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.

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