Evaluation of approaches for accommodating interactions and non-linear terms in multiple imputation of incomplete three-level data

TL;DR

This study evaluates various multiple imputation methods for handling missing data in three-level health research data, especially when the analysis involves interactions or non-linear effects, highlighting the superior performance of the three-level SMC MI approach.

Contribution

It provides a comprehensive comparison of existing approaches for imputing incomplete three-level data with interactions and non-linear terms, including the evaluation of a novel three-level SMC MI method.

Findings

All methods performed well with time interaction analyses.

Three-level SMC MI outperformed others with complex interactions.

The study offers practical guidance for handling missing data in multilevel models.

Abstract

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.