Abstract
A model is presented that describes bivariate longitudinal count data by conditioning on a progressive illness-death process where the two living states are latent. The illness-death process is modelled in continuous time, and the count data are described by a bivariate extension of the binomial distribution. The bivariate distributions for the count data approach include the correlation between two responses even after conditioning on the state. An illustrative data analysis is discussed, where the bivariate data consist of scores on two cognitive tests, and the latent states represent two stages of underlying cognitive function. By including a death state, possible association between cognitive function and the risk of death is accounted for.
Highlights
In ageing research, longitudinal data are often collected for various tests of cognitive function
We propose a statistical framework which allows inference on change in cognitive function by modelling longitudinal count data for two correlated tests conditional on two latent states of cognitive function, and with death as an observable third state
It often the case that the process of interest is latent and that it is investigated via observable response variables
Summary
Longitudinal data are often collected for various tests of cognitive function. When two tests are available, it make sense to look at options to model both tests simultaneously For this reason, we propose a statistical framework which allows inference on change in cognitive function by modelling longitudinal count data for two correlated tests conditional on two latent states of cognitive function, and with death as an observable third state. Our statistical framework is an extension of this approach by introducing a bivariate state-dependent distribution This allows us to model two tests for cognitive function simultaneously. This assumption underlies some of the hidden multi-state models that are discussed in the literature; see, for example, Jackson et al (2016) This will be explored in the data analysis as a comparison to the bivariate approach. The first model is the bivariate binomial distribution of the count data conditional on the latent state.
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