8. Supplementary material (statistical details of model extensions)
SEPARATION, DECAY
Correlation structures in an SW-CRCT design are more complicated than a parallel CRT where measurements are taken at a single cross-section only. While Hussey and Hughes’s model is commonly used for the analysis of SW-CRCT trials, it makes several assumptions such as the same underlying time trend across all the clusters, exchangeable or uniform correlation structure (observations within any cluster share the same correlation structure irrespective of how far apart in time measurement are taken) and intra-cluster correlation (ICC) is independent of time period of measurement. However, these assumptions may be untenable, and correlations might decay with increasing separation in time between observations, which can be studied in the alternative discrete-time decay model by Hooper (model extension 1). Thus, to handle the complex correlation structure in our study we performed model extensions.Our study may be regarded as a multi-centric study as there are many clusters and each cluster is exposed and unexposed to intervention therefore, treatment-effect heterogeneity can be investigated by including treatment by cluster interaction (model extension 2) This model allows the variability between clusters to differ between intervention and control periods. In addition to treatment heterogeneity across clusters, treatment effect might vary with time as SW-CRCT runs over multiple time periods and can be investigated using a treatment-by-time interaction (model extension 3). This model explores the interaction between intervention and time period, and modifies fixed effect components only with no modifications to the correlation structure. We present data on these model extensions exploring the sensitivities to deviations from the basic assumptions in Hughes and Hussey’s model around time points, treatment effect, and correlation structure.