The integration and collaboration of computer science, health sciences, and statistics have been developed and implemented extensively. Given this trend, understanding of the importance and necessity of statistical science is crucial for scholars in all research fields.  This talk will first briefly introduce some areas of advances in statistical research. The discussion following will mainly focu  s on two areas on the forefront of statistical research: one, an improved piecewise exponential model for cancer survival; two, the analysis of complex computer models having qualitative and quantitative inputs.

1. In medical research, statistical models for survival data are typically non- or semi-parametric, e.g., the Kaplan-Meier curve. A major constraint of the existing parametric models is the lack of flexibility due to distribution assumptions. A flexible and parsimonious piecewise exponential model is introduced in this talk. Such modeling provides an additional descriptive tool in understanding differences in patient response and can also serve as a validation tool for exponential failure. An application in a lung cancer study is presented.

2. Gaussian Stochastic Process models are a popular way to model output from computer experiments. Unfortunately, the correlation functions typically used in these models assume inputs are quantitative. This talk introduces a method for handling both quantitative and qualitative inputs. The proposed method builds on an ANOVA-type decomposition of the response variable and a Bayesian hierarchical approach with an empirical prior. It improves some existing approaches when there is a common underlying shape in the response for each level of the qualitative variables. An application is demonstrated in a hip prosthetic device finite element analysis computer simulation model.