Nonparametric Modeling and Testing of Chemical-Chemical Interaction

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mingyu Xi*+
• Companies: University of Maryland Baltimore County
• Keywords: Bernstein polynomial ; cytotoxicity ; nonparametric interaction test ; shape restricted model ; Likelihood ratio test

Abstract

In environmental studies, people are often interested in understanding how exposures to multiple chemicals affect cell survival. One of the key questions is understanding interaction between the chemicals and often understanding the direction of interaction is important. In the absence of known joint models, we take a nonparametric approach using Bernstein Polynomials to model the probability of cell survivals under multiple chemical effects and propose a two -stage procedure for testing for multiplicative interaction in the nonparametric setting. We first choose a best model using model selection and then use the "best" model to construct a likelihood ratio test for interaction. We use resampling methods to approximate the critical region of the test. We illustrate our methodology using a reconstructed designed experiment involving cytotoxicity from exposure to common chemicals in batteries such as Nickel, Cadmium and Chromium. The Bernstein model is well-suited for testing for directional interaction in terms of the coefficients of the model. We propose a test for synergy/antagonism based on the fitted coefficients.