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Abstract
Nonlinear models with switching functions are flexible and powerful tools for the analysis of hormetic data in many areas such as biology, public health, and toxicology. The purpose of this dissertation is to study ways of detecting and estimating hormesis precisely by using nonlinear models and designs. In this dissertation, we propose a new non-monotonic weighting function that can be used with any type of switching function to form a nonlinear non-monotonic hormetic model, which can be used to detect hormesis and estimate the location and the size of the maximum hormetic effect. Based on the nonlinear non-monotonic hormetic model, a sub-partial nonlinear regression method (SPNRM) is proposed to maximize the D-optimality criteria of a nonlinear hormetic design. Following that, we create a hormesisNMF module based on the R platform to provide users a user-friendly interface for analyzing hormetic data. Finally, we apply the logistic model with the non-monotonic weighting function to Escherichia coli (E. coli) data to examine the differences between various E. coli groups. We find that the new non-monotonic weighting function can be used in various scenarios to obtain the least biased parameter estimates.
