Bayesian Semi- and Non-parametric Models for Longitudinal Data with Multiple Membership Effects in R

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Software Development

Background:

• Repeated measures data with multiple membership (MM) structures, where subjects participate in overlapping sets of intervention elements, present unique analytical challenges.
• Existing methods may not fully capture the complex dependencies and individual trajectories inherent in such data, particularly in group-based interventions like cognitive behavioral therapy (CBT).

Purpose of the Study:

• To introduce `growcurves`, an R package designed for the comprehensive analysis of repeated measures MM data.
• To provide flexible hierarchical modeling approaches, including semi-parametric and fully non-parametric options, for understanding subject and element-level effects.
• To facilitate the extraction of by-subject growth curves and enhance information extraction from complex longitudinal study designs.

Main Methods:

• The `growcurves` package implements two hierarchical model frameworks: one with separate subject and MM element random effects (using Dirichlet process priors) and another with joint subject-by-MM effects.
• A dependent Dirichlet process formulation enables exploration of subject response differences across MM elements, allowing for information borrowing among subjects with similar trajectories.
• Estimation is performed via posterior sampling using compiled C++ for computational efficiency, complemented by plotting functions for visualizing individual growth curves.

Main Results:

• The package provides tools for robust estimation and visualization of longitudinal data within MM structures.
• The implemented models allow for flexible and semi-parametric analyses, accommodating complex dependencies and subject heterogeneity.
• Computational efficiency is achieved through C++ implementation, enabling practical application to real-world datasets.

Conclusions:

• The `growcurves` package offers a powerful and flexible solution for analyzing repeated measures MM data, particularly in intervention studies.
• It enables researchers to gain deeper insights into individual growth trajectories and the impact of multi-element interventions.
• The software is designed to anticipate inferential goals, maximizing information extraction from complex longitudinal data.