Quantile regression with a change-point model for longitudinal data: An application to the study of cognitive changes in preclinical alzheimer's disease

Abstract

Progressive and insidious cognitive decline that interferes with daily life is the defining characteristic of Alzheimer's disease (AD). Epidemiological studies have found that the pathological process of AD begins years before a clinical diagnosis is made and can be highly variable within a given population. Characterizing cognitive decline in the preclinical phase of AD is critical for the development of early intervention strategies when disease-modifying therapies may be most effective. In the last decade, there has been an increased interest in the application of change-point models to longitudinal cognitive outcomes prior to and after diagnosis. Most of the proposed statistical methodology for describing decline relies upon distributional assumptions that may not hold. In this article, we introduce a quantile regression with a change-point model for longitudinal data of cognitive function in persons bound to develop AD. A change-point in our model reflects the transition from the cognitive decline due to normal aging to the accelerated decline due to disease progression. Quantile regression avoids common distributional assumptions on cognitive outcomes and allows the covariate effects and the change-point to vary for different quantiles of the response. We provided an approach for estimating the model parameters, including the change-point, and presented inferential procedures based on the asymptotic properties of the estimators. A simulation study showed that the estimation and inferential procedures perform reasonably well in finite samples. The practical use of our model was illustrated by an application to longitudinal episodic memory outcomes from two cohort studies of aging and AD.

Keywords: Alzheimer's disease; Change-point model; Cognitive aging; Disease progression; Longitudinal data; Quantile regression.

Figure 1

Spaghetti plots of episodic memory score against age (a) and time to AD diagnosis (b)

Figure 2

Episodic memory score against time to diagnosis of AD conditional on ApoE4 status with fitted 80th (dotted), 50th (dashed) and 20th (solid) quantile regression lines. The fitted quantile regression lines are for the sample mean of age at diagnosis in the sample used to fit model (22): 86.1 years old.