  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 two-level
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 single-level 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 two-level 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.
