[Paper Review] Bayesian design and analysis of two-arm cluster randomised trials using assurance

Kevin J Wilson|arXiv (Cornell University)|Aug 26, 2022

Statistical Methods and Bayesian Inference4 citations

TL;DR

This paper proposes a Bayesian sample size determination method for two-arm cluster randomized trials with continuous outcomes, using assurance based on posterior inference via Markov chain Monte Carlo (MCMC). It introduces a two-loop Monte Carlo scheme to evaluate assurance under prior uncertainty, demonstrating that incorporating informative priors can reduce required sample sizes compared to frequentist power calculations, especially when prior belief in a clinically meaningful effect is strong.

ABSTRACT

We consider the design of a two-arm superiority cluster randomised controlled trial (RCT) with a continuous outcome. We detail Bayesian inference for the analysis of the trial using a linear mixed-effects model. The treatment is compared to control using the posterior distribution for the treatment effect. We develop the form of the assurance to choose the sample size based on this analysis, and its evaluation using a two loop Monte Carlo sampling scheme. We assess the proposed approach, considering the effect of different forms of prior distribution, and the number of Monte Carlo samples needed in both loops for accurate determination of the assurance and sample size. Based on this assessment, we provide general advice on each of these choices. We apply the approach to the choice of sample size for a cluster RCT into post-stroke incontinence, and compare the resulting sample size to those from a power calculation and assurance based on a Wald test for the treatment effect. The Bayesian approach to design and analysis developed in this paper can offer advantages in terms of an increase in the robustness of the chosen sample size to parameter mis-specification and reduced sample sizes if prior information indicates the treatment effect is likely to be larger than the minimal clinically important difference.

Motivation & Objective

• To develop a Bayesian approach to sample size determination for two-arm cluster RCTs with continuous outcomes.
• To integrate prior uncertainty in nuisance parameters (ICC, variance) and treatment effect into sample size calculation via assurance.
• To compare the proposed Bayesian assurance method with frequentist power calculations and hybrid approaches using Wald tests.
• To evaluate the impact of different analysis prior distributions and Monte Carlo sampling strategies on assurance accuracy and efficiency.
• To apply the method to the ICONS trial on post-stroke incontinence and demonstrate practical advantages in sample size reduction.

Proposed method

• Uses a linear mixed-effects model with fixed treatment effect and random cluster effects for analysis.
• Performs Bayesian inference via MCMC to obtain posterior distributions for the treatment effect.
• Employs a two-loop Monte Carlo simulation: outer loop samples from the design prior, inner loop performs MCMC using analysis priors.
• Defines assurance as the probability that the posterior probability of treatment efficacy exceeds a threshold, conditional on the minimal clinically important difference (MCID).
• Uses conjugate inverse-gamma priors for variance components and evaluates hyperparameter choices (e.g., 0.1, L=1000) for robustness.
• Recommends 1000 outer and inner loop samples and 35 repeated calculations to stabilize sample size estimates.

Experimental results

Research questions

• RQ1 How can assurance be redefined in a fully Bayesian framework for cluster RCTs, where final analysis is based on posterior inference rather than hypothesis testing?
• RQ2 What is the impact of different analysis prior distributions on the accuracy and efficiency of assurance-based sample size calculations?
• RQ3 How do the number of Monte Carlo samples in the outer and inner loops affect the stability and precision of the assurance estimate?
• RQ4 How does the choice of design prior for the treatment effect influence the required sample size, especially when prior belief in efficacy exceeds the MCID?
• RQ5 Can a fully Bayesian design approach reduce sample size compared to traditional power calculations or hybrid methods that use Bayesian design with frequentist analysis?

Key findings

• The fully Bayesian approach can reduce required sample size compared to standard power calculations when prior belief in a treatment effect above the MCID is strong.
• When the design prior mean for the treatment effect is ≥3.5 and prior standard deviation is <1.8, the Bayesian method yields smaller sample sizes than both power and hybrid approaches.
• Using 1000 outer and 1000 inner loop Monte Carlo samples ensures accurate and efficient assurance estimation.
• Repeating the sample size calculation 35 times and selecting the modal result leads to a high probability of identifying the correct sample size.
• The Bayesian analysis approach, when combined with assurance, can lead to further sample size reductions compared to hybrid methods using frequentist inference.
• The method demonstrates that incorporating prior uncertainty in ICC and variance components improves robustness to parameter mis-specification.