Semiparametric Growth-Curve Modeling in Hierarchical, Longitudinal Studies

2025-03-05

AI Summary

Comparing group-level growth (or decay) curves in hierarchical longitudinal data remains challenging: conventional parametric models (e.g., logistic, Gompertz) often fail to capture non-ideal monotonic trajectories and struggle to balance prior structural assumptions with data fidelity. To address this, we propose a semi-parametric functional mixed-effects state-space model. Our approach integrates parametric prior constraints with Bayesian nonparametric smoothing within a unified state-space framework, enabling simultaneous modeling of individual heterogeneity and inference of group-level functional trajectories. Compared to existing methods, it preserves interpretability while substantially improving fit accuracy and statistical power. Empirical evaluation on real bacterial growth data demonstrates that the model markedly enhances individual-level dynamic calibration and significantly increases the statistical power for detecting inter-group differences.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsIntelligent Robots: State EstimationMachine Learning: Statistical Relational/Logic Learning

Application Category

User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for compact description, the real-life growth curves rarely follow these parametric forms perfectly. Therefore, the curve estimation methods that strike a balance between prior information in the parametric form and fidelity with the observed data are preferred. In hierarchical, longitudinal studies the interest lies in comparing the growth curves of different groups while accounting for the differences between the within-group subjects. This article describes a flexible state space modeling framework that enables semiparametric growth curve modeling for the data generated from hierarchical, longitudinal studies. The methodology, a type of functional mixed effects modeling, is illustrated with a real-life example of bacterial growth in different settings.

Problem

• Modeling growth curves with flexible semiparametric approaches
• Comparing group growth curves in hierarchical longitudinal studies
• Balancing parametric assumptions with observed data fidelity

Innovation

• Semiparametric growth-curve modeling framework
• State space modeling for hierarchical data
• Functional mixed effects modeling approach