Flexible link functions in a joint hierarchical Gaussian process model.

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Medical Statistics

Background:

• Longitudinal studies often jointly model biomarkers and event outcomes for improved disease progression prediction.
• Cystic Fibrosis (CF) research benefits from joint models, particularly for lung function and survival.
• Existing models may not fully capture nonlinear biomarker trajectories or complex event associations.

Purpose of the Study:

• To propose a novel joint model accommodating nonlinear lung-function trajectories in CF.
• To enhance inference on lung-function decline and its association with pulmonary exacerbation (PE) recurrence risk.
• To improve dynamic prediction of disease progression in CF patients.

Main Methods:

• Utilized a shared-parameter framework with a two-level Gaussian process (GP) for nonlinear longitudinal trajectories.
• Introduced a flexible link function to accurately model the binary outcome of PE recurrence.
• Employed Bayesian model assessment for evaluating model components in simulations and real CF data.

Main Results:

• A nonlinear structure was identified in both continuous lung function and binary PE event data.
• The inclusion of a flexible link function significantly improved model fit.
• The proposed hierarchical GP model with a flexible power link function (spep) demonstrated the best fit, linking accelerated lung function decline to higher PE odds.

Conclusions:

• The novel joint model effectively characterizes the relationship between lung function decline and PE recurrence in CF.
• The model's ability to handle nonlinearities and flexible associations offers more accurate inference and prediction.
• This approach advances the statistical methodology for analyzing complex longitudinal health data.