A comparison of non-homogeneous Markov regression models with application to Alzheimer's disease progression

Markov regression models are useful tools for estimating risk factor effects on transition rates between multiple disease states. Alzheimer's disease (AD) is an example of a multi-state disease process where great interest lies in identifying risk factors for transition. In this context, non-homogeneous models are required because transition rates change as subjects age. In this report we propose a non-homogeneous Markov regression model that allows for reversible and recurrent states, transitions among multiple states between observations, and unequally spaced observation times. We conducted simulation studies to compare performance of estimators for covariate effects from this model and alternative models when the underlying non-homogeneous process was correctly specified and under model misspecification. In simulation studies, we found that covariate effects were biased if non-homogeneity of the disease process was not accounted for. However, estimates from non-homogeneous models were robust to misspecification of the form of the non-homogeneity. We used our model to estimate risk factors for transition to mild cognitive impairment (MCI) and AD in a longitudinal study of subjects included in the National Alzheimer's Coordinating Center's Uniform Data Set. We found that subjects with MCI affecting multiple cognitive domains were significantly less likely to revert to normal cognition.