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Non-homogeneous Markov process models with informative observations with an application to Alzheimer’s disease. (English) Zbl 1213.62132
Summary: 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.
We develop methods to deal with non-homogeneous Markov processes through time scale transformations 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.

62M05 Markov processes: estimation; hidden Markov models
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C60 Computational problems in statistics (MSC2010)
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