Amy Laird
Multi-state models are appealing tools for analyzing data about the progression of a disease over time. In a 2007 Statistics in Medicine paper, Salazar et al consider a multi-state Markov chain with two competing absorbing states: dementia and death, and three transient non-demented states: congnitively normal, amnestic mild cognitive impairment, and non-amnestic mild cognitive impairment. Using a polytomous logistic regression model with shared random effects, the authors derive the likelihood function and estimates for the effects of the covariates on transitions. The presence of the shared random effect complicates the form and maximization of the likelihood function. Three approaches to likelihood maximization are compared via simulation: one based on Gauss quadrature, one on importance sampling, and one on Taylor expansion. The approach with the best performance is used in an application to a longitudinal study on a cohort of cognitively normal subjects, followed annually for conversion to mild congnitive impairment of dementia, conducted at the Sanders Brown Center on Aging at the University of Kentucky. In this talk, I will review their work and discuss possible future directions.
