In this article, we present the novel approach of using a multi-state model to describe longitudinal changes in cognitive test scores. Scores are modelled according to a truncated Poisson distribution, conditional on survival to a fixed endpoint, with the Poisson mean dependent upon the baseline score and covariates. The model provides a unified treatment of the distribution of cognitive scores, taking into account baseline scores and survival. It offers a simple framework for the simultaneous estimation of the effect of covariates modulating these distributions, over different baseline scores. A distinguishing feature is that this approach permits estimation of the probabilities of transitions in different directions: improvements, declines and death. The basic model is characterised by four parameters, two of which represent cognitive transitions in survivors, both for individuals with no cognitive errors at baseline and for those with non-zero errors, within the range of test scores. The two other parameters represent corresponding likelihoods of death. The model is applied to an analysis of data from the Canadian Study of Health and Aging (1991-2001) to identify the risk of death, and of changes in cognitive function as assessed by errors in the Modified Mini-Mental State Examination. The model performance is compared with more conventional approaches, such as multivariate linear and polytomous regressions. This model can also be readily applied to a wide variety of other cognitive test scores and phenomena which change with age.
Keywords: Ageing; cognitive function; dementia; longitudinal data; mortality; multi-state model; transition probabilities; truncated Poisson distribution.
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