Fast penalized generalized estimating equations for large longitudinal functional datasets

Area of Science:

• Neuroscience
• Biostatistics
• Computational Biology

Background:

• Longitudinal functional data, common in neuroscience (e.g., neural recordings), are often too large for existing functional regression methods.
• Analyzing large-scale datasets with complex outcomes like binary or count data presents significant computational challenges.

Purpose of the Study:

• To propose a novel, efficient, and scalable statistical method for analyzing large longitudinal functional data.
• To support generalized functional outcomes (binary, count, proportion, continuous) and both functional and scalar covariates.
• To enable fast estimation and valid inference even with large numbers of clusters and observations per cluster.

Main Methods:

• Development of one-step penalized generalized estimating equations (GEE) for functional data analysis.
• A semi-parametric approach allowing for efficient smoothing parameter selection and joint confidence interval construction.
• General theory for adaptive one-step M-estimation to ensure asymptotic normality and efficiency of coefficient estimates.

Main Results:

• The proposed method is computationally efficient, analyzing a large calcium imaging dataset (150,000 binary outcomes, 120 domain points) in ~6.5 minutes on a laptop.
• It reveals important timing effects in neural recordings that were obscured by non-functional analyses.
• Coefficient confidence intervals are asymptotically valid, even if the working correlation structure is misspecified.

Conclusions:

• The one-step penalized GEE method provides a fast and scalable solution for analyzing large-scale longitudinal functional data in neuroscience.
• The method offers valid statistical inference and uncovers biologically relevant patterns in complex neural data.
• The implementation is available in the R package `fastFGEE`.