Inference for the treatment effect in staircase designs with continuous outcomes: a simulation study

Background Staircase designs are incomplete stepped wedge designs that, unlike standard stepped wedge designs, require clusters to contribute data for only a limited number of trial periods. Previous work has provided formulae based on asymptotic results for the calculation of the power of staircase designs to detect treatment effects of interest. Methods We conduct a simulation study to assess the finite sample performance of these formulae, and the impact of misspecifying the correlation structure when analysing data from staircase designs on inference for the treatment effect, under a range of realistic trial settings. This study focuses on basic staircase designs with one control period followed by one intervention period in each sequence. We simulate staircase trial datasets with continuous outcomes and a repeated cross-sectional measurement scheme under exchangeable and block-exchangeable intracluster correlation structures, and then fit linear mixed models with linear and categorical time period effects. For settings with a small number of clusters, Kenward-Roger and Satterthwaite small-sample corrections are applied. Comparisons are made between nominal and observed Type I error rates, and theoretically-derived study power and empirical power. The impact on inference for the treatment effect when misspecifying the intracluster correlation structure is assessed through considering performance metrics including bias and 95% confidence interval coverage. Results Data analysis assuming an exchangeable correlation structure and application of the Satterthwaite correction controls Type I error well when the correlation structure is correctly specified, and there are a sufficient number of clusters. For the true block-exchangeable model, when fitting the correct model with the Satterthwaite correction, the observed Type I error (empirical power) can be higher (lower) than the nominal (i.e., theoretical) value when there is only 1 cluster per sequence, but otherwise, it aligns well with the nominal (theoretical) value. Misspecification of the correlation structure (fitting an exchangeable model when the true structure is block-exchangeable) can lead to inflated Type I error and poor confidence interval coverage. Conclusions Staircase designs with one cluster per sequence should be used with caution. Additionally, using a correlation structure that allows for decay is preferable for making valid inferences for the estimation of the treatment effect.