Guidance for Addressing Individual Time Effects in Cohort Stepped Wedge Cluster Randomized Trials: A Simulation Study

TL;DR

The study addresses bias and inference in cohort SW-CRTs by evaluating how individual time effects influence intervention estimates. Using a Monte Carlo framework, four linear mixed models with two random intercepts are compared under closed/open cohorts and linear/nonlinear covariate effects, with emphasis on time adjustment via fixed effects and covariate-based adjustments. The main finding is that models including fixed time effects plus two random intercepts yield unbiased intervention estimates across scenarios, while nonlinear time effects require cluster-robust variance estimation (CRVE), particularly CR3VE with Satterthwaite DF, to control Type I error. Practically, the work provides guidance to analysts: incorporate fixed time effects and use CRVEs (preferably CR3VE) to ensure valid inference in cohort SW-CRTs, and clearly distinguish cohort designs in reporting guidelines like CONSORT.

Abstract

Background: Stepped wedge cluster randomized trials (SW-CRTs) involve sequential measurements within clusters over time. Initially, all clusters start in the control condition before crossing over to the intervention on a staggered schedule. In cohort designs, secular trends, cluster-level changes, and individual-level changes (e.g., aging) must be considered. Methods: We performed a Monte Carlo simulation to analyze the influence of different time effects on the estimation of the intervention effect in cohort SW-CRTs. We compared four linear mixed models with different adjustment strategies, all including random intercepts for clustering and repeated measurements. We recorded the estimated fixed intervention effects and their corresponding model-based standard errors, derived from models both without and with cluster-robust variance estimators (CRVEs). Results: Models incorporating fixed categorical time effects, a fixed intervention effect, and two random intercepts provided unbiased estimates of the intervention effect in both closed and open cohort SW-CRTs. Fixed categorical time effects captured temporal cohort changes, while random individual effects accounted for baseline differences. However, these differences can cause large, non-normally distributed random individual effects. CRVEs provide reliable standard errors for the intervention effect, controlling the Type I error rate. Conclusions: Our simulation study is the first to assess individual-level changes over time in cohort SW-CRTs. Linear mixed models incorporating fixed categorical time effects and random cluster and individual effects yield unbiased intervention effect estimates. However, cluster-robust variance estimation is necessary when time-varying independent variables exhibit nonlinear effects. We recommend always using CRVEs.

Figures (9)

• Figure 1: Schematic representation of a standard SW-CRT with four arms/steps.
• Figure 2: Estimated intervention effects from 1,000 simulations per parameter combination ($I= 8, 16, 32$; $K = 10, 100$; $J = 4, 8$) using four analysis models (Table \ref{['tab:mixed_models']}; cov. adj. = covariate adjustment), including only converged models. Closed cohort data with a covariate affecting the outcome (a) linearly and (b) nonlinearly.
• Figure 3: Percentage error of model-based standard errors (SE) compared to empirical SE from 1,000 simulations per parameter combination ($I = 8, 16, 32; K = 10, 100; J = 4, 8$). The analysis model includes fixed categorical time effects (Equation 2) and is presented with standard estimation (red line) and three cluster-robust variance estimation methods: CR0VE (purple line), CR2VE (blue line), and CR3VE (green line). Results are displayed for four scenarios: (a) closed cohort with linear covariate influence, (b) closed cohort with nonlinear covariate influence, (c) open cohort with linear covariate influence, and (d) open cohort with nonlinear covariate influence.
• Figure 4: Type I error Percentage error of model-based standard errors (SE) compared to empirical SE from 1,000 simulations per parameter combination ($I = 8, 16, 32; K = 10, 100; J = 4, 8$). The analysis model includes fixed categorical time effects (Equation 2) and is presented with standard estimation (red line) and three cluster-robust variance estimation methods: CR0VE (purple line), CR2VE (blue line), and CR3VE (green line). Results are displayed for four scenarios: (a) closed cohort with linear covariate influence, (b) closed cohort with nonlinear covariate influence, (c) open cohort with linear covariate influence, and (d) open cohort with nonlinear covariate influence.
• Figure 5: Main simulation results. Equation 2 yielded unbiased intervention effect estimates for both closed and open cohort data, even with unmeasured or misspecified individual time effects. Random individual effects absorb baseline heterogeneity, and fixed categorical time effects capture changes over time (e.g., aging). Complex residual dependencies did not bias intervention effects, but substantially biased fixed effect inference. The figure shows the assessment of the percentage error in the averaged model-based standard error (SE) relative to the empirical SE (Perc. SE Bias) and Type I error rates for models using the standard variance estimator (standard VE) and cluster-robust variance estimators (CR0VE: standard CRVE, CR3VE: bias-reduced correction, CR2VE: bias-reduced linearization method). The CR3VE with Satterthwaite's degrees of freedom (DF) correction produced unbiased variance estimates and maintained Type I error across all parameter settings.