Thesis Title: Statistical Detection and Survival Analysis with Applications in Sensor Networks and Healthcare

Advisors: 

Dr. Yao Xie, School of Industrial and Systems Engineering, Georgia Tech

Dr. Pinar Keskinocak, School of Industrial and Systems Engineering, Georgia Tech

Committee members:

Dr. Joel Sokol, School of Industrial and Systems Engineering, Georgia Tech

Dr. Kamran Paynabar, School of Industrial and Systems Engineering, Georgia Tech

Dr. Brian M. Gurbaxani, CDC

Date and Time: 4:00 - 6:00 pm, Tuesday, June 30, 2020

Meeting URL (for BlueJeans):

https://bluejeans.com/996452816

Meeting ID (for BlueJeans):

996452816

Abstract:



In this thesis, we present novel statistical methods for detecting abnormalities in a sequence of observations. We focus on two topics in statistics: change-point detection and survival analysis, and we demonstrate the application of our new methods in real data problems in the healthcare and the sensor network domains. We are particularly interested in cases in which the observations or predictors are related, and we summarize the relations graphically to develop new methodologies based on the graphs. 

The thesis consists of three major studies. The first is on sequential graph scan statistics in sensor networks. Given a sequence of random graphs with fixed vertices and changing edges, we are interested in detecting a change that causes a shift in the distribution of a subgraph. We present two graph scanning statistics that can detect local changes in the distribution of edges in a subset of the graph. The first statistic assumes a parametric model, and we present a theoretical approximation to the false alarm rate, which is verified to be accurate numerically. The second statistic adopts a nonparametric approach based on k-Nearest Neighbors. We demonstrate the efficiency of our detection statistics using a real dataset that records real-time seismic signals around the Old Faithful Geyser in the Yellowstone National Park.

The second study is on the application of survival analysis in a healthcare problem. Survival prediction is key to making efficient organ allocation decisions and optimizing patient outcomes. We develop a statistical machine learning model that accurately predicts the post-transplant survival curves for pediatric recipients of kidney transplants. The prediction is made based on statistically selected risk factors. We develop a new predicting model with higher concordance index than the existing models. 

The last study of the thesis is on a graph based variable selection method in survival analysis. When developing an accurate survival predicting model, identifying the proper variables to include in the model is often essential. In many applications, there exists an underlying graphical structure for the predictors. For example, some predictors may have strong correlations or interactions. When predicting the survival probability of a transplant recipient, it is important to consider the compatibility of the recipient and the organ donor. In such cases, incorporating the predictor graph into the penalty function for variable selection would allow more accurate inference and prediction. In this section, we propose to incorporate a fused lasso type of constraint in the Cox proportional hazard model, which takes advantage of the predictor graph generated by the relations among the predicting variables. We derive theoretical performance guarantees to the model and demonstrate the benefits of it using simulations and real data examples.