gms | German Medical Science

Introduction: In health services research complex interventions are more and more evaluated in intervention studies with a cluster-randomized stepped wedge design. Clusters are randomized to several different sequence groups, each group of clusters starts with the control condition and changes to the intervention at a specific cross-over point. While individual randomisation is precluded by the character of the intervention, the choice for stepped wedge design is driven by promise of increased efficiency in comparison to a parallel design. It allows for efficiently drawing information from comparison of intervention with control both within clusters and between clusters. Although similar in character to a classical cross over study applied to clusters, it is not evident how aggregated data for each cluster and period enter in to the treatment effect estimate.

Methods: We therefore propose a tool for visualising the contribution of each cluster period mean of the outcome to the treatment effect estimated. In the case of continuous outcome a linear mixed model is set up, that allows for a fixed period effect (i.e. a categorical time effect) a random cluster effect, a fixed intervention effect and, possibly, a random cluster by intervention interaction effect. If the random effects covariance parameters are known, the maximum likelihood estimate of the parameter vector under normality assumptions may be written as a generalized weighted least square estimate. In particular, the intervention effect estimate can be presented as linear combination of cluster period means. The linear coefficients disclose the information content of each cluster period and are displayed in a rectangular scheme with symbols of different size and coloured according to the sign of the coefficient. Typically, intervention periods obtain a positive sign and control periods obtain a negative sign. If covariance parameters are unknown, there estimates are plugged into the afore-mentioned expressions. The method is generalized to the case of binary outcomes by exploiting the score equations at the point of convergence in the framework of generalized linear mixed models.

Results: The method is illustrated for several instances of stepped wedge designs, outcome scales and model parameters. Two phenomena become apparent: periods in distance to the crossover point are less influential than those in its proximity, and periods with a more balanced distribution of intervention and control condition have more influence.

Discussion: The results also suggest that in some situations, a stepped wedge design may be made more efficient by dropping the periods that are most distant to cross over points. But that has to be weighed against the option of being able to assess learning effects and whether intervention effects fade out later on after their introduction.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.