Model misspecification in stepped wedge trials: Random effects for time or treatment

Abstract

Mixed models are commonly used to analyze stepped wedge trials (SWTs) to account for clustering and repeated measures on clusters. One critical issue researchers face is whether to include a random time effect or a random treatment effect. When the wrong model is chosen, inference on the treatment effect may be invalid. We explore asymptotic and finite-sample convergence of variance component estimates when the model is misspecified and how misspecification affects the estimated variance of the treatment effect. For asymptotic results, we rely on analytical solutions rather than simulation studies, which allow us to succinctly describe the convergence of misspecified estimates, even though there are multiple roots for each misspecified model. We found that both direction and magnitude of the bias associated with model-based standard errors depends on the study design and magnitude of the true variance components. We identify some scenarios in which choosing the wrong random effect has a large impact on model-based inference. However, many trends depend on trial design and assumptions about the true correlation structure, so we provide tools for researchers to investigate specific scenarios of interest. We use data from an SWT on disinvesting from weekend services in hospital wards to demonstrate how these results can be applied as a sensitivity analysis, which quantifies the impact of misspecification under a variety of settings and directly compares the potential consequences of different modeling choices. Our results will provide guidance for prespecified model choices and supplement sensitivity analyses to inform confidence in the validity of results.

Analysis of stepped wedge cluster randomized trials in the presence of a time‐varying treatment effect

“…The results are consistent with findings from previous studies on variance structures in the context of stepped wedge designs. 40,41 When a random treatment effect is present in the data but we fail to account for it, we suffer considerably in terms of coverage and MSE. We also performed an analogous set of simulations in which data were instead generated without a random treatment effect (ie, with 𝜈 = 0).…”

Random effect misspecification in stepped wedge designs

“…in a classic 2-sequence design, fitting a random time model is less likely to lead to anti-conservative inference compared with fitting a random intervention model; note that this may not be true for non-classic designs, however). 11 Our results also suggest that using robust variances for inference is recommended when possible.…”

“…We summarize our findings in Table 1. Further details are available in Voldal et al 11 In case 1 (true model is random intervention but random time is fit), validity can be greater than (2 sequences) or less than (>2 sequences) 1.0 depending on the number of sequences. Validity deviates further from 1.0 as the ACC increases, as K increases and usually as the proportion of the cluster variance attributable to the mis-specified variance component increases.…”

Enhancing doctor-patient relationships in community health care institutions: the Patient Oriented Four Habits Model (POFHM) trial—a stepped wedge cluster randomized trial protocol

“…For all primary outcomes, an intention-to-treat analysis will be performed. To evaluate the effects of the primary outcomes of the three interventions, generalized linear mixed models will be used, specifying the PHC effect as random and the time effect as fixed [ 59 , 60 ]. Multiple imputations using chained equations will be used in case of missing data.…”