Fitting joint models of longitudinal observations and time to event by sequential Bayesian updating

Area of Science:

• Biostatistics
• Statistical modeling
• Longitudinal data analysis

Background:

• Joint modeling of longitudinal and time-to-event data is crucial in biostatistics.
• Standard methods face computational challenges with high-dimensional and large electronic health record datasets.
• Numerical integration for latent state variable marginalization is often prohibitive.

Purpose of the Study:

• To present an alternative, computationally efficient approach for fitting joint models.
• To enable analysis of complex, high-dimensional longitudinal and time-to-event data.
• To facilitate the use of these models with large electronic health record datasets.

Main Methods:

• Sequential Bayesian updating for model fitting.
• Factorization of the likelihood into state-space and Poisson regression models.
• Utilizing Kalman filter for efficient updates in linear Gaussian state-space models.

Main Results:

• The proposed method offers a computationally feasible alternative to standard joint modeling techniques.
• The approach effectively handles high-dimensional data by avoiding intensive numerical integration.
• Demonstrated successful application on a publicly available dataset.

Conclusions:

• Sequential Bayesian updating provides an efficient framework for joint modeling.
• This method significantly reduces computational burden for complex biostatistical analyses.
• The approach is implementable with existing statistical software, promoting wider adoption.