## Graduate Students Seminar

Wednesday, October 23, 2019 · 11 AM - Noon

Session Chair: | Sumaya Alzuhairy |

Discussant: | Dr. Guler |

###### Speaker 1: Mingkai Yu

**Title***Analysis and Simulation of Fluorescence Correlation Spectroscopy***Abstract**- Fluorescence Correlation Spectroscopy (FCS) is a tool to determine the diffusivity of fluorescently labeled molecules in the solution by measuring the fluctuation of fluorescence intensity. We provide a mathematical derivation to illustrate how the correlation of the intensity signal reveals the diffusivity. To quantify the uncertainty, we also derive a formula for the variance of the autocorrelation function in integral form and we find a closed-form upper bound. Monte Carlo simulations will be presented to compare with the theory.

###### Speaker 2: Nivya George

**Title***Joint Analysis of Survival Time and Longitudinal Categorical Outcomes***Abstract**- In biomedical or public health research, it is common for both survival time and longitudinal categorical outcomes to be collected for a subject, along with the subject’s characteristics or risk factors. Investigators are often interested in finding important variables for predicting both survival time and longitudinal outcomes which could be correlated within the same subject. Existing approaches for such joint analyses deal with continuous longitudinal outcomes. New statistical methods need to be developed for categorical longitudinal outcomes. A proposed method is simultaneously model the survival time with a Cox proportional hazards model and the longitudinal categorical outcomes with a generalized linear mixed model. The results of analyses based on simultaneous model and separate analysis of outcomes were compared.