The relative efficiency of staircase and stepped wedge cluster randomised trial designs

Abstract

The stepped wedge design is an appealing longitudinal cluster randomised trial design. However, it places a large burden on participating clusters by requiring all clusters to collect data in all periods of the trial. The staircase design may be a desirable alternative: treatment sequences consist of a limited number of measurement periods before and after the implementation of the intervention. In this article, we explore the relative efficiency of the stepped wedge design to several variants of the 'basic staircase' design, which has one control followed by one intervention period in each sequence. We model outcomes using linear mixed models and consider a sampling scheme where each participant is measured once. We first consider a basic staircase design embedded within the stepped wedge design, then basic staircase designs with either more clusters or larger cluster-period sizes, with the same total number of participants and with fewer total participants than the stepped wedge design. The relative efficiency of the designs depends on the intracluster correlation structure, correlation parameters and the trial configuration, including the number of sequences and cluster-period size. For a wide range of realistic trial settings, a basic staircase design will deliver greater statistical power than a stepped wedge design with the same number of participants, and in some cases, with even fewer total participants.

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

Figure 1.

Design schematics for three-sequence designs, shown with a fixed number of clusters per sequence for illustrative purposes: (a) a stepped wedge design with one cluster per sequence and a cluster-period size of $m$ , (b) an embedded basic staircase design with one cluster per sequence and a cluster-period size of $m$ , (c) an extended basic staircase design with two clusters per sequence and a cluster-period size of $m$ , and (d) a basic staircase design with one cluster per sequence and a cluster-period size of $2m$ . Cells contain either 0 for the control condition, 1 for the intervention condition, or a slash to indicate that no measurements are taken.

Figure 2.

Correlation between cluster-period means under a block-exchangeable correlation structure, for cluster-period sizes of $m=10$ (top panel) and $m=100$ (bottom panel), for different combinations of intracluster correlation values.

Figure 3.

Relative efficiency for $SC(S,K,1,1)$ embedded basic staircase designs compared to $SW(S,K)$ stepped wedge designs, with $S=3,5,7,9$ and $11$ sequences, for the block-exchangeable intracluster correlation structure assuming categorical period effects.

Figure 4.

Relative efficiency for $SC(S,K,1,1)$ embedded basic staircase designs compared to $SW(S,K)$ stepped wedge designs, with $S=3$ sequences (left column) and $S=9$ sequences (right column), and with cluster-period sizes of $m=10$ (top row) and $m=100$ (bottom row), for the block-exchangeable intracluster correlation structure assuming categorical period effects.

Figure 5.

Relative efficiency for $SC(S,qK,1,1)$ extended staircase designs compared to $SW(S,K)$ stepped wedge designs, with $S=3,5,7,9$ and $11$ sequences and $q=(S+1)/2=2,3,4,5$ and $6$ , respectively, for the block-exchangeable intracluster correlation structure assuming categorical period effects.

Figure 6.

Relative efficiency for $SC(S,qK,1,1)$ extended staircase designs compared to $SW(S,K)$ stepped wedge designs, with $S=3$ sequences and $q=2$ (left column) and $S=9$ sequences and $q=5$ (right column), and with cluster-period sizes of $m=10$ (top row) and $m=100$ (bottom row), for the block-exchangeable intracluster correlation structure assuming categorical period effects.

Figure 7.

Relative efficiency for $SC(S,K,1,1)$ basic staircase designs compared to $SW(S,K)$ stepped wedge designs, with $S=3$ sequences (left column) and $S=9$ sequences (right column), and with cluster-period sizes of $m_{SW}=10$ and $m_{SC}=20$ (top left), $m_{SW}=10$ and $m_{SC}=50$ (top right), $m_{SW}=100$ and $m_{SC}=200$ (bottom left) and $m_{SW}=10$ and $m_{SC}=500$ (bottom right), for the block-exchangeable intracluster correlation structure assuming categorical period effects.

Figure 8.

Design schematics for the designs inspired by the PROMPT trial: a stepped wedge design (top left), a basic staircase design with the same cluster-period size as the stepped wedge design (top middle), a basic staircase design with a 50% larger cluster-period size than the stepped wedge design (top right), each with five sequences $(S_{SW}=S_{SC}=5)$ and eight clusters per sequence $(K_{SW}=K_{SC}=8)$ and spanning six periods, and five-sequence extended basic staircase designs with 10 clusters per sequence (bottom left) and 12 clusters per sequence (bottom right).

Figure A1.

Design schematics for the nine-sequence designs to be compared, shown with a fixed number of clusters per sequence for illustrative purposes: (a) a stepped wedge design with one cluster per sequence and a cluster-period size of $m$ , (b) a basic staircase design with one cluster per sequence and a cluster-period size of $m$ , (c) an extended basic staircase design with five clusters per sequence and a cluster-period size of $m$ , and (d) a basic staircase design with one cluster per sequence and a larger cluster-period size of $5m$ .