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 graphi- cally 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 scan- ning statistics that can detect local changes in the distribution of edges in a subset of the graph. The second study is on the application of survival analysis in a healthcare problem. We develop a statistical machine learning model that accurately predicts the post-transplant survival curves for pediatric recipients of kidney transplants. The last study of the thesis is on a graph based variable selection method in survival analysis. We propose to incorporate a fused lasso type of constraint in the Cox proportional hazard model, which takes advan- tage 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.
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Statistical detection and survival analysis with applications in sensor networks and healthcare
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