## Graduate Students Seminar

Wednesday, March 6, 2019 · 11 AM - Noon

Session Chair: | Janita Patwardhan |

Discussant: | Dr. Sousedik |

###### Speaker 1: Luan Nguyen

**Title***Chemical reaction simulation and application in diffusion***Abstract**- Chemical reaction describes the transformation process of substances and matter. It is a building block and commonly studied in physical and life science. In this talk we will discuss different methods of modeling elementary chemical reactions: stochastic simulation algorithm (SSA), chemical Langevin equation (CLE) and reaction rate equation (RRE). Underlying these methods are high-level differences such as stochastic/deterministic or continuous/discrete. However, their connection can be drawn with appropriate assumption.

We use the Michaelis-Menten model from enzyme kinetics to illustrate the numerical experiment. Finally, we show how the simulation method is applied as an compartment-based approach to the problem of diffusion and conclude with some remarks.

###### Speaker 2: Rabab Elnaiem

**Title***Some tests for the assessment of univariate and multivariate bioequivalence***Abstract**- Bioequivalence testing deals with assessing the similarity of two drug products with respect to the rate and extent to which the active drug ingredient is absorbed into the blood, and becomes available at the site of drug action.

A common bioequivalence criterion is that of average bioequivalence (ABE), which deals with testing if the difference between appropriate mean responses is within predefined equivalence limits. A popular test for ABE is the two one-sided t-test (TOST), introduced by Schuirmann (1981). However, the TOST is very conservative when the variability becomes large. While this may not always be a practical concern, we noticed that the conservatism of the TOST can be easily fixed by applying a bootstrap calibration. The type I error then becomes close to the nominal level, giving significant gain in power. Consequently, the bootstrap-calibrated TOST results in a reduction in sample size.

For assessing multivariate bioequivalence, we explore a test due to Munk and Pfluger (1999), when the hypothesis is stated in terms of a quadratic form, and the test is derived by inverting Hotelling's T2. We have characterized the test somewhat explicitly using results from Dong and Mathew (2015).