[Paper Review] Joint analysis for multivariate longitudinal and event time data with a change point anchored at interval-censored event time

Yue Zhan, Cheng Zheng+1 more|arXiv (Cornell University)|Feb 16, 2026

Genetic Neurodegenerative Diseases0 citations

TL;DR

The paper develops a two-phase joint model for multivariate longitudinal biomarkers with a change point anchored at interval-censored disease onset, and applies it to Huntington’s disease (PREDICT-HD) data to study cognitive-motor progression.

ABSTRACT

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.

Motivation & Objective

• Motivate the study of prodromal Huntington’s disease progression using joint modeling of longitudinal cognitive biomarkers and interval-censored motor onset time.
• Develop a causal two-phase joint modelling framework that allows a change point in biomarker trajectories at the interval-censored onset time.
• Provide estimation via spline-based semiparametric sieve maximum likelihood with an adaptive Newton-Raphson algorithm and bootstrap SEs.
• Assess finite-sample performance through simulations and apply the method to the PREDICT-HD cohort to infer interactions between cognition and motor onset.

Proposed method

• Extend the joint model to a two-phase structure with biomarker trajectories M_infty(t) before onset and M_E(t) after onset, incorporating a change-point gamma anchored at E.
• Model the hazard for onset time with a baseline lambda_0(t) and covariate effects theta_X, theta_A, and theta_M.
• Estimate the baseline hazard with cubic monotone B-spline basis and enforce monotonicity via reparameterization.
• Handle interval-censored onset times using an integral over (V, U] with Delta indicating observed onset within the interval.
• Compute parameters using a Fisher scoring algorithm with line search, Gauss-Legendre quadrature for time integrals, and Gauss-Hermite quadrature for random effects.
• Use finite-difference approximations for score and bootstrap (B=50) for standard errors, with initial values built from separate longitudinal and survival fits via the JM package.

Experimental results

Research questions

• RQ1 Does cognitive decline in multiple domains predict time to motor onset in prodromal HD?
• RQ2 Does motor onset act as a change point that accelerates subsequent cognitive decline?
• RQ3 Can a two-phase joint model with interval-censored onset provide unbiased inferences about these relationships?
• RQ4 How do baseline covariates (e.g., CAP, age, education, sex) influence cognitive trajectories and onset risk within this framework?

Key findings

• In the PREDICT-HD analysis, sydigtot significantly predicted HD onset after adjusting for CAP (HR=0.955, p=0.021).
• Stroopwo showed a weaker, non-significant trend for onset risk (HR=0.981, p=0.0624).
• Baseline CAP (per 1 unit/100 scale) strongly predicted onset (HR=2.159, p<0.0001).
• The change-point effect gamma was highly significant and negative for both biomarkers: sydigtot (gamma=-1.288, p<0.0001) and stroopwo (gamma=-2.206, p<0.0001), indicating acceleration of decline after onset.
• Random effects terms for the longitudinal processes were non-significant in the survival model (p-values: 0.976 and 0.592), suggesting the association is driven by the longitudinal trajectory itself.
• Simulation results showed negligible biases, bootstrap SEs aligned with Monte Carlo SDs, and 95% Wald CIs with proper coverage; standard errors decreased ~1/sqrt(n) when n doubled.