Syllabus database for doctoral courses
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Syllabus database for doctoral courses
SYLLABI FOR DOCTORAL COURSES
| Swedish title | Överlevnadsanalys med hjälp av räkneprocesser |
|---|---|
| English title | Theory of Survival Analysis Using Counting Processes |
| Course number | 5400 |
| Credits | 7.5 |
| Responsible KI department | Institutionen för medicinsk epidemiologi och biostatistik |
| Specific entry requirements | The specific entry requirements are one of the following: 1/. At least 60 higher education credits (HEC) from 1st and/or 2nd cycle courses in the subjects: statistics, probability, mathematics, or data science, of which at least 20 HEC must be in statistics or probability; or 2/. A course in probability theory of at least 7.5 HEC at 2nd cycle level, a course in statistical inference of at least 7.5 HEC at 1st or 2nd cycle level. and A course in statistical inference of at least 7.5 HEC at 3rd cycle level. The student should also have attended a doctoral course in applied survival analysis. |
| Grading | Passed /Not passed |
| Established by | The Committee for Doctoral Education |
| Established | 2021-08-19 |
| 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 | 1. Overview and some basics about the empirical process and modern empirical process theory;
2. Motivation of counting processes including notation and terminology. 3. Representation of Nelson-Aalen, Kaplan-Meier, and Aalen-Johansen Estimators in terms of counting processes. 4. Types of censoring and assumptions about censoring. 5. Basic terminology and notation about martingales. Limit theorems involving martingales and how to apply them. 6. Statistical inference, asymptotic normality and efficiency of Nelson-Aalen and Kaplan-Meier estimators. Logrank tests and its variants, asymptotic theory, confidence bands. 7. Proportional hazards and additive hazards models from the counting process perspective. 7. Parametric survival models, including accelerated failure time and flexible parametric models. 8. Frailty models, noncollapsibility, and causal inference. |
| Teaching and learning activities | The course will run over 10 weeks, with 3 meeting days of coursework per week. Each week will consist of 3 - 5 hours of traditional lecture, group discussion, plus independent or group work on written problem sets. Students will be provided with reading material and written assignments that will be worked on independently and discussed in groups. |
| Compulsory elements | All lectures, group discussions, and in-class exercises are compulsory. If a student misses one of these, they will be given an opportunity to compensate by presenting the topic for the teacher at a separate occasion or doing an additional written assignment. |
| Examination | To pass the course the student must show that the learning outcomes are achieved. This will be assessed with a take-home written assignment that is done during the final week of the course. The assignment is to choose from a list of research papers (provided by the teacher), and answer a list of short questions that prompt the student to demonstrate achievement of the learning outcomes by applying them to the selected paper. Written feedback will be provided by the examiner, and the assignment is graded pass-fail. |
| Literature and other teaching material | 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. 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. |
Course responsible |
Michael Sachs Institutionen för medicinsk epidemiologi och biostatistik 0765780983 michael.sachs@ki.se Nobels väg 12A 17177 Solna |
| Contact person |
Gunilla Nilsson Roos Institutionen för medicinsk epidemiologi och biostatistik 08-524 822 93 gunilla.nilsson.roos@ki.se |
