Estimating a change-point of baseline age in the longitudinal trajectories of biomarkers: application to an imaging study of preclinical Alzheimer disease.

Background: Biomarkers are routinely measured from human biospecimens and imaging scans in Alzheimer disease (AD) research. Age is a well-known risk factor for AD. Detecting the age at which the longitudinal change in biomarkers starts to accelerate, i.e., a change-point in age, is important to design preventive interventions. Methods: We analyzed longitudinal biomarker data by a random intercept and random slope model where the slope (longitudinal rate of change) was modeled as a piecewise linear and continuous function of baseline age. We proposed to estimate the intersection of the two linear functions, i.e., the change-point in age by multiple methods: maximum (profile) likelihood, minimum squared pseudo bias, minimum variance, minimum mean square error (MSE), and a two-stage method. We simulated large numbers of data sets to evaluate the performance of these estimators and implemented them to analyze the longitudinal white matter hypointensity from brain magnetic resonance imaging scans in an AD cohort study of 616 participants to estimate the age when the longitudinal rate of change starts to accelerate. Results: Our simulations indicated that performance was universally poor for all point estimators and CI estimates when the true change-point was near the boundary or when sample size was small (N=100). Yet, the proposed change-point estimators became approximately unbiased and showed relatively small MSE when sample size increased (N>200) and the true change-point was away from boundary. The 95% CIs from these methods also provided good nominal coverage with large sample sizes if the change-point was away from boundary. When applied to the AD biomarker study, we found that almost all methods yielded similar estimates to the change-point from 59.19 years to 65.78 years, but the profile likelihood approach led to a much later estimate. Conclusions: Our proposed estimators for the change-point performed reasonably well, especially when it is away from the boundary and the sample sizes are large. Our methods revealed a largely consistent age when the longitudinal change in white matter hypointensity started to accelerate. Further research is needed to tackle more complex challenges, i.e., multiple change-points that may depend on other AD risk factors.