Estimation of bivariate measurements having different change points, with application to cognitive ageing

Longitudinal studies of ageing make repeated observations of multiple measurements on each subject. Change point models are often used to model longitudinal data. We demonstrate the use of Bayesian and profile likelihood methods to simultaneously estimate different change points in the longitudinal course of two different measurements of cognitive function in subjects in the Bronx Aging Study who developed Alzheimer's disease (AD). Analyses show that accelerated memory decline, as measured by Buschke Selective Reminding, begins between seven and eight years before diagnosis of AD, while decline in performance on speeded tasks as measured by WAIS Performance IQ begins slightly more than two years before diagnosis, significantly after the decline in memory.