Recommendations for the analysis of individually randomised controlled trials with clustering in one arm - a case of continuous outcomes

Abstract

Background: In an individually randomised controlled trial where the treatment is delivered by a health professional it seems likely that the effectiveness of the treatment, independent of any treatment effect, could depend on the skill, training or even enthusiasm of the health professional delivering it. This may then lead to a potential clustering of the outcomes for patients treated by the same health professional, but similar clustering may not occur in the control arm. Using four case studies, we aim to provide practical guidance and recommendations for the analysis of trials with some element of clustering in one arm.

Methods: Five approaches to the analysis of outcomes from an individually randomised controlled trial with clustering in one arm are identified in the literature. Some of these methods are applied to four case studies of completed randomised controlled trials with clustering in one arm with sample sizes ranging from 56 to 539. Results are obtained using the statistical packages R and Stata and summarised using a forest plot.

Results: The intra-cluster correlation coefficient (ICC) for each of the case studies was small (<0.05) indicating little dependence on the outcomes related to cluster allocations. All models fitted produced similar results, including the simplest approach of ignoring clustering for the case studies considered.

Conclusions: A partially clustered approach, modelling the clustering in just one arm, most accurately represents the trial design and provides valid results. Modelling homogeneous variances between the clustered and unclustered arm is adequate in scenarios similar to the case studies considered. We recommend treating each participant in the unclustered arm as a single cluster. This approach is simple to implement in R and Stata and is recommended for the analysis of trials with clustering in one arm only. However, the case studies considered had small ICC values, limiting the generalisability of these results.

Keywords: Clustering; Individually clustered randomised controlled trials; Randomised controlled trial; Statistical models; Therapist effects.

Fig. 1

Schematic of a trial with clustering in only one arm (the treatment arm) where n ₁,…,n _m is the number of patients in the m treatment clusters (clusters are not necessarily of equal size but this is often fixed in advance) and l is the number of subjects in the control arm

Fig. 2

Summary of models for the analysis of iRCTs with clustering in one arm only y denotes the continuous outcome, i is the patient indicator, j is the cluster indicator, t is the treatment indicator variable (t=1 for the treatment arm and t=0 for the control arm), θ is treatment effect, ε, u and r are error terms

Fig. 3

Box plot of the case studies. Patients with missing outcome data have been removed

Fig. 4

Forest plot of models fitted using R for each of the case studies where RE is random effects, PC is partial clustering, Het. is heteroskedastic model. The vertical, black dashed line represents the target treatment difference. We are not using the primary outcome from the Ulcer case study and so this line is not marked. The vertical, red dotted line marks a zero treatment difference