# Duration data analysis

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

The textbook for the course is

• Klein and Moeschberger (2003) Survival analysis - techniques for censored and truncated data, second edition.

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 11.10.18).

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, 9 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.

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 12.10.18). Last part of slides regarding estimation of survival function. Log rank test. Cox's proportional hazards model. Solve exercise 15, 16, 23 in ex-cat (updated 11.10.18). The theoretically inclined may also consider exercise 13. Read KM 8.1-8.3.

7. Oct 26 8.15-12 We will finish slides from last time regarding Cox's proportional hazards model. Next we consider model assessment (updated 24.10.18). We will also conduct a mid-term evaluation. Solve 17, 18, 19 in exercise catalogue. Also give a detailed account of the profile likelihood approach. Read KM 8.4, 8.5, 8.8, 9.3 and 11.1-11.6.

8. Oct 30 8.15-12 We consider an example of model assessment and consider a simulation study. Some code regarding model assessment. Code for simulation study of model assessment. We next consider first 15 slides in counting processes (updated 06.11.18). Read KM section 3.6. You may also take a look at this paper. Show results regarding distributions of S(X) and H(X) on Cox-Snell slide. Solve exercises 1 and 2 in counting process slides. Start working on miniproject (updated 29.09.17) if time allows.

9. Nov 2 Miniproject: analysis of cirrhosis data.

11. Nov 6 8.15-12 We finish counting processes. We will probably also start on the material for Wednesday. Solve exercise 3.9 in KM.

12. Nov 7 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 (updated 05.11.18). Code for analysis of bone marrow transplant data. Some advice on timedependent covariates in R. We also start considering frailty (updated 16.11.18) models.

10. Nov 13 8.15-12 Presentation of miniproject and exercises 16, 17, 18, 19 as well as counting process exercises 1,2.

14. Nov 16 8.15-12 We continue with frailty models. Some code for frailty models. We also consider competing risks. Read KM 13.1, 13.3, 13.4 and 2.7. Note on competing risks.

13. Nov 19 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.

15. Nov 27 8.15-12 Presentation of exercises regarding parametric models and exercises from November. Opsummering af kursets indhold.

5218 9.3KM, afprøv parametrisk model på cirrhosis data
5222: 2.3KM, 2.15KM, Exercise 3 fra frailty.pdf
5230 2.9KM, 2.13KM, Exercise 1 fra frailty.pdf