The staircase cluster randomised trial design: A pragmatic alternative to the stepped wedge

Abstract

This article introduces the 'staircase' design, derived from the zigzag pattern of steps along the diagonal of a stepped wedge design schematic where clusters switch from control to intervention conditions. Unlike a complete stepped wedge design where all participating clusters must collect and provide data for the entire trial duration, clusters in a staircase design are only required to be involved and collect data for a limited number of pre- and post-switch periods. This could alleviate some of the burden on participating clusters, encouraging involvement in the trial and reducing the likelihood of attrition. Staircase designs are already being implemented, although in the absence of a dedicated methodology, approaches to sample size and power calculations have been inconsistent. We provide expressions for the variance of the treatment effect estimator when a linear mixed model for an outcome is assumed for the analysis of staircase designs in order to enable appropriate sample size and power calculations. These include explicit variance expressions for basic staircase designs with one pre- and one post-switch measurement period. We show how the variance of the treatment effect estimator is related to key design parameters and demonstrate power calculations for examples based on a real trial.

Keywords: Clinical trial design; cluster randomised trial; incomplete design; intracluster correlation; sample size.

Figure 1.

Design schematics for several staircase designs with 6 clusters: a basic staircase with two clusters assigned to each of three unique sequences (top left), a basic staircase with one cluster assigned to each of six unique sequences (top right), a balanced staircase with two control periods followed by two intervention periods in each sequence and one cluster assigned to each of six unique sequences (bottom left), and an imbalanced staircase with one control period followed by two intervention periods in each sequence and one cluster assigned to each of six unique sequences (bottom right).

Figure 2.

(a) Design schematic for a four-sequence basic staircase design; (b) visualisation of the treatment effect estimator in terms of the mean outcomes from the measured cluster-periods, assuming categorical period effects; (c) visualisation of the treatment effect estimator in terms of the mean outcomes from the measured cluster-periods, assuming a linear time effect.

Figure 3.

Variance of the treatment effect estimator for varying within-period intracluster correlation (ICC) values, assuming categorical period effects, for a basic staircase design with three and 10 sequences (columns) and cluster-period sizes of 10 and 100 (rows), where each subject is measured just once. The lines within each subplot correspond to different cluster autocorrelation values.

Figure 4.

Variance of the treatment effect estimator for varying cluster-period sizes, assuming categorical period effects, for a basic staircase design with 10 sequences, where each subject is measured just once, and for within-period ICC values of 0.05 (left) and 0.2 (right). The lines within each subplot correspond to different cluster autocorrelation values.

Figure 5.

Variance of the treatment effect estimator for varying within-period intracluster correlation (ICC) values, assuming linear period effects, for a basic staircase design with three and 10 sequences (columns) and cluster-period sizes of 10 and 100 (rows), where each subject is measured just once. The lines within each subplot correspond to different cluster autocorrelation values.

Figure 6.

Variance of the treatment effect estimator for varying cluster-period sizes, assuming linear period effects, for a basic staircase design with 10 sequences, where each subject is measured just once, and for within-period intracluster correlation (ICC) values of 0.05 (left) and 0.2 (right). The lines within each subplot correspond to different cluster autocorrelation values.

Figure 7.

Design schematics for a basic staircase design with one cluster assigned to each of four unique sequences (left) and an imbalanced staircase design with one control period followed by three intervention periods in each sequence and one cluster assigned to each of four unique sequences (right).