STATS 331: Survival Analysis
The 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 Health Research and Policy, lutian@stanford.edu
Richard Olshen, Department of Statistics and Department of Health Research and Policy,
olshen@stanford.edu
Content
The 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 KaplanMeier estimator, logrank test, proportional hazards regression model and various extensions.
Specifically, we will cover the following topics:
1. basic concepts and parametric distributions
2. right-censoring/Interval-censoring and informative censoring .
3. counting process and martingale theory
4. Kaplan-Meier estimator
5. Mantel-Haenszel/log-rank/Cox
6. proportional hazards
7. Breslow estimator and prediction based on proportional hazards model
8. Time-dependent covariates and coefficients
9. Tree-structured survival analysis
If time allows, we will also cover
1. Accelerated failure time model
2. Recurrent event and correlated survival time
3. Competing risks
Textbook
There 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.
Software
The course will teach how to perform survival analysis using R
Assessment
The 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%).