Graduate Student Seminar

Speaker 1: Mingyu Xi

Title

Statistical Modeling and Hypothesis Testing of Chemical-Chemical Interaction: a Nonparametric Approach

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.  We propose a test for interaction based on the fitted coefficients.

Speaker 2: Shuyan Zhai

Title

Equivalence Testing of Dissolution Profiles

Abstract

Emphasis has been put on the meaningful comparisons of dissolution profiles by the pharmaceutical sponsors and the regulatory authorities. A dissolution profile is recorded as the percent amount of active drug ingredient dissolved at specific  time points. Records of multiple sample tablets from lab batches form multiple dissolution profiles. The approaches for such comparisons among two or more dissolution profiles include formulating the problem as testing the equivalence of the mean profiles. In the method we describe, bootstrap procedure, along with bootstrap calibration are employed for estimating the distribution of test statistic under null hypothesis, and thus building a reliable rejection area. In some cases, it states that batch effects are not ignorable. We take the problem into consideration by introducing a random effect model where batch effect is considered to be a random effect. Simulations under various scenarios are conducted to show the performance of the method. An real data example is then introduced to illustrate the usage of the method in practice.