Stepped-wedge cluster randomised controlled trials: a generic framework including parallel and multiple-level designs

Abstract

Stepped-wedge cluster randomised trials (SW-CRTs) are being used with increasing frequency in health service evaluation. Conventionally, these studies are cross-sectional in design with equally spaced steps, with an equal number of clusters randomised at each step and data collected at each and every step. Here we introduce several variations on this design and consider implications for power. One modification we consider is the incomplete cross-sectional SW-CRT, where the number of clusters varies at each step or where at some steps, for example, implementation or transition periods, data are not collected. We show that the parallel CRT with staggered but balanced randomisation can be considered a special case of the incomplete SW-CRT. As too can the parallel CRT with baseline measures. And we extend these designs to allow for multiple layers of clustering, for example, wards within a hospital. Building on results for complete designs, power and detectable difference are derived using a Wald test and obtaining the variance-covariance matrix of the treatment effect assuming a generalised linear mixed model. These variations are illustrated by several real examples. We recommend that whilst the impact of transition periods on power is likely to be small, where they are a feature of the design they should be incorporated. We also show examples in which the power of a SW-CRT increases as the intra-cluster correlation (ICC) increases and demonstrate that the impact of the ICC is likely to be smaller in a SW-CRT compared with a parallel CRT, especially where there are multiple levels of clustering. Finally, through this unified framework, the efficiency of the SW-CRT and the parallel CRT can be compared.

Keywords: cluster; multiple levels of clustering; sample size; stepped-wedge.

© 2014 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Figures

Figure 1

Illustration of a stepped-wedge study of complete design.

Figure 2

Illustration of a stepped-wedge study of incomplete design with one before and two after measurements.

Figure 3

Illustration of a stepped-wedge study of incomplete design with an implementation period.

Figure 4

Illustrative example of staggered, but parallel, CRT.

Figure 5

Illustrative example of SW-CRT with two layers of clustering (wards within a hospital).

Figure 6

Design effects for parallel CRT (solid line) and before and after (dashed line) designs.

Figure 7

The sweeping study, an illustrative example of stepped-wedge study of incomplete design (Example 1).

Figure 8

Influence of clustering within clustering in a parallel CRT.

Figure 9

Influence of clustering within clustering in a SW-CRT.

Figure 10

The nursery study, an illustrative example of a staggered but parallel cluster trial (Example 3)