoints included the proportions of achieving 5 and 10% weight loss at 24 months. We reanalyzed the data using a three-level Bayesian hierarchical model. The posterior distributions of weight loss at 24 months for each arm were obtained using Hamiltonian Monte Carlo. We then estimated the probability of having a higher weight loss and the probability of having greater proportion achieving 5 and 10% weight loss between groups. Additionally, a four-level hierarchical model was used to assess the partially nested intervention group effect which was not investigated in the original REPOWER analyses.

Results: The Bayesian analyses estimated 99.5% probability that in-clinic group visits, compared with in-clinic individual visits, resulted in a higher percent weight loss (posterior mean difference: 1.8%[95% CrI: 0.5,3.2%]), a greater probability of achieving 5% threshold (posterior mean difference: 9.2% [95% CrI: 2.4, 16.0%]) and 10% threshold (posterior mean difference: 6.6% [95% CrI: 1.7, 11.5%]). The phone-based group visits had similar result. We also concluded that including intervention group did not impact model fit significantly.

Conclusions: We unified the analyses of continuous (the primary endpoint) and categorical measures (the secondary endpoints) of weight loss with one single Bayesian hierarchical model. This approach gained statistical power for the dichotomized endpoints by leveraging the information in the continuous data. Furthermore, the Bayesian analysis enabled additional insights into data interpretation and inference by providing posterior distributions for parameters of interest and posterior probabilities of different hypotheses that were not available with the frequentist approach.

Trial registration: ClinicalTrials.gov Identifier NCT02456636 ; date of registry: May 28, 2015.

Keywords: Bayesian paradigm; Hierarchical model; Randomized clinical trial.

Conflict of interest statement

None.

© 2022. The Author(s).

Figures

Fig. 1

Posterior distributions of the expected weight loss(%) (A) and posterior distributions of the absolute difference in weight loss(%) when compared with in-clinic individual visits (B) at 24 months

Fig. 2

Posterior distributions of the probability of achieving 5% weight loss (A) and Posterior distributions of the absolute difference in the probability of achieving 5% weight loss when compared with in-clinic individual visits (B)

Fig. 3

Posterior distributions of the probability of achieving 10% weight loss (A) and Posterior distributions of the absolute difference in the probability of achieving 10% weight loss when compared with in-clinic individual visits (B)