A mixed-effects model for cognitive decline with non-monotone non-response from a two-phase longitudinal study of dementia

Most longitudinal studies of elderly are characterized by substantial drop-out due to death and many other factors beyond the control of the investigators. In a two-phase longitudinal study of dementia, subjects with cognitive impairment skip the first phase survey in the next follow-up, leading to intermittent missing variables measured in that phase. In the context of analysing pre-dementia cognitive decline in an elderly population, both of the two causes of non-response can potentially be informative in the sense that the missingness is dependent on the unobserved outcome. To take these factors into account, mixed-effects models are constructed to allow the outcome and the multiple causes of missing values to share the same 'random parameter' or random effect. The crucial assumption of our model is that the random effects of the model for the outcome and that of the model for the missing-data indicators are linked in a deterministic manner. It can be thought of as an approximation of a more general and realistic situation, in which the two models have distinct, yet dependent, random effects. We conduct a simulation study to investigate possible deviations of the estimates under such a scenario. A second simulation illustrates the magnitude of the bias in estimating the difference of decline rate between two groups when the random effects are linked in different manners for the two groups.