Professor

Abstract

This thesis aims to advance pharmacokinetic (PK) analysis by introducing both new modeling strategies and rigorous inference frameworks. A key focus is on developing growth models that address nonlinearity and possible oscillations in drug concentration–time data, capturing more realistic absorption and elimination patterns than conventional methods. These models enable improved estimation of pivotal metrics, such as the Area Under the Curve (AUC), particularly when the data exhibits steep initial uptake, prolonged decay, or periodic fluctuations. Beyond refining point estimates, the thesis also aims to provide enhanced tools for uncertainty quantification. In many PK studies—especially those involving serial sacrifice or other destructive sampling protocols—samples cannot be collected repeatedly from the same subjects. As a result, traditional confidence interval methods can become fragmented or overly simplistic. To remedy this, the thesis proposes a joint confidence ellipsoid framework, pooling limited or scattered observations into a unified view of variability across all time points. This approach is then extended to encompass batch designs, where multiple groups of subjects are measured at discrete intervals, as well as complete designs, in which each subject is measured fully over time. By integrating latent-variable modeling with advanced distributional theory, these methods ensure that high-dimensional inference remains tractable and informative. In pursuit of these aims, multiple real datasets are analyzed, including one that assesses a biodegradable polymer patch intended for treating spina bifida. Because each patch can only be measured once, the research highlights how the proposed methods capture the overall kinetic behavior of the material’s interaction with different fluids, despite limited per-sample information. Through these demonstrations, the thesis ultimately seeks to improve the reliability and interpretive power of PK analyses, even when experiments are constrained by sparse sampling, complex dynamics, or unorthodox data collection designs.