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 11.09.17).

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 (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 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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