Admissible multiarm stepped-wedge cluster randomized trial designs

Abstract

Numerous publications have now addressed the principles of designing, analyzing, and reporting the results of stepped-wedge cluster randomized trials. In contrast, there is little research available pertaining to the design and analysis of multiarm stepped-wedge cluster randomized trials, utilized to evaluate the effectiveness of multiple experimental interventions. In this paper, we address this by explaining how the required sample size in these multiarm trials can be ascertained when data are to be analyzed using a linear mixed model. We then go on to describe how the design of such trials can be optimized to balance between minimizing the cost of the trial and minimizing some function of the covariance matrix of the treatment effect estimates. Using a recently commenced trial that will evaluate the effectiveness of sensor monitoring in an occupational therapy rehabilitation program for older persons after hip fracture as an example, we demonstrate that our designs could reduce the number of observations required for a fixed power level by up to 58%. Consequently, when logistical constraints permit the utilization of any one of a range of possible multiarm stepped-wedge cluster randomized trial designs, researchers should consider employing our approach to optimize their trials efficiency.

Keywords: admissible design; cluster randomized trial; multiple comparisons; optimal design; stepped-wedge.

Figure 1

Optimal allocation matrices for cross‐sectional designs with D = 2. The optimal allocation matrices in the case $\mathfrak{I}=\{6\}$, $\mathfrak{C}=\{{\mathfrak{C}}_6\}=\{10\}$, $\mathfrak{M}={\mathfrak{M}}_{10,6}=\{10\}$, and σ ² = 1, with w = 0 and β = 1 are shown for a range of possible combinations of $({\sigma }_c^2,{\sigma }_{\epsilon }^2)\in [0.001,0.25]\times [0.25,4]$. No restrictions are placed on $\mathfrak{X}$ other than the identifiability of Equation (1). Each allocation matrix was identified via our exhaustive search method [Colour figure can be viewed at wileyonlinelibrary.com]

Figure 2

The ratio of the variance of the intervention effect when using design matrices X ₁ (top) and X ₂ (bottom) relative to the optimal design (given in Figure 1) is shown for a range of possible combinations of $({\sigma }_c^2,{\sigma }_{\epsilon }^2)\in [0.001,0.25]\times [0.25,4]$ [Colour figure can be viewed at wileyonlinelibrary.com]