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.

Three-level data structures arising from repeated measures on individuals clustered within larger units are common in health research studies. Missing data are prominent in such studies and are often handled via multiple imputation (MI). Although several MI approaches can be used to account for the three-level structure, including adaptations to single-and twolevel approaches, when the substantive analysis model includes interactions or quadratic effects these too need to be accommodated in the imputation model. In such analyses, substantive model compatible (SMC) MI has shown great promise in the context of singlelevel data. While there have been recent developments in multilevel SMC MI, to date only one approach that explicitly handles incomplete three-level data is available. Alternatively, researchers can use pragmatic adaptations to single-and two-level MI approaches, or twolevel SMC-MI approaches. We describe the available approaches and evaluate them via simulation in the context of a three three-level random effects analysis models involving an interaction between the incomplete time-varying exposure and time, an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. Results showed that all approaches considered performed well in terms of bias and precision when the target analysis involved an interaction with time, but the three-level SMC MI approach performed best when the target analysis involved an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. We illustrate the methods using data from the Childhood to Adolescence Transition Study.

Background There are limited longitudinal studies on the effects of the COVID-19 pandemic on mental health and well-being, including the effects of imposed restrictions and lockdowns. Aims This study investigates how living in a pandemic, and related lockdowns and restrictions, affected the mental health of people living in Australia during the first year of the COVID-19 pandemic. Method A total of 875 people living in Australia participated in a longitudinal survey from 27 May to 14 December 2020. This time period includes dates that span pre-, during and post-wave 2 lockdowns in Australia, with strict and sustained public health measures. Linear mixed models were fitted to investigate the effect of lockdown on depression and anxiety symptoms. Results Symptoms of depression and anxiety improved over time, during and after lockdowns. More adverse mental health symptoms were observed for people with a history of medical or mental health problems, caring responsibilities, more neurotic personality traits or less conscientiousness, and for people who were younger. People who reported being more conscientious reported better mental health. Conclusions Despite notoriously strict lockdowns, participants did not experience a deterioration of mental health over time. Results suggest a lack of significant adverse effects of lockdown restrictions on mental health and well-being. Findings highlight cohorts that could benefit from targeted mental health support and interventions, so that public policy can be better equipped to support them, particularly if future strict public health measures such as lockdowns are being considered or implemented for the COVID-19 pandemic and other disasters.