Likelihood for Generally Coarsened Observations from Multistate or Counting Process Models
该文针对流行病学中常见的混合离散-连续观测模式，严格推导了多状态模型（包括非马尔可夫情况）的似然函数，并推广到更一般的粗化观测方案，对处理临床随访数据的研究者有用。
Abstract. We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other events are observed exactly. A heuristic likelihood can be written for such models, at least for Markov models; however, a formal proof is not easy and has not been given yet. We present a general class of possibly non-Markov multistate models which can be represented naturally as multivariate counting processes. We give a rigorous derivation of the likelihood based on applying Jacod's formula for the full likelihood and taking conditional expectation for the observed likelihood. A local description of the likelihood allows us to extend the result to a more general coarsening observation scheme proposed by Commenges & Gégout-Petit. The approach is illustrated by considering models for dementia, institutionalization and death.