Penalized spline modeling of the ex-vivo assays dose-response curves and the HIV-infected patients' bodyweight change

Abstract

A semi-parametric approach incorporates parametric and nonparametric functions in the model and is very useful in situations when a fully parametric model is inadequate. The objective of this dissertation is to extend statistical methodology employing the semi-parametric modeling approach to analyze data in health science research areas. This dissertation has three parts. The first part discusses the modeling of the dose-response relationship with correlated data by introducing overall drug effects in addition to the deviation of each subject-specific curve from the population average. Here, a penalized spline regression method that allows modeling of the smooth dose-response relationship is applied to data in studies monitoring malaria drug resistance through the ex-vivo assays.The second part of the dissertation extends the SiZer map, which is an exploratory and a powerful visualization tool, to detect underlying significant features (increase, decrease, or no change) of the curve at various smoothing levels. Here, Penalized Spline Significant Zero Crossings of Derivatives (PS-SiZer), using a penalized spline regression, is introduced to investigate significant features in correlated data arising from longitudinal settings. The third part of the dissertation applies the proposed PS-SiZer methodology to analyze HIV data. The durability of significant weight change over a period is explored from the PS-SiZer visualization. PS-SiZer is a graphical tool for exploring structures in curves by mapping areas where rate of change is significantly increasing, decreasing, or does not change. PS-SiZer maps provide information about the significant rate of weigh change that occurs in two ART regimens at various level of smoothing. A penalized spline regression model at an optimum smoothing level is applied to obtain an estimated first-time point where weight no longer increases for different treatment regimens.