Background

Typical advice on the design and analysis of cluster randomized trials (C-RCTs) focuses on allowance for the clustering at the level of the unit of allocation. However often C-RCTs are also organised spatially as may occur in the fields of Public Health and Primary Care where populations may even overlap.

Methods

We allowed for spatial effects on the error variance by a multiple membership model. These are a form of hierarchical model in which each lower level unit is a member of more than one higher level unit. Membership may be determined through adjacency or through Euclidean distance of centroids or in other ways such as the proportion of overlapping population. Such models may be estimated for Normal, binary and Poisson responses in Stata (v10 or above) as well as in WinBUGS or MLWin. We used this to analyse a dummy trial and two real, previously published cluster-allocated studies (one allocating general practices within one City and the other allocating general practices within one County) to investigate the extent to which ignoring spatial effects affected the estimate of treatment effect, using different methods for defining membership with Akaike's Information Criterion to determine the "best" model.

Results

The best fitting model included both a fixed North-South gradient and a random cluster effect for the dummy RCT. For one of the real RCTs the best fitting model included both a random practice effect plus a multiple membership spatial term, while for the other RCT the best fitting model ignored the clustering but included a fixed North-South gradient. Alternative models which fitted only slightly less well all included spatial effects in one form or another, with some variation in parameter estimates (greater when less well fitting models were included).

Conclusions

These particular results are only illustrative. However, we believe when designing C-RCTs in a primary care setting the possibility of spatial effects should be considered in relation to the intervention and response, as well as any explanatory effect of fixed covariates, together with any implications for sample size and methods for planned analyses.