Multi-state model for dementia, institutionalization, and death

We consider a multi-state model for jointly modeling dementia, institutionalization and death from data of cohort studies. Such a model could help understanding the relationships between dementia and institutionalization and also allow to make correct inferences when the initial sample of a cohort was selected as not living in institution. We consider the case where times of death and entrance in institution are known exactly while the clinical status of dementia is observed only at discrete time points. We give the likelihood in this setting and propose a penalized likelihood approach for estimating the transition intensities. A simulation study demonstrates that this non-parametric approach yields satisfactory results in this complex setting.