Semiparametric Growth-Curve Modeling in Hierarchical, Longitudinal Studies

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.