A latent-variable marginal method for multi-level incomplete binary data

Incomplete multi-level data arise commonly in many clinical trials and observational studies. Because of multi-level variations in this type of data, appropriate data analysis should take these variations into account. A random effects model can allow for the multi-level variations by assuming random effects at each level, but the computation is intensive because high-dimensional integrations are often involved in fitting models. Marginal methods such as the inverse probability weighted generalized estimating equations can involve simple estimation computation, but it is hard to specify the working correlation matrix for multi-level data. In this paper, we introduce a latent variable method to deal with incomplete multi-level data when the missing mechanism is missing at random, which fills the gap between the random effects model and marginal models. Latent variable models are built for both the response and missing data processes to incorporate the variations that arise at each level. Simulation studies demonstrate that this method performs well in various situations. We apply the proposed method to an Alzheimer's disease study.