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 5 8.15-12 Slides (updated 07.09.17). 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 7 8.15-12 Slides (updated 18.09.17). Estimation of the survival function and the cumulative hazard. Read KM 4.1-4.3. Solve exercises 6, 8, 10 (first part), 11 in exercise catalogue. Code for simulation study.

3. Sep 12 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 14 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. Sep 18 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.

6. Sep 25 12.30-16 room 2.115 Groups present exercises. If time allows we also consider Cox's proportional hazards model.

5.222: exercise 4, 5, 4.1, 4.5.

5.224: 3, 10, 3.1.

5.219a: 3.3, 3.7, 3.8.

5.219b: 11, 12.

7. Sep 28 room 5.034 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. Sep 29 room 2.115 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. Oct 5 Miniproject: analysis of cirrhosis data.

10. Oct 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.

5.222: miniproject 2. Exercise 9.

5.224: miniproject 4. Exercise 16.

5.219a: miniproject 5. Exercise 17, 18.

5.219b: miniproject 1, 3, 6. Exercise 19.

11. Oct 19 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. Oct 23 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. Oct 31 Study-relevant lectures at the two-day meeting in Aarhus.

14. Nov 7 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.

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.

15. Nov 14 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.

16. Nov 21 Presentation of exercises regarding parametric models and exercises from November 14.

5.222: parametric analysis of cirrhosis data. Exercise 1 from 14/11.

5.224: 2.1, 2.3, Exercise 2 from 14/11.

5.219a: 2.9, 2.13, Exercise 3 from 14/11.

5.219b: 2.15, Exercise 4 from 14/11.


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