Stat Colloquium: Dr. Siddhartha Nandy

Title: Personalized growth modeling using local polynomials

Abstract: The evolutionary laws of growth in fundamental sciences are often modeled using a dynamical systems framework. In several personalized medicine and healthcare problems the parameters that govern the dynamical system depend on the characteristics of the individual, and hence there is a need for a personalized growth curve modeling. We propose locally weighted polynomial regression algorithms to discover such growth-related dynamical systems from noisy observations. Our proposed methodology traces the intricate balance between borrowing strength across individuals to ensure high precision and accuracy, and the two tasks of fitting the local polynomial regression and the elicitation of the parameters of the dynamical system. We develop two competitive approaches: one where we first fit the local regression and use its results to obtain the dynamical system, and another where we estimate both the local regression and dynamical system simultaneously. To address the cascading dependency of bandwidth-dependent curve estimation leading into dynamical systems elicitation, we introduce a principled strategy for obtaining a bandwidth estimate. We develop the methodology for both single and multiple subject scenarios. Multi-subject variability is adjusted by random effects to accommodate subject-specific heterogeneity in initial conditions and growth rates. Our simulation studies demonstrate that second-degree local regression optimizes single-subject dynamical parameters, whereas higher-degree models improve multi-subject global parameter estimation. We validate these personalized growth feature models, which show reduced covariance estimation errors, using a real-world simulation of tumor growth in mice.