Flexible Distributed Lag Models for Count Data Using mgcv.

Area of Science:

• Environmental Epidemiology
• Biostatistics
• Statistical Modeling

Background:

• Distributed Lag Non-Linear Models (DLNMs) are crucial for analyzing environmental exposures and health outcomes.
• Flexible implementation and robust model checking are essential for reliable epidemiological research.
• The R package mgcv offers powerful tools for advanced statistical modeling.

Purpose of the Study:

• To demonstrate the flexible implementation of DLNMs using the R package mgcv.
• To showcase methods for uncertainty quantification and comprehensive model checking.
• To illustrate the application of DLNMs in epidemiological research with real-world data.

Main Methods:

• Utilizing the mgcv package in R for DLNM implementation.
• Employing approximate Bayesian inference by interpreting smoothing splines as random quantities.
• Incorporating temporal structures, mixture distributions for outliers, covariate interactions, and spatial components (smooth variability, Markov random fields, hierarchical formulations).

Main Results:

• Demonstrated flexible DLNM implementation in R.
• Showcased uncertainty quantification and model checking capabilities.
• Illustrated handling of temporal structures, outliers, covariate interactions, and spatial dependencies.

Conclusions:

• The R package mgcv provides a flexible framework for implementing DLNMs.
• Approximate Bayesian inference facilitates robust uncertainty quantification and model validation.
• The methods are applicable to complex epidemiological data with various structures.