Random change point models: investigating cognitive decline in the presence of missing data

With the aim of identifying the age of onset of change in the rate of cognitive decline while accounting for the missing observations, we considered a selection modelling framework. A random change point model was fitted to data from a population-based longitudinal study of ageing (the Cambridge City over 75 Cohort Study) to model the longitudinal process. A missing at random mechanism was modelled using logistic regression. Random effects such as initial cognitive status, rate of decline before and after the change point, and the age of onset of change in rate of decline were estimated after adjustment for risk factors for cognitive decline. Among other possible predictors, the last observed cognitive score was used to adjust the probability of death and dropout. Individuals who experienced less variability in their cognitive scores experienced a change in their rate of decline at older ages than individuals whose cognitive scores varied more.