A Simulation Study of Statistical Approaches to Data Analysis in the Stepped Wedge Design

Abstract

This paper studies model-based and design-based approaches for the analysis of data arising from a stepped wedge randomized design. Specifically, for different scenarios we compare robustness, efficiency, Type I error rate under the null hypothesis, and power under the alternative hypothesis for the leading analytical options including generalized estimating equations (GEE) and linear mixed model (LMM)-based approaches. We find that GEE models with exchangeable correlation structures are more efficient than GEE models with independent correlation structures under all scenarios considered. The model-based GEE Type I error rate can be inflated when applied with a small number of clusters, but this problem can be solved using a design-based approach. As expected, correct model specification is more important for LMM (compared to GEE) since the model is assumed correct when standard errors are calculated. However, in contrast to the model-based results, the design-based Type I error rates for LMM models under scenarios with a random treatment effect show Type I error inflation even though the fitted models perfectly match the corresponding data-generating scenarios. Therefore, greater robustness can be realized by combining GEE and permutation testing strategies.

Appendix: R, Stata, and SAS code

Here we present basic R, Stata, and SAS code for fitting common models for stepped wedge designs with cross-sectional data collection at each time point. See [5,6,7].

• I Linear mixed models

  • (1) ${\text{Random cluster effect}}:Y_{ijt} = \mu + a_{i} + \beta_{t} + X_{it} \theta + e_{ijt}$

  • (2) ${\text{Random cluster and cluster}} \times {\text{time effect}}:Y_{ijt} = \mu + a_{i} + \beta_{t} + b_{it} + X_{it} \theta + e_{ijt}$

  • (3) ${\text{Random cluster}},{\text{ cluster}} \times {\text{time and treatment effect }}({\text{corr}}(a_{i} ,_{{}} c_{i} ) = 0):Y_{ijt} = \mu + a_{i} + \beta_{t} + b_{it} + X_{it} (\theta + c_{i} ) + e_{ijt}$

  • (4) ${\text{Random cluster, cluster}} \times {\text{time and treatment effect }}({\text{corr}}(a_{i} ,_{{}} c_{i} ) = \rho ):Y_{ijt} = \mu + a_{i} + \beta_{t} + b_{it} + X_{it} (\theta + c_{i} ) + e_{ijt},$

    where

    a_i ~ N(0, τ²)

    b_it ~ N(0, γ²)

    c_i ~ N(0, ν²)

    e_ijt ~ N(0, σ²).

    

• II Generalized estimating equation models

  • (5) Independent working correlation

  • (6) Exchangeable working correlation