Bias through time-varying covariates in the analysis of cohort stepped wedge trials: a simulation study

In stepped wedge cluster randomized trials (SW-CRTs), observations collected under the control condition are, on average, from an earlier time than observations collected under the intervention condition. In a cohort design, participants are followed up throughout the study, so correlations between measurements within a participant are dependent of the timing in which the observations are made. Therefore, changes in participants' characteristics over time must be taken into account when estimating intervention effects. For example, participants' age progresses, which may impact the outcome over the study period. Motivated by an SW-CRT of a geriatric care intervention to improve quality of life, we conducted a simulation study to compare model formulations analysing data from an SW-CRT under different scenarios in which time was related to the covariates and the outcome. The aim was to find a model specification that produces reliable estimates of the intervention effect. Six linear mixed effects (LME) models with different specification of fixed effects were fitted. Across 1000 simulations per parameter combination, we computed mean and standard error of the estimated intervention effects. We found that LME models with fixed categorical time effects additional to the fixed intervention effect and two random effects used to account for clustering (within-cluster correlation) and multiple measurements on participants (within-individual correlation) seem to produce unbiased estimates of the intervention effect even if time-varying confounders or their functional influence on outcome were unknown or unmeasured and if secular time trends occurred. Therefore, including (time-varying) covariates describing the study cohort seems to be avoidable.