Purpose of the course
The analysis of survival data is critical in medical research,
whether one is studying the lifetimes of cells, tumors, or humans. This
course aims to develop an intuitive understanding of the theory of
survival analysis methods using counting processes and martingales. This
will provide participants with a deeper understanding of survival data
analysis methods in medical research, enabling them to better interpret
and analyze them.
Intended learning outcomes
After successfully completing this course, students will be able
to:
- Summarize basic asymptotic theory for processes and sketch
derivations of basic results involving the empirical cumulative
distribution function.
- Identify notation and terminology for counting processes and connect
them to survival statistics.
- Reframe nonparametric estimators of survival quantities in terms of
counting processes.
- Paraphrase the martingale central limit theorem and describe how it
can be used to perform inference for the Kaplan-Meier estimator.
- Interpret the proportional hazards, additive hazards, and parametric
regression models from the counting process perspective.
- Compare and contrast theoretical and methodological advances in
survival analysis, including frailty models, multi-state models, joint
models, causal inference and prediction for survival analysis.
Contents of the course
The course will cover the following topics:
- Overview of the course. Counting process introduction, notation and
terminology.
- Martingale introduction, terminology, and limit theorems. Censoring,
types, assumptions.
- Representation of Nelson-Aalen and Kaplan-Meier Estimators.
Asymptotic analysis. Logrank tests and variants, Confidence bands.
- General regression models, likelihood and asymptotic analysis. Time
dependent covariates and censoring assumptions.
- Proportional hazards models, stratified models, residuals. Additive
hazards models, relative survival.
- Non martingale analysis using empirical process theory. Functional
delta method and examples.
- Parametric models, including AFT and flexible parametric, frailty
(Andrea Discacciati).
- Multi state models introduction and regression. Competing risks and
illness death models (Therese Andersson).
- Causal inference, pseudo-observations, multiple time scales,
recurrent events.
Literature
The required course textbook is
Odd O. Aalen, Ørnulf Borgan and Håkon K. Gjessing. Survival and Event
History Analysis: A process point of view. Springer-Verlag, 2008.
[ABG]
other required papers will be provided by the teacher.
Recommended textbooks for further reading are
Thomas R. Fleming, David P. Harrington. Counting Processes and
Survival Analysis. Wiley-New York, 1991.
Per K. Andersen, Ørnulf Borgan, Richard D. Gill, Niels Keiding.
Statistical Models Based on Counting Processes. Springer-Verlag,
1993.