# Messages

We will start by discussing the solution to the obligatory exercise, which is now posted under "Exercises and solutions". We may also have a look at the solution to the Extra exercises 5 that were given for the previous week. We will then continue the discussion of earlier exam exercises. First wel finish Exercise 1 from 2012 (on the Nelson-Aalen estimator) and then we have a look at Exercise 1 from 2016 (on the Kaplan-Meier estimator). Then we will consider Exercise 3 from 2016 (on survival regression), Exercise 3 from 2018 (nonparametric tests), Exercise 2 from 2016 (parametric survival models), Exercise 2 from 2014 (frailties). [The ordering of these may be changed].

We will finish the presentation of .Slides 16 (Chapter 7 in book). on multivariate frailty models. We will then briefly discuss the obligatory exercise and other exercises given for this lecture and the previous lecture. Then we will start looking at earlier exam exercises, trying to cover as much as possible in the curriculum. We will start by Exercise 1 in the exam from 2012 (Nelson-Aalen estimator) and will reconsider Slides 6 first, for notation and a repetition of the counting process theory. Next will be Exercise 1 from 2016 (Kaplan-Meier estimator).

We will finish the presentation of .unobserved heterogeneity in Slides 15 (Chapter 6 in book). Then we will go on to Slides 16, "Multivariate frailty models" (Chapter 7 in book), which concerns statistical inference in connection with frailkty models. We will also have a look at the exercises for this week.

Note that some earlier exams are posted on the course website, two of them with sketches of solutions. As far as I can see, they are essentially all relevant for this year's course. A selected subset of them will be discussed in the last two lectures, and some will be given as exercises for the two last weeks.

We will continue the presentation of .Slides 14, "Parametric survival models", restarting at page 27. The next topic will be "Unobserved heterogeneity", which is treated in Slides 15 (a preliminary version can now be downloaded). And remember the deadline for the oblligatory exercise!

We will start by a short recap of Aalen's additive model (Slides 13) and look at a couple of examples. The main topic of the lecture will be from Slides 14, ``Parametric survival models". which corresponds to Chapter 5 in the book. After the lecture, from 15:00-16:00, you may discuss issues in the obligatory exercise (which has deadline on Thursday next week).

Guidance for the obligatory exercise will be given after the lecture on Thursday October 24; from 15:00 to 16:00. Otherwise, you may send emails, preferably to the email address bo.lindqvist@ntnu.no.

The main topic for the lecture is Aalen's additive model as presented in Slides 13. We will also discuss some issues from last week's lecture and from the exercises for this week. The obligatory exercise will be posted before the lecture, and we may have a short look at it. The deadline is October 31.

We will og 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. We will also discuss the exercises for today as needed. If there is time, we will continue With Slides 13 (to be posted later) on Aalen's additive hazard model which is an interesting alternative to the Cox model.

We will complete the discussion of Slides 10 on nonparametric tests. In particular we will have a closer look at the logrank test (from p. 9 on) for two samples and its extension to several samples. Then we will go to regression modeling (Slides 11). We will also briefly discuss the exercises for today.

Last time we started to look at Slides 9 on multistate models (pages 1-7). We will start from the beginning today and go through the complete set. Then we will turn to Slides 10 on nonparametric tests. The main focus will here be on the log-rank test for testing whether two samples of survival data come from the same underlying survival distribution. In the last 45 minutes the plan is to go througn the announced exercises for week 39.

We will go through Slides 8 on the Kaplan-Meier estimator and the product-integral. Then we consider multistate models in Slides 9. Finally, we will go through the exercises for this week.

We will first sum up (Slides 6) the main concepts and results from Chapters 1 and 2 that will be needed in Chapter 3. Then we go on with a closer study of the Nelson-Aalen estimator and its various applications in multiplicative intensity models (Slides 7), and, if time permits, we start looking at the Kaplan-Meier estimator.

After discussion in class, we agreed that the deadline for the "Oblig" should be Thursday October 31, with posting on the course website two weeks before that.

A revision of Slides 5 can be downloaded under 'Slides for STK4080...'. We will go through the slides from approximately page 35, where we finished last time. When finishing Slides 5, we have covered the curriculum of Chapters 1 and 2 in the book, and we will start on Chapter 3 next week. Slides 5 (revised) contain several exercises, and we will discuss them in class as we go on. We will also have a look at the exercises from the first half of Slides 5.

We will start by a quick reconsideration of the Kaplan-Meier estimator and the Nelson-Aalen estimator as presented in Slides 4. The main task for the lectures will be to go through Slides 5 which cover most of Chapter 2 in the book. This theory is basic to the theoretical derivations of the above estimators, as well as extensions of them to be considered later. As time permits, we will go through the exercises for the present week, 1.1-1.5 in book. A solution will be posted after the lecture.

In the first lecture, I will try to go through all or most of Slides 1-4, which can be downloaded from this homepage. These slides are meant to cover the core of Chapter 1 in the book. Slides 5 will be the topic of the second lecture on August 29.

The first lecture is on Thursday August 22 at 12:15-15:00 in NHA 108.

We will use the course book:

Aalen, O.O., Borgan, Ø., and Gjessing, H.: *Event History Analysis: A Process Point of View.* Springer-Verlag, 2008. ISBN: 978-0-387-20287-7

The book is availabe as an e-book if you are working on a computer at the University of Oslo.