TY - JOUR
T1 - A nonstationary Markov transition model for computing the relative risk of dementia before death
AU - Yu, Lei
AU - Griffith, William S.
AU - Tyas, Suzanne L.
AU - Snowdon, David A.
AU - Kryscio, Richard J.
PY - 2010/3/15
Y1 - 2010/3/15
N2 - This paper investigates the long-term behavior of the k-step transition probability matrix for a nonstationary discrete-time Markov chain in the context of modeling transitions from intact cognition to dementia with mild cognitive impairment and global impairment as intervening cognitive states. The authors derive formulas for the following absorption statistics: (1) the relative risk of absorption between competing absorbing states and (2) the mean and variance of the number of visits among the transient states before absorption. As absorption is not guaranteed, sufficient conditions are discussed to ensure that the substochastic matrix associated with transitions among transient states converges to zero in limit. Results are illustrated with an application to the Nun Study, a cohort of 678 participants, 75-107 years of age, followed longitudinally with up to 10 cognitive assessments over a 15-year period.
AB - This paper investigates the long-term behavior of the k-step transition probability matrix for a nonstationary discrete-time Markov chain in the context of modeling transitions from intact cognition to dementia with mild cognitive impairment and global impairment as intervening cognitive states. The authors derive formulas for the following absorption statistics: (1) the relative risk of absorption between competing absorbing states and (2) the mean and variance of the number of visits among the transient states before absorption. As absorption is not guaranteed, sufficient conditions are discussed to ensure that the substochastic matrix associated with transitions among transient states converges to zero in limit. Results are illustrated with an application to the Nun Study, a cohort of 678 participants, 75-107 years of age, followed longitudinally with up to 10 cognitive assessments over a 15-year period.
KW - Absorption statistics
KW - Dementia
KW - Mild cognitive impairment
KW - Nonhomogeneous Markov chain
KW - Nun study
KW - Random effect
KW - Transition model
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U2 - 10.1002/sim.3828
DO - 10.1002/sim.3828
M3 - Article
C2 - 20087848
AN - SCOPUS:77649195144
SN - 0277-6715
VL - 29
SP - 639
EP - 648
JO - Statistics in Medicine
JF - Statistics in Medicine
IS - 6
ER -