# Lectures in STK4080 autumn 2019

Week 46: We finished the presentation of .Slides 16 (Chapter 7 in book) on multivariate frailty models. As part of this, we went through the exercises that were given inside these slides. We then started to og through Exercise 1 in the exam from 2012 (on the Nelson-Aalen estimator). In this connection we first revisited Slides 6 in order to recall notation and give a repetition of the main aspects of counting process theory. A solution to the obligatory exercise was posted, and we will discuss it next week.

Week 45: We finished the presentation of .unobserved heterogeneity in Slides 15 (Chapter 6 in book). Then we went on with Slides 16, "Multivariate frailty models" (Chapter 7 in book), which concerns statistical inference in connection with frailty models. We almost finsihed, but the last part on recurrent events remain. The exercises for this week were not discussed, but will be considered next week.

Week 44: We finished Slides 14 on parametric survival modeling. Then we went through pages 1-17 of Slides 15 on unobserved heterogeneity.

Week 43: We first give a short recap of additive regression, looking at the examples of Lecture 9 from the lecture notes "Modern Survival Analysis" by David Steinsaltz. Then we og on with Slides 14 on parametric survival modeling.

Week 42: We started by going through the basics of competing risks, which is the main topic for the obligatory exercise. We then went back to some of the model checking methods for Cox regression which were discussed last week, in particular methods for transformation of covariates. A method from Practical exercise 8 was discussed in particular. The new topic was Aalen's additive model, as presented in Slides 13.

Week 41: We went through Slides 12 which specializes on Cox regression and techniques for model checking etc. Slides 12 also contains a brief discussion of asymptotics for Cox regression.

Week 40: We completed the discussion of Slides 10 on nonparametric tests. In particular we considered the logrank test (from p. 9 on) for two samples and its extension to several samples. A hand-calculation scheme was given and will be used in one of the exercises for next week. Then we went on with regression modeling (Slides 11), presenting a classical case study in the end (the case study has now been added at the end of Slides 11).

Week 39: We went through in some detail p. 1-14 of Slides 9 on multistate models. Then we went more quickly through p. 15-22, looking at Example 3.16 for motivation. Finally we had a brief look at the general setup of p. 23-24. We next went through in some detail p. 1-8 in Slides 10. We will start next time by having a closer look at the logrank test (from p. 9 on).

Week 38: We went through Slides 8 on the Kaplan-Meier estimator and the product-integral. Then we went through the exercises for this week, and started to go through Slides 9 on multistate models, covering pages 1-7 (will repeat this Next week).

Week 37: We went through Slides 6, which sums up the main concepts and results from Chapters 1 and 2, needed in Chapter 3 and later. We then went through at Slides 7 which gives a closer look at the Nelson-Aalen estimator and its various applications in multiplicative intensity models. Finally, we looked at some of the exercises for today's lecture.

Week 36: We went through pages 34 to 58 in Slides 5 (revised). Pages 52 to 58 are important since they show how the theory applies to counting processes. We considered the derivation of the Nelson-Aalen estimator, while its properties (including asymptotics) will be taken NeXT week in connection with Chapter 3. Pages 68-71 in the slides were not covered in the lecture, but you are encouraged to look at them yourself and do the corresponding exercises. You are also encouraged to do all the exercises in the full set of slides that are not taken in class. Note that solutions to the exercises is given as a separate set of slides.

Week 35: We looked briefly at the Kaplan-Meier and Nelson-Aalen estimators in Slides 4. Then we went through Slides 5 from page 1 to page 35. Some of the exercises in the slides were done in class, the rest are due for the exercises for next week.

Week 34: We went through Slides 1-3 and the first part of Slides 4 (until slide 10/20). This covers the main parts of Sections 1.1 and 1.2, and parts of 1.4 and 1.5 (censoring, Cox-model, frailties).