Use of information criteria for selecting a correlation structure for longitudinal cluster randomised trials

Background: When designing and analysing longitudinal cluster randomised trials, such as the stepped wedge, the similarity of outcomes from the same cluster must be accounted for through the choice of a form for the within-cluster correlation structure. Several choices for this structure are commonly considered for application within the linear mixed model paradigm. The first assumes a constant intra-cluster correlation for all pairs of outcomes from the same cluster (the exchangeable/Hussey and Hughes model); the second assumes that correlations of outcomes measured in the same period are higher than outcomes measured in different periods (the block exchangeable model) and the third is the discrete-time decay model, which allows the correlation between pairs of outcomes to decay over time. Currently, there is limited guidance on how to select the most appropriate within-cluster correlation structure. Methods: We simulated continuous outcomes under each of the three considered within-cluster correlation structures for a range of design and parameter choices, and, using the ASReml-R package, fit each linear mixed model to each simulated dataset. We evaluated the performance of the Akaike and Bayesian information criteria for selecting the correct within-cluster correlation structure for each dataset. Results: For smaller total sample sizes, neither criteria performs particularly well in selecting the correct within-cluster correlation structure, with the simpler exchangeable model being favoured. Furthermore, in general, the Bayesian information criterion favours the exchangeable model. When the cluster auto-correlation (which defines the degree of dependence between observations in adjacent time periods) is large and number of periods is small, neither criteria is able to distinguish between the block exchangeable and discrete time decay models. However, for increasing numbers of clusters, periods, and subjects per cluster period, both the Akaike and Bayesian information criteria perform increasingly well in the detection of the correct within-cluster correlation structure. Conclusions: With increasing amounts of data, be they number of clusters, periods or subjects per cluster period, both the Akaike and Bayesian information criteria are increasingly likely to select the correct correlation structure. We recommend that if there are sufficient data available when planning a trial, that the Akaike or Bayesian information criterion is used to guide the choice of within-cluster correlation structure in the absence of other compelling justifications for a specific correlation structure. We also suggest that researchers conduct supplementary analyses under alternate correlation structures to gauge sensitivity to the initial choice.