Estimating the incidence of dementia from two-phase sampling with non-ignorable missing data

Two-phase sampling designs have been used in the field of psychiatry to estimate prevalence and incidence of a rare disease such as dementia and Alzheimer's disease. In a longitudinal study on dementia, since the repeated two-phase sampling is conducted several years after the baseline wave, some subjects may die before the follow-up wave, thus their disease status prior to death is missing. There are reasons to suggest that the missing due to death is non-ignorable. Estimation of disease incidence from longitudinal dementia study has to appropriately adjust for data missing by death as well as the sampling design used at each study wave. In this paper we adopt a selection model approach to model the missing data by death and use a likelihood approach to derive incidence estimates. A modified EM algorithm is used to deal with data from sampling selection. The non-parametric jack-knife variance estimator is used to derive variance estimates for the model parameters and the incidence estimates. The proposed approaches are applied to data from the Indianapolis-Ibadan Dementia Study.