Sample size calculation for stepped-wedge cluster-randomized trials with more than two levels of clustering

Power and sample size calculation formulas for stepped-wedge trials with two levels (subjects within clusters) are available. However, stepped-wedge trials with more than two levels are possible. An example is the CHANGE trial which randomizes nursing homes (level 4) consisting of nursing home wards (level 3) in which nurses (level 2) are observed with respect to their hand hygiene compliance during hand hygiene opportunities (level 1) in the care of patients. We provide power and sample size methods for such trials and illustrate these in the setting of the CHANGE trial.

We extend the original sample size methodology derived for stepped-wedge trials based on a random intercepts model, to accommodate more than two levels of clustering. We derive expressions that can be used to determine power and sample size for p levels of clustering in terms of the variances at each level or, alternatively, in terms of intracluster correlation coefficients. We consider different scenarios, depending on whether the same units in a particular level are repeatedly measured as a cohort sample or whether different units are measured cross-sectionally.

A simple variance inflation factor is obtained that can be used to calculate power and sample size for continuous and by approximation for binary and rate outcomes. It is the product of (1) variance inflation due to the multilevel structure and (2) variance inflation due to the stepped-wedge manner of assigning interventions over time. Standard and non-standard designs (i.e. so-called "hybrid designs" and designs with more, less, or no data collection when the clusters are all in the control or are all in the intervention condition) are covered.

The formulas derived enable power and sample size calculations for multilevel stepped-wedge trials. For the two-, three-, and four-level case of the standard stepped wedge, we provide programs to facilitate these calculations.