Duration data analysis

This course is concerned with analysis of duration data - also known as survival analysis.

The textbook for the course is

The course will be evaluated (pass/fail) by active participation in solving exercises and presenting solutions of exercises.

Vemmetofte data and Thieles report concerning establishing a "klosterforsikring" (materiale venligst stillet til rådighed af Professor Steffen L. Lauritzen).
Catalogue of exercises (updated 11.09.17).

Cirrhosis data and background on these data.



1. Sep 7 8.15-12 Slides (updated 07.09.18). We will consider examples of duration data and discuss particular aspects of such data. Read KM Chapter 1. Solve exercises 4, 5 and 7 in catalogue of exercises.

2. Sep 14 8.15-12 Slides (updated 14.09.18). Estimation of the survival function and the cumulative hazard. Read KM 4.1-4.3. Solve exercises 6, 8, 10, 11 in exercise catalogue. Code for simulation study.

3. Sep 21 8.15-12 (selfstudy) basic concepts: survival function, hazard function, mean residual life time. Read KM 2.1-2.4. Solve exercises 1, 2, 3 and 12 in catalogue of exercises.

Solve exercises 4.1 (a)-(d) and exercise 4.5 (a)-(c) in KM (you're welcome to use R survfit() - check documentation via help(survfit.formula)). Data from KM are available in the R-package KMsurv.

CAUTION: the std.err returned by survfit() is for the estimate of the cumulative hazard - not for the estimate of the survival function.

4. Sep 28 8.15-12 (selfstudy) censoring and likelihoods. Read KM 3.1-3.5. Solve exercises 3.1, 3.3, 3.7 (a) and 3.8 in KM.

5. Oct 5 8.15-12 Groups present exercises.

6. Oct 12 8.15-12 Slides (updated 12.10.17). Last part of slides regarding estimation of survival function. Log rank test. Cox's proportional hazards model. Solve exercise 9 and 10 (last part) and 15 in ex-cat. The theoretically inclined may also consider exercise 13. Read KM 8.1-8.3.

7. Oct 26 8.15-12 Cox's proportional hazards model. Solve 16, 17, 18, 19 in exercise catalogue. Also give a detailed account of the profile likelihood approach. Read KM 8.4, 8.5 and 8.8. Solution to computation of mean and variance in exercise 3.8 in KM.

8. Oct 30 8.15-12 Slides. Some code. Model assessment. Read KM 9.3 and 11.1-11.6. We will also conduct a mid-term evaluation. Show results regarding distributions of S(X) and H(X) on Cox-Snell slide. Start working on miniproject (updated 29.09.17).

9. Nov 2 Miniproject: analysis of cirrhosis data.

10. Nov 7 8.15-12 Presentation of miniproject and exercises 9, 16, 17, 18, 19. Followed by lecture: Cox's partial likelihood in case of ties. Exercise: check the expression for Cox's discrete time partial likelihood. If time allows we will also discuss model selection.

11. Nov 13 8.15-12 We start by considering model assessment in a simulation study. Then we consider counting processes. Read KM section 3.6. You may also take a look at this paper. Counting process slides (updated 23.10.17). Solve exercise 3.9 in KM and exercises 1 and 2 in slides.

12. Nov 16 8.15-12 Counting processes and time-varying covariates. Read KM sections 9.1-9.2. Solve KM exercises 9.1 and 9.3 (note: you can use the tt() functionality for this). Slides on time-dependent covariates. Code for analysis of bone marrow transplant data. Some advice on timedependent covariates in R. Code for simulation study of model assessment.

13. Nov 27 8.15-12 Selfstudy: parametric models and parametric inference. Read KM 2.5-2.6 and KM 12.1-12.5. KM exercises 2.1, 2.3, 2.9, 2.13, 2.15 (try in exercise 2.9 b) to replace 2 in front of W with 2/1.8 where 1.8 is the standard deviation of W).

Continuation of analysis for cirrhosis data: try to apply a parametric model for the data (survreg() procedure in R). Can you identify a suitable parametric model by considering the estimate of the baseline cumulative hazard H_0 fitted under the Cox regression model ? Compare the results with the Cox regression results.

14. Nov 30 8.15-12 Competing risks. Read KM 2.7. Correlated survival data and frailty models. Read KM 13.1, 13.3, 13.4. Slides (updated 14.11.17) and code. Note on competing risks.

15. Dec 4 8.15-12 Presentation of exercises regarding parametric models and exercises from November xx.


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