Statistical modeling and hypothesis testing of chemical-chemical interaction: a non-parametric approach


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Mathematics and Statistics



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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 procedures for testing for interaction in the nonparametric setting. We propose tests for the two most common forms of interaction, Bliss independence and Loewe additivity. To test for Bliss independence we use a two stage approach. 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. In the second part we generalize conventional parametric Loewe additive reference models to semiparametric and nonparametric zero interaction models. For the semiparametric model we use a one degree of freedom test for interaction that is analogous to classical one degree of freedom test in ANOVA. In the nonparametric approach we use procedures for likelihood ratio tests in non-nested model and investigate the performance of the test via simulation studies. The final part of the investigation deals with directional interaction. 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. In the Loewe additive model we use a contour based test to investigate directional interaction. We also discuss some future directions for the research.