Morning Sessions:10:40-11:55 am

Recent Advances in Statistics and Applied Math

1. Dr Candidate: Xi Ning (Title: A Semiparametric Cox-Aalen Transformation Model with Censored Data)

2. Xu Cao (Title:Two-phase outcome-auxiliary-dependent sampling with failure time data)

3. Kaylen Forney and Anastasiia Unzhakova (Extracting Critical Elements of Bridge Design Using 2D Modeling)

1 Title: A Semiparametric Cox-Aalen Transformation Model with Censored Data

Abstract: We propose a broad class of so-called Cox-Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function within a transformation. The proposed models provide a highly flexible and versatile class of semiparametric models that include the transformation models and the Cox-Aalen model as special cases. Specifically, it extends the transformation models by allowing potentially time-dependent covariates to work additively on the baseline hazard and extends the Cox-Aalen model through a predetermined transformation function. We propose an estimating equation approach and devise an Expectation-Solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via modern empirical process techniques. The ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we demonstrate the performance of our procedures through extensive simulation studies and applications in two randomized, placebo-controlled HIV prevention efficacy trials. The data example shows the utility of the proposed Cox-Aalen transformation models in enhancing statistical power for discovering covariate effects.

2. Title: Two-phase outcome-auxiliary-dependent sampling with failure time data

Abstract: Epidemiological studies often seek to relate time to a failure event to some exposure variables that are expensive to obtain, thus large cohort studies under simple random sampling could be prohibitive to conduct with limited budget. Outcome-dependent sampling (ODS) is a commonly used cost-effective sampling strategy in such studies. To further enhance study efficiency upon ODS, we propose a two-phase outcome-auxiliary-dependent sampling (OADS) design by incorporating cheaply available auxiliary variables. It allows the probability of obtaining the expensive exposures to depend on both the failure time and auxiliary variables. To account for the sampling bias, we develop a two-step pseudo-likelihood approach for inference and a non-parametric bootstrap procedure for variance estimation. The proposed method is shown to bemore efficient than other competing sampling schemes. Its application to an epidemiological study is provided.

3 Title: Extracting Critical Elements of Bridge Design Using 2D Modeling

Abstract: Currently, many bridges in the United States are designed sub-optimally for natural disasters they may face. In this project, vertical and horizontal forces meant to mimic traffic and natural disasters are placed upon a two-dimensional bridge model using MATLAB. By employing classical mechanics as well as analysis from numerical linear algebra, important features of bridging design that can better resist adverse weather and carry heavy traffic are established. To stimulate a magnitude 6.84 earthquake, real life data from San Jose, California has been used. Similarly, real-world traffic data from large, metropolitan areas is used to calculate the traffic loading placed upon the simulated structure. To make the design more realistic, the optimized bridge uses a mixture of steel and wood beams. Various government and manufacturing standards are considered in the design, such as factor of safety, residual forces, relative deformation, and cost of bridge materials. These features in tandem create a realistic model whose results are then analyzed and used to determine the quality of the structure’s performance.

The goal of this study is to determine how all of the new features developed in this study perform in a single design. The results from these simulations will be used to determine the most critical elements of a bridge’s design. By understanding the most critical elements of bridge design, bridges that are better able to withstand extreme conditions can be built.