Estimating the baseline age when longitudinal changes in biomarkers accelerate: application to an imaging study of preclinical Alzheimer disease

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 baseline age at which the longitudinal change in biomarkers starts to accelerate is important to design preventive interventions. 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 baseline age at the intersection of the two linear functions 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. Finally, we implemented them to analyze the longitudinal white matter hypointensity from brain magnetic resonance imaging scans in an AD cohort study of 616 participants conducted by the Washington University (WU) Knight Alzheimer Disease Research Center (ADRC) to estimate the baseline age when the longitudinal rate of change starts to accelerate. Our simulations indicated that performance was universally poor for all point estimators and confidence interval (CI) estimates when the true baseline age corresponding to the accelerated longitudinal change was near the boundary or when the sample size was small (N = 100). Yet, the proposed estimators became approximately unbiased and showed relatively small mean squared error when the sample size increased (N > 200) and the true baseline age was away from the boundary. The 95% CIs from these methods also provided good nominal coverage with large sample sizes if the true baseline age when the rate of change started to accelerate was away from the boundary. When applied to the AD biomarker study, we found that almost all methods yielded similar estimates of baseline age from 59.19 years to 65.78 years, but the profile likelihood approach led to a much later estimate. We proposed a novel longitudinal statistical model to estimate the baseline age when the rate of change in a biomarker started to accelerate and presented multiple methods to estimate the parameter. Our proposed estimators performed reasonably well, especially when the true parameter was away from the boundary and the sample sizes were large. When applied to an imaging study of preclinical AD, our methods revealed a largely consistent baseline age when the longitudinal change in white matter hypointensity started to accelerate. Further research is needed to tackle more complex challenges, i.e., multiple accelerations in the longitudinal change that may also depend on other AD risk factors. N/A.