Huntington's disease (HD) is an autosomal dominant neurodegenerative disorder characterized by motor dysfunction, psychiatric disturbances, and cognitive decline. The onset of HD is marked by severe motor impairment, which may be predicted by prior cognitive decline and, in turn, exacerbate cognitive deficits. Clinical data, however, are often collected at discrete time points, so the timing of disease onset is subject to interval censoring. To address the challenges posed by such data, we develop a joint model for multivariate longitudinal biomarkers with a change point anchored at an interval-censored event time. The model simultaneously assesses the effects of longitudinal biomarkers on the event time and the changes in biomarker trajectories following the event. We conduct a comprehensive simulation study to demonstrate the finite-sample performance of the proposed method for causal inference. Finally, we apply the method to PREDICT-HD, a multisite observational cohort study of prodromal HD individuals, to ascertain how cognitive impairment and motor dysfunction interact during disease progression.
Huntington's disease (HD) is an inherited, autosomal dominant neurodegenerative disorder characterized by progressive motor dysfunction, cognitive decline, and psychiatric disturbances. The disease is caused by an abnormal expansion of CAG trinucleotide repeats in the HTT gene on chromosome 4, which leads to the production of a mutant huntingtin protein that disrupts normal cellular function [1,2]. Currently, there is no effective treatment available for HD patients.
Huntington’s disease encompasses motor, cognitive, and psychiatric manifestations, but the clinical diagnosis of onset is determined primarily by the emergence of motor symptoms [3]. However, cognitive impairment has been found to appear prior to HD motor diagnosis [4,5,6,7,8]. Zhang et al. [8] have thoroughly studied mild cognitive impairment (MCI) in various cognitive domains characterized by Harrington et al. [9], which is regarded as an early landmark for disease progression in prodromal HD individuals. Although a rapid cognitive decline at the early stage, attributed to the onset of HD, has been observed [10], an overarching study of how cognitive impairment interacts with HD onset was lacking, but will be helpful to understand the HD progression in prodromal HD individuals. In this work, we propose a holistic model to uncover the relationship between cognitive decline in multiple domains and HD onset using joint modeling of multivariate longitudinal and event time data.
Joint modeling of longitudinal and event time data has become increasingly important in biomedical studies, especially in chronic diseases, HIV/AIDS, cardiovascular research, etc, when understanding the interplay between longitudinal biomarkers and clinical events is crucial. The joint modeling framework was developed by simultaneously modeling the longitudinal and event time data under a structure with shared subject-specific random effects [11,12,13,14,15,16,17]. Recent development of the joint modeling method allows researchers to study the causal effect of the exposure on the survival outcome through the longitudinal marker [18,19]. Previous work showed that by including both the random effect and the longitudinal marker in the survival model, the joint model framework allows the researcher to separate the direct causal effect of the longitudinal marker on the outcome and the time-independent unmeasured confounding between the marker and the outcome [20,21]. The maximum likelihood method equipped with the EM algorithm has been a popular approach to estimate parameters in a joint model [22] for making statistical inferences. It is worth noting that most of the joint models were developed for longitudinal biomarkers and right-censored event time, emphasizing either unbiased inference for event time outcome using timedependent longitudinal biomarkers [13,14,23] or unbiased inference of longitudinal trajectories of the biomarkers subject to informative drop-out [24,25,26]. These methods are not applicable to study the relationship between cognitive impairments and the HD onset in prodromal HD individuals, which is subject to interval censoring bracketed by two adjacent motor diagnostic times, where the first time shows negative and the second time yields the motor diagnosis of HD. Although joint models of longitudinal biomarkers and interval-censored event times have been studied more recently [27,28,29,30], the methods did not concern the changes of longitudinal biomarkers triggered by the event time. Some two-phase changing-point analyses of longitudinal data around an interval-censored event time have been explored [31,32,33], but they did not address how the longitudinal data impacted the interval-censored event time. In addition, none of the aforementioned approaches were concerned with causal inferences.
In this work, we propose a two-phase approach by extending the likelihood method for joint modeling of longitudinal and interval-censored event time data to incorporate a potential change point in longitudinal biomarkers anchored at an unobserved event time, depicted in Figure (1), using the causal framework for the joint modeling [21].
The first phase of the model emphasizes how the longitudinal data impacts the event time, and the second phase investigates whether/how the event time changes the trajectories of longitudinal biomarkers. We use an adaptive Newton-Raphson algorithm to compute the maximum likelihood estimates (MLE) of all coefficients in this joint model, and the nonparametric bootstrap method to estimate the standard error of all estimated coefficients. F I G U R E 1 A hypothetical model for the HD disease progression: V and U are the two adjacent diagnosed times, with V being negative and U being positive for the HD diagnosis.
The rest of this paper is organized as follows: in Section 2, we describe our notation, models, and the likelihood method for the causal two-phase joint modeling of changing-point longitudinal data and interval-censored eve
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