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

UR - http://www.scopus.com/inward/record.url?scp=77649195144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77649195144&partnerID=8YFLogxK

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 -