Journal Article

Evaluating the performance of Bayesian and restricted maximum likelihood estimation for stepped wedge cluster randomized trials with a small number of clusters

Carlin, John B., Kasza, Jessica, Forbes, Andrew B., Heritier, Stephane, Grantham, Kelsey L.

2022

Overview

Background Stepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials. Methods We conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect. Results Both REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias. Conclusions The use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

• Publisher: BioMed Central,BioMed Central Ltd,Springer Nature B.V,BMC
• Subject: Analysis / Approximation / Bayes Theorem / Bayesian inference / Bayesian statistical decision theory / Cluster Analysis / Cluster randomized trial / Computer Simulation / Health Sciences / Humans / Intracluster correlation / Likelihood Functions / Medical research / Medicine / Medicine & Public Health / Methods / Randomized Controlled Trials as Topic / Research Design / Research methodology / Restricted maximum likelihood / Sample Size / Selection methods (Regression analysis) / Simulation / Simulation methods / Simulation study / Statistical Theory and Methods / Statistics for Life Sciences / Stepped wedge / Theory of Medicine/Bioethics