Pattern-mixture models with proper time dependence

Recently, pattern-mixture modelling has become a popular tool for modelling incomplete longitudinal data.Such models are under-identified in the sense that, for any drop-out pattern, the data provide no direct information on the distribution of the unobserved outcomes, given the observed ones. One simple way of overcoming this problem, ordinary extrapolation of sufficiently simple pattern-specific models, often produces rather unlikely descriptions; several authors consider identifying restrictions instead. Molenberghs et al. (1998) have constructed identifying restrictions corresponding to missing at random. In this paper, the family of restrictions where drop-out does not depend on future, unobserved observations is identified. The ideas are illustrated using a clinical study of Alzheimer patients