Relaxing the MAR Assumption with a Multiple Imputation Model for Longitudinal Data

In observational longitudinal research, people may miss a study wave due to their person-specific latent trajectories on variables of interest. This situation describes a missing not at random (MNAR) mechanism that is called random coefficient-dependent (RC-D). RC-D missingness may occur in longitudinal studies with missing outcomes and with missing predictors. When missing data are missing due to a RC-D process, estimates of the parameters governing change, and predictors of change, may be biased. We propose a multiple imputation (MI) model that assesses the sensitivity of parameter estimates to the assumption that missing data are missing at random (MAR). We hypothesize that our MNAR imputation model, which is designed to handle RC-D missingness, will produce regression parameter estimates relating predictors to change parameters that are less biased than the estimates obtained under the MAR assumption.

We compare model performance of the proposed model with an imputation model that assumes that missing data are MAR. Both models are applied to simulated longitudinal datasets that contained missingness generated under a MAR mechanism, and to datasets with MNAR missingness that was generated under a RC-D mechanism. The MNAR-MI model produces parameter estimates that are less biased than the MAR-MI model when missing data are RC-D; the MNAR-MI and MAR-MI perform equivalently when missing data are MAR.

We apply the MNAR-MI model to data from a longitudinal analysis of change in positive alcohol expectancies among adolescents. Parental monitoring, early pubertal status, and gender are included as predictors of expectancy trajectories. We hypothesize that monitoring buffers effects of early puberty on alcohol expectancy trajectories, and that these associations may differ by gender. Data contain five waves of measurement from N=1023 adolescents. We find a modest degree of parameter sensitivity that follows patterns consistent with the simulation results. We use this analysis to further characterize the ways in which substantive conclusions may be unduly influenced by nonignorable patterns of missing data.