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01.12.2017 | Research | Ausgabe 1/2017 Open Access

Trials 1/2017

Minimum number of clusters and comparison of analysis methods for cross sectional stepped wedge cluster randomised trials with binary outcomes: A simulation study

Zeitschrift:
Trials > Ausgabe 1/2017
Autoren:
Daniel Barker, Catherine D’Este, Michael J. Campbell, Patrick McElduff
Wichtige Hinweise

Electronic supplementary material

The online version of this article (doi:10.​1186/​s13063-017-1862-2) contains supplementary material, which is available to authorized users.

Abstract

Background

Stepped wedge cluster randomised trials frequently involve a relatively small number of clusters. The most common frameworks used to analyse data from these types of trials are generalised estimating equations and generalised linear mixed models. A topic of much research into these methods has been their application to cluster randomised trial data and, in particular, the number of clusters required to make reasonable inferences about the intervention effect. However, for stepped wedge trials, which have been claimed by many researchers to have a statistical power advantage over the parallel cluster randomised trial, the minimum number of clusters required has not been investigated.

Methods

We conducted a simulation study where we considered the most commonly used methods suggested in the literature to analyse cross-sectional stepped wedge cluster randomised trial data. We compared the per cent bias, the type I error rate and power of these methods in a stepped wedge trial setting with a binary outcome, where there are few clusters available and when the appropriate adjustment for a time trend is made, which by design may be confounding the intervention effect.

Results

We found that the generalised linear mixed modelling approach is the most consistent when few clusters are available. We also found that none of the common analysis methods for stepped wedge trials were both unbiased and maintained a 5% type I error rate when there were only three clusters.

Conclusions

Of the commonly used analysis approaches, we recommend the generalised linear mixed model for small stepped wedge trials with binary outcomes. We also suggest that in a stepped wedge design with three steps, at least two clusters be randomised at each step, to ensure that the intervention effect estimator maintains the nominal 5% significance level and is also reasonably unbiased.
Zusatzmaterial
Additional file 1: TIFF image, LZW compression. Per cent bias in the intervention effect estimate \( \left({\widehat{\mathit{\ss}}}_1\right) \) for models that fail to adjust for time. Estimates are obtained from fitting models (1) to (4). Simulated data have six steps, a cell size equal to n jk , a true intervention effect odds ratio of 1.33 and a time effect odds ratio of 1.03. (TIF 269 kb)
13063_2017_1862_MOESM1_ESM.tif
Additional file 2: TIFF image, LZW compression. Per cent bias in the intervention effect estimate \( \left({\widehat{\ss}}_1\right) \) for models that correctly adjust for time. Estimates are obtained from fitting models (1) to (4). Simulated data have six steps, a cell size equal to n jk , a true intervention effect odds ratio of 1.33 and a time effect odds ratio of 1.03. (TIF 267 kb)
13063_2017_1862_MOESM2_ESM.tif
Additional file 3: TIFF image, LZW compression. Type I error rate in the intervention effect estimate \( \left({\widehat{\mathit{\ss}}}_1\right) \) for models that correctly adjust for time. Estimates are obtained from fitting models (1) to (4). Simulated data have six steps, a cell size equal to n jk , a true intervention effect odds ratio of 1 and a time effect odds ratio of 1.03. (TIF 279 kb)
13063_2017_1862_MOESM3_ESM.tif
Additional file 4: Power to detect intervention effect (OR = 1.33) in a six-step SW-CRT with different methods of analysis. Each estimate is based on 2000 simulations. All methods adjust for time in the model. (RTF 153 kb)
13063_2017_1862_MOESM4_ESM.rtf
Additional file 5: Simulation code for scenario A. (DOCX 22 kb)
13063_2017_1862_MOESM5_ESM.docx
Additional file 6: Simulation code for scenario B. (DOCX 22 kb)
13063_2017_1862_MOESM6_ESM.docx
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