Abstract
Random coefficient-dependent (RCD) missingness is a non-ignorable mechanism through which missing data can arise in longitudinal designs. RCD, for which we cannot test, is a problematic form of missingness that occurs if subject-specific random effects correlate with propensity for missingness or dropout. Particularly when covariate missingness is a problem, investigators typically handle missing longitudinal data by using single-level multiple imputation procedures implemented with long-format data, which ignores within-person dependency entirely, or implemented with wide-format (i.e., multivariate) data, which ignores some aspects of within-person dependency. When either of these standard approaches to handling missing longitudinal data is used, RCD missingness leads to parameter bias and incorrect inference. We explain why multilevel multiple imputation (MMI) should alleviate bias induced by a RCD missing data mechanism under conditions that contribute to stronger determinacy of random coefficients. We evaluate our hypothesis with a simulation study. Three design factors are considered: intraclass correlation (ICC; ranging from .25 to .75), number of waves (ranging from 4 to 8), and percent of missing data (ranging from 20 to 50%). We find that MMI greatly outperforms the single-level wide-format (multivariate) method for imputation under a RCD mechanism. For the MMI analyses, bias was most alleviated when the ICC is high, there were more waves of data, and when there was less missing data. Practical recommendations for handling longitudinal missing data are suggested.
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Acknowledgements
We would like to thank Dan Bauer and Kris Preacher for feedback on previous drafts of this manuscript. We are also grateful for the highly constructive and insightful feedback that we received from our anonymous reviewers.
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Research reported in this publication was supported by the National Institutes of Health through grant funding awarded to Dr. Gottfredson (K01 DA035153) and Dr. Jackson (K02 AA13938 and R01 AA016838). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
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Gottfredson, N.C., Sterba, S.K. & Jackson, K.M. Explicating the Conditions Under Which Multilevel Multiple Imputation Mitigates Bias Resulting from Random Coefficient-Dependent Missing Longitudinal Data. Prev Sci 18, 12–19 (2017). https://doi.org/10.1007/s11121-016-0735-3
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DOI: https://doi.org/10.1007/s11121-016-0735-3