The use of random effects models to allow for clustering in individually randomized trials

Background We describe different forms of clustering that may occur in individually randomized trials, where the observed outcomes for different individuals cannot be regarded as independent. We propose random effects models to allow for such clustering, across a range of contexts and trial designs, and investigate their effect on estimation and interpretation of the treatment effect.

Methods We apply our proposed models to two individually randomized trials with potential for clustering, a trial of teleconsultation in hospital referral (the main outcome being offer of a further hospital appointment) and a trial of exercise therapy delivered by physiotherapists for low back pain (the outcome being a back pain score). Extensions to the methods include the possibility of explaining heterogeneity between clusters using cluster level characteristics and the potential dilution of cluster effects due to noncompliance.

Results In the teleconsultation trial, the odds ratio was significant (1.52, 95% CI 1.27 to 1.82) when clustering was ignored, but smaller and nonsignificant (1.36, 95% CI 0.85 to 2.13) when clustering by hospital consultant was taken into account. The 95% range of estimated treatment effects across consultants was from 0.21 to 8.76. This variability was only partially explained by the specialty of the consultant. In the back pain trial, although there was an overall benefit of exercise (change of 20.51 points on the back pain score) and little evidence of clustering, the estimated treatment effects for different physiotherapists ranged from 21.26 to +0.26 points.

Conclusions Clustering is an important issue in many individually randomized trials. Ignoring it can lead to underestimates of the uncertainty and too extreme P-values. Even when there is little apparent heterogeneity across clusters, it can still have a large impact on the estimation and interpretation of the treatment effect.