STATS 331: Survival Analysis



STATS 331/BIODS 231-01: Survival AnalysisThe course will introduce basic concepts, theoretical basis and statistical methods associated with survival data. Topics include censoring, Kaplan-Meier estimation, logrank test, proportional hazards regression, accelerated failure time model and competing risks. The traditional counting process/martingale methods as well as modern empirical process methods will be covered. Prerequisite: Understanding of basic probability theory and statistical inference methods.Instructors:Lu Tian Department of Biomedical Data Science, lutian@stanford.edu Richard Olshen, Department of Biomedical Data Science, olshen@stanford.eduContentThe class will begin with an introduction to the basic concepts such as survival function, hazards and censoring as well as commonly used parametric models in survival analysis. We will then introduce the counting process and martingale theory, which are the the mathematical tools for deriving statistical inference method in survival analysis. Lastly we will introduce the Kaplan-Meier estimator, logrank test, proportional hazards regression model and various extensions. Specifically, we will cover the following topics (tentative): basic concepts and parametric distributions right-censoring/Interval-censoring and informative censoring .counting process and martingale theoryKaplan-Meier estimatorMantel-Haenszel/log-rank/Cox proportional hazardsBreslow estimator and prediction based on proportional hazards modelTime-dependent covariates and coefficientsfrailty models, general transformation model and accelerated failure-time models Tree-structured survival analysis Fixed effects versus random effects; competing risks Inverse probability weighting methodsTextbookThere will be no assigned textbook for this class in addition to the lecture slides and notes. However, the following is a list of useful references starting from the most applied book:Survival Analysis: Techniques for censored and truncated data (Statistics for biology and health) by John P. Klein and Melvin L Moeschberger (2005) The statistical analysis of failure time data by John D Kalbfleisch and Ross L. Prentice (2002)Counting Processes and survival analysis by Thomas Fleming and David P. Harrington (2005)Statistical models based on counting processes by Per Kragh Andersen, Ornulf Borgan, Richard, D Gill and Niels Keiding (1997)We will also supplement the lecture notes with selected landmark research papers such as Cox’s original JRSSB paper on proportional hazards model. SoftwareThe course will teach how to perform survival analysis using RAssessmentThe assessment consists of weekly homework (40%), requiring either mathematical derivation using technique taught in the class or conduction of some real data analysis with R, and a take home course project, which will be given in the last week of the quarter (60%). Course website may find the lecture notes, slides and homework at the website. ................
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