# Duration data analysis

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

The textbook for the course is KM:

• 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 13.11.20).

Cirrhosis data and background on these data.

1. September 8 8.15-12 Slides (updated 18.11.20). 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. September 15 8.15-12 Slides (updated 15.09.20). 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. Lidt om regning med infinitesimale størrelser.

3. September 22 (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. September 24 (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. October 1 8.15-12 Groups present exercises.

6. October 8 8.15-12 Slides (updated 05.10.20). Cox's proportional hazards model (excluding slides on case of data with ties). Solve exercise 14, 15, and 23 in ex-cat. Consider also 16 and 13 if time allows. Read KM 8.1-8.3.

7. October 20 8.15-12 Cox PH in case of data with ties and Cox's model for discrete time data (video lecture). Next model assessment (updated 24.10.18). Code for an example of model assessment. Code for Andersen plot. 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. October 27 8.15-12 We consider a simulation study of model assessment. Code for simulation study of model assessment. We next consider first 15 slides in counting processes (updated 26.10.20). 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 2.1 in counting process slides. Start working on miniproject (updated 29.09.17) if time allows.

9. Miniproject: analysis of cirrhosis data.

10. November 10 8.15-12 We finish counting processes. Review of counting processes and martingales. Solve exercise 2.2 and 3 in counting process slides and exercise 3.9 in KM.

11. November 17 8.15-12 Counting processes and time-varying covariates. Slides on time-dependent covariates (updated 16.11.20). Code for analysis of bone marrow transplant data. Some advice on timedependent covariates in R. Read KM sections 9.1-9.2. Solve KM exercises 9.1 and 9.3 (note: you can use the tt() functionality for this) and exercise 27 in exercise catalogue (just updated).

We also start considering frailty (updated 16.11.20) models. Start solving exercises from frailty slides.

12. November 19 8.15-12 Presentation of exercises - see Moodle for allocation of exercises to groups.

13. November 24 8.15-12 We continue with frailty models. Some code for frailty models. Solve remaining exercises from frailty slides. We also consider competing risks. Read KM 13.1, 13.3, 13.4 and 2.7. Note on competing risks.

If remaining time: start on selfstudy.

14. November 26 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), KM12.1, KM12.9 a+b, KM12.13 a+b.

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. December 1 8.15-12 Presentation of exercises regarding parametric models and exercises from November. Opsummering af kursets indhold.