Stepped wedge designed trials are a type of cluster‐randomized study in which the intervention is introduced to each cluster in a random order over time. This design is often used to assess the effect of a new intervention as it is rolled out across a series of clinics or communities. Based on a permutation argument, we derive a closed‐form expression for an estimate of the intervention effect, along with its standard error, for a stepped wedge design trial. We show that these estimates are robust to misspecification of both the mean and covariance structure of the underlying data‐generating mechanism, thereby providing a robust approach to inference for the intervention effect in stepped wedge designs. We use simulations to evaluate the type 1 error and power of the proposed estimate and to compare the performance of the proposed estimate to the optimal estimate when the correct model specification is known. The limitations, possible extensions, and open problems regarding the method are discussed.

Stepped wedge cluster randomized controlled trials are typically analyzed using models that assume the full effect of the treatment is achieved instantaneously. We provide an analytical framework for scenarios in which the treatment effect varies as a function of exposure time (time since the start of treatment) and define the “effect curve” as the magnitude of the treatment effect on the linear predictor scale as a function of exposure time. The “time‐averaged treatment effect” (TATE) and “long‐term treatment effect” (LTE) are summaries of this curve. We analytically derive the expectation of the estimator trueδ^$$ \hat{\delta} $$ resulting from a model that assumes an immediate treatment effect and show that it can be expressed as a weighted sum of the time‐specific treatment effects corresponding to the observed exposure times. Surprisingly, although the weights sum to one, some of the weights can be negative. This implies that trueδ^$$ \hat{\delta} $$ may be severely misleading and can even converge to a value of the opposite sign of the true TATE or LTE. We describe several models, some of which make assumptions about the shape of the effect curve, that can be used to simultaneously estimate the entire effect curve, the TATE, and the LTE. We evaluate these models in a simulation study to examine the operating characteristics of the resulting estimators and apply them to two real datasets.

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Background Stepped-wedge designs (SWD) are increasingly used to evaluate the impact of changes to the process of care within health care systems. However, to generate definitive evidence, a correct sample size calculation is crucial to ensure such studies are properly powered. The seminal work of Hussey and Hughes (Contemp Clin Trials 28(2):182–91, 2004) provides an analytical formula for power calculations with normal outcomes using a linear model and simple random effects. However, minimal development and evaluation have been done for power calculation with non-normal outcomes on their natural scale (e.g., logit, log). For example, binary endpoints are common, and logistic regression is the natural multilevel model for such clustered data. Methods We propose a power calculation formula for SWD with either normal or non-normal outcomes in the context of generalized linear mixed models by adopting the Laplace approximation detailed in Breslow and Clayton (J Am Stat Assoc 88(421):9–25, 1993) to obtain the covariance matrix of the estimated parameters. Results We compare the performance of our proposed method with simulation-based sample size calculation and demonstrate its use on a study of patient-delivered partner therapy for STI treatment and a study that assesses the impact of providing additional benchmark prevalence information in a radiologic imaging report. To facilitate adoption of our methods we also provide a function embedded in the R package “swCRTdesign” for sample size and power calculation for multilevel stepped-wedge designs. Conclusions Our method requires minimal computational power. Therefore, the proposed procedure facilitates rapid dynamic updates of sample size calculations and can be used to explore a wide range of design options or assumptions.

Summary The natural mediation effects are desirable estimands to study causal mechanisms in a population, but complications arise in defining and estimating natural indirect effects through multiple mediators with an unspecified causal ordering. We first propose a decomposition of the natural indirect effect of multiple mediators into individual components, termed exit indirect effects, and a remainder interaction term, and study the similarities and differences with existing natural and interventional effects proposed in the literature. We provide a set of identification assumptions for estimating all components of the proposed natural effect decomposition and derive the semiparametric efficiency bounds for the effects. The efficient influence functions contain conditional densities that are variational dependent, which is uncommon in existing problems and may lead to model incompatibility. By ensuring model compatibility through a reparameterization based on copulas, our estimator is quadruply robust, which means it remains consistent and asymptotically normal under four types of possible misspecification, and is also locally semiparametric efficient. We further propose a stabilized quadruply robust estimator to improve the practical performance under possibly misspecified models and a nonparametric extension based on sample splitting.