Uncertainty intervals for multilevel models with missing not at random data

Abstract

We propose a sensitivity analysis method for missing not at random (MNAR) data in the context of linear multilevel (mixed-effects) models. The outcome and dropout risk are both modelled using multilevel models and a bias adjustment due to MNAR data is derived. This bias can be estimated from observed data conditional on specified values of sensitivity parameter(s). Under the assumption that these parameters lie within a plausible range, the method partially identify the parameters of interest, yielding bounds for estimation and inference under assumptions weaker than missing at random. The proposed analysis is investigated in a simulation study and illustrated with an analysis of the association between loneliness and physical activity with memory trajectories, adjusting for demographic, socioeconomic, and health covariates.