Non-homogeneous Markov process models with informative observations with an application to Alzheimer's disease

Baojiang Chen, Xiao Hua Zhou

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Identifying risk factors for transition rates among normal cognition, mildly cognitive impairment, dementia and death in an Alzheimer's disease study is very important. It is known that transition rates among these states are strongly time dependent. While Markov process models are often used to describe these disease progressions, the literature mainly focuses on time homogeneous processes, and limited tools are available for dealing with non-homogeneity. Further, patients may choose when they want to visit the clinics, which creates informative observations. In this paper, we develop methods to deal with non-homogeneous Markov processes through time scale transformation when observation times are pre-planned with some observations missing. Maximum likelihood estimation via the EM algorithm is derived for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. An application to the Alzheimer's disease study identifies that there is a significant increase in transition rates as a function of time. Furthermore, our models reveal that the non-ignorable missing mechanism is perhaps reasonable.

Original languageEnglish (US)
Pages (from-to)444-463
Number of pages20
JournalBiometrical Journal
Volume53
Issue number3
DOIs
StatePublished - May 2011
Externally publishedYes

Keywords

  • Markov
  • Missing data
  • Non-homogeneous
  • Transformation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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