PPubMed3 Mar 2026

Bayesian design and analysis of two-arm cluster randomised trials using assurance: Extension to binary outcomes and comparison of Markov chain Monte Carlo and Integrated Nested Laplace Approximations

Abdullah Aloufi, Kevin J Wilson, Nina Wilson, Lisa Shaw, Christopher Price

Abstract

The elicited design prior distributions associated with the thrombectomy rate from expert 1, expert 2 and the average are given in [table1-17407745261421842] and plotted in [fig5-17407745261421842]. We use these to calculate the assurance, and hence sample size, with a target assurance value of 90%. In this case, we used INLA for our assurance and sample size calculations based on the general conclusions from the simulation comparison result. The estimated sample sizes using the design prior distributions from expert 1, expert 2 and the average are 4800, 1650 and 3150, respectively. In this ca

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Bayesian assurance is extended to binary outcomes in two‑arm cluster randomised trials, and INLA is shown to provide faster yet accurate inference compared with MCMC, guiding efficient sample‑size planning.

What’s new

i.Extended Bayesian assurance methodology to binary outcomes for two‑arm CRTs
ii.Compared MCMC and INLA for inference on treatment effects, evaluating accuracy and computation time
iii.Provided practical guidance on when to use MCMC versus INLA based on cluster number and sample size
iv.Applied the approach to the SPEEDY trial using expert‑elicited priors to calculate required sample sizes
v.Demonstrated that INLA scales better to large trials while maintaining accuracy

How they did it

The authors used a two‑loop Monte Carlo scheme to compute assurance, drawing design priors in the outer loop and obtaining posterior treatment‑effect samples via MCMC in the inner loop. They replaced the inner‑loop MCMC with Integrated Nested Laplace Approximations (INLA) and ran simulation studies across varying numbers of clusters, ICC values, and total sample sizes, then illustrated the workflow on the SPEEDY trial.

What they found

For C=8 clusters, rho=0.05, INLA matched MCMC with 10,000 posterior samples in accuracy; MCMC with only 100 samples was inaccurate for N=2,000 and 10,000
For C=12 clusters, rho=0.01, MCMC was generally more accurate, but INLA’s runtime grew much slower than MCMC as N increased
INLA’s computation time scaled well with larger sample sizes, while MCMC became substantially slower, especially with more clusters
Using expert‑elicited priors, the assurance calculation yielded required sample sizes for the SPEEDY trial’s continuous and binary co‑primary outcomes

Caveats

✕Full MCMC remains computationally intensive for each Monte Carlo iteration
✕INLA provides an approximation that may be less accurate in very small sample or extreme ICC settings
✕Simulation scenarios were limited to specific linear mixed‑effects models and a few cluster/ICC configurations
✕Results depend on the quality of elicited prior distributions, which may vary between experts

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