Likelihood for interval-censored observations from multi-state models

We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation of the likelihood for the illness-death model based on applying Jacod's formula to an observed bivariate counting process

A Latent Process Model for Dementia and Psychometric Tests

We jointly model longitudinal values of a psychometric test and diagnosis of dementia. The model is based on a continuous-time latent process representing cognitive ability. The link between the latent process and the observations is modeled in two phases. Intermediate variables are noisy observations of the latent process; scores of the psychometric test and diagnosis of dementia are obtained by categorizing these intermediate variables. We propose maximum likelihood inference for this model and we propose algorithms for performing this task. We estimated the parameters of such a model using the data of the five-year follow-up of the PAQUID study. In particularThis analysis yielded interesting results about the effect of educational level on both latent cognitive ability and specific performance in the mini mental test examination. The predictive ability of the model is illustrated by predicting diagnosis of dementia at the eight-year follow-up of the PAQUID study bsed on the information of the first five years.Comment: 29 pages 3 figure