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Joint modelling of survival and cognitive decline in the Australian Longitudinal Study of Ageing


Petra L. Graham, Department of Statistics, Faculty of Science, Macquarie University, North Ryde, NSW 2109, Australia.


Summary.  The paper describes the use of a longitudinal tobit model to characterize cognitive decline over a 13-year period in a cohort of 2087 elderly Australians. Use of a tobit formulation allows for the so-called ‘ceiling effect’ wherein many subjects achieve perfect test scores. A Bayesian hierarchical joint model is presented that allows for random subject-specific intercepts and slopes, as well as for informative dropout. Results suggest several potential areas of intervention. For example, there is a clear dose–response effect of exercise whereby increasing levels of exercise are associated with higher cognitive scores.