Estimating the longitudinal trajectory of cognitive function measurement using short‐term data with different disease stages: Application in Alzheimer's disease

Alzheimer's disease (AD) is a chronic neurodegenerative disease characterized by a gradual decline in cognitive function over a few decades. The Mini‐Mental State Examination (MMSE) is a widely used measure for evaluating global cognitive functioning. Characterizing the longitudinal trajectory of the MMSE in the population of interest is important to detect AD onset for preventive intervention. In this study, we formulate a new class of longitudinal trajectory modeling for MMSE from short‐term individual data based on an ordinary differential equation. The proposed method models the relationship between individual decline speed of MMSE and the average MMSE using the fractional polynomial function model and subsequently estimates the longitudinal trajectory of MMSE by solving the ordinary differential equation for the estimated model. The appropriate model for trajectory estimation is selected based on the proposed criterion for quantifying the goodness of trajectory fit. The accuracy of the trajectory estimation of the proposed method was demonstrated via simulation studies. The proposed method was successfully applied to MMSE data from the Japanese Alzheimer's Disease Neuroimaging Initiative study.