A continuous latent factor model for non-ignorable missing data

Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable. However, this assumption leads to unrealistic simplification and is implausible for many cases.When non-ignorable missingness is preferred, classical pattern-mixture models with the data stratified according to a variety of missing patterns and a model specified for each stratum are widely used for longitudinal data analysis. But this assumption usually results in under-identifiability because of the need to estimate many stratum-specific parameters. Further, pattern mixture models have the drawback that a large sample is usually required. In this paper, a continuous latent factor model is proposed and this novel approach overcomes limitations which exist in pattern mixture models by specifying a continuous latent factor. The advantages of this model, including small sample feasibility, are demonstrated by comparing with Roy's pattern mixturemodel using an application to a clinical study of AIDS patients with advanced immune suppression.