A nonstationary Markov transition model for computing the relative risk of dementia before death

Yu et al have a new paper in Statistics in Medicine. This is concerned with estimating the risk of dementia before death. A 5 state multi-state model is used, with three transient states representing levels of cognitive impairment, plus two absorbing states dementia and death. Unlike other recent dementia studies using multi-state models, improvements, as well as deteriation, in cognitive ability are assumed possible. A discrete-time approach is taken. This has some advantages in terms of the flexibility in modelling possible in terms of incorporating non-homogeneity over time and a frailty term - the Markov assumption. A drawback of using a discrete-time approach in the current study was that the study did not have equally spaced observation times, but it was necessary to assume this was the case for the discrete-time model. This is likely to cause some bias.

The main theoretical development in the paper is expressions for the mean and variance of the time spent in each transient state before absorption in the non-homogeneous case.