Evaluation of approaches for multiple imputation of three-level data

Abstract

Background: Three-level data arising from repeated measures on individuals who are clustered within larger units are common in health research studies. Missing data are prominent in such longitudinal studies and multiple imputation (MI) is a popular approach for handling missing data. Extensions of joint modelling and fully conditional specification MI approaches based on multilevel models have been developed for imputing three-level data. Alternatively, it is possible to extend single-and two-level MI methods to impute three-level data using dummy indicators and/or by analysing repeated measures in wide format. However, most implementations, evaluations and applications of these approaches focus on the context of incomplete two-level data. It is currently unclear which approach is preferable for imputing three-level data. Methods: In this study, we investigated the performance of various MI methods for imputing three-level incomplete data when the target analysis model is a three-level random effects model with a random intercept for each level. The MI methods were evaluated via simulations and illustrated using empirical data, based on a case study from the Childhood to Adolescence Transition Study, a longitudinal cohort collecting repeated measures on students who were clustered within schools. In our simulations we considered a number of different scenarios covering a range of different missing data mechanisms, missing data proportions and strengths of level-2 and level-3 intra-cluster correlations. Results: We found that all of the approaches considered produced valid inferences about both the regression coefficient corresponding to the exposure of interest and the variance components under the various scenarios within the simulation study. In the case study, all approaches led to similar results. Conclusion: Researchers may use extensions to the single-and two-level approaches, or the three-level approaches, to adequately handle incomplete three-level data. The two-level MI approaches with dummy indicator extension or the MI approaches based on three-level models will be required in certain circumstances such as when there are longitudinal data measured at irregular time intervals. However, the single-and two-level approaches with the DI extension should be used with caution as the DI approach has been shown to produce biased parameter estimates in certain scenarios.

Can holistic school readiness evaluations predict academic achievement and special educational needs status? Evidence from the Early Years Foundation Stage Profile

“…using mice in R (van Buuren & Groothuis-Oudshoorn 2011), the mi function in STATA) were unsuccessful due to poor model convergence. A dummy indicator approach, whereby the multilevel structure is taken into account by including a dummy variable for each cluster (Lüdtke et al, 2017) was not feasible due to the presence of a large number of schools (>170; Wijesuriya et al, 2020) .…”

Multiple imputation for handling missing outcome data in randomized trials involving a mixture of independent and paired data

“…For paired observations, standard imputation procedures such as FCS or a joint imputation model could be applied once data have been rearranged into wide format; that is, with a single row for each pair and separate columns for and (and similarly for and ). This approach is consistent with recommendations for the application of MI in longitudinal studies with a fixed number of repeated measurements, where the wide format allows the imputation model to account for the correlation between repeated measurements 30‐32 . Following imputation, the completed datasets for the paired data would be rearranged into long format and appended with completed datasets for the independent observations for subsequent analysis.…”

Handling missing data in cross-classified multilevel analyses: An evaluation of different multiple imputation approaches

“…As an alternative to CC-MI, crossclassified data can also be accommodated with simpler imputation models (e.g., for single-or two-level data) by including the effects of cluster membership through fixed effects or additional cluster means (Andridge, 2011;Drechsler, 2015;Lüdtke et al, 2017;Wijesuriya et al, 2020).…”