Week 16 (21.04): This was the last lecture. The plan was to discuss some important topics of the course via earlier exam exercises. A list of recommended exercises, covering the basic topics of the course, is found under "Earlier exams STK4080". Together with todays participants it was, however, decided to end the lecture after some introductory general discussion. Instead, the students are encouraged to work on their own with the curriculum and exam exercises, and email the lecturer whenever there are problems. Personal digital meetings is also a possible option. There was no Canvas recording of this lecture.
Week 15 (14.04): We started by going through Slides 16 (we did pages 1-24 last time, but went through these pages today, too, for completeness). Then we discussed some aspects of the obligatory exercise. After this, we started the discussion of relevant previous exam exercises. A list of recommended exercises has been put under "Earlier exams STK4080". The plan is to go more or less thoroughly through (today and next week, in the cited order, as far as we get....): 2019,2 (counting processes) 2016,1 (Kaplan-Meier); 2016,3 (survival regression); 2019,4 (nonparametric tests). Today we discussed 2019,2, and in this connection we had a new look at Slides 6 on counting processes. These slides sum up the theory for counting processes based on martingales, on which much of the course is built. The lecture was recorded is available in Canvas.
Week 14 (07.04): We started by going through the extract of Slides 15 which can be found here. Recall that Slides 15 contain the main ideas of modeling.unobserved heterogeneity (Chapter 6 in ABG). In this connection we also went through Problem 4 of the exam from 2020 (this was given as one of the exercises for today). With all this as the background, we started to go through Slides 16 on multivariate frailty models (Chapter 7 in ABG). This topic concerns statistical inference in connection with frailty models. Slides 16 combine this with using R. We ended the lecture with page 24. The lecture was recorded is available in Canvas.
Week 12 (24.03): We finished Slides 14 on parametric survival modeling. We started from the beginning, going quickly through the first 20 pages (that were also considered last week). From page 21 started the more theoretical part on the derivation of the likelihood in general under the counting process framework. Then we continued with a special modeling approach using Poisson regression for analysis of Cox-like models. The tutorial on Weibull and Poisson regression contains an example of this. Afterwards, we started going through Slides 15 on unobserved heterogeneity. Slides 15 contain the theoretical basis for the so called frailty models, and we were able to go through all of the pages (except the last). We will then next time in Slides 16 come back to the use of frailty models (and some variations of them) in statistical inference (Wednesday April 7). The lecture was recorded and will be available in Canvas.
Week 11 (17.03): We went through all of Slides 13 on Aalen's additive regression model. We had a very quick look at the tutorial on additive regression which may be downloaded from Computing. You are encouraged to go through this for yourself, trying the commands in R. We went on with Slides 14 on parametric survival modeling where we covered pages 1-20. We continue next week with the last part of Slides 14. There was also a question from the audience regarding the obligatory exercise. The lecture was recorded and can be found by login to Canvas.
Week 10 (10.03): We started by going through Slides 12 on Cox regression, with emphasis on model checking techniques. The last pages on asymptotic theory of the maximum partial likelihood estimator was not covered (you are encouraged to do this yourself). Instead, we were able to go through the first part of Slides 13 on Aalen's additive regression model (p. 1-14). We also had a look at the solution of exercises E.3.1. The lecture was recorded and can be found by login to Canvas.
Week 9 (03.03): We started by recalling some of the main ideas and results for the logrank test and other tests in Slides 10. This was mainly done via the "extract of Slides 10" that can be found here.Then we started to go through Slides 11, which is the introduction to regression modeling, including a first presentation of Cox regression. These slides end with some R-code, which you are recommended to go through yourself using R. The original plan was to cover also parts of Slides 12, but it was time for only a very quick look. Topics from Slides 12 are, however, part of exercise E.4 for next week, so you are advised to have a closer look at some of Slides 12. We had a brief look at the solutions for exercises E.2 and ASAUR 4.1 and 4.2. The lecture was recorded and can be found by login to Canvas.
Week 8 (24.02): We started from the beginning of Slides 9 on multistate models, with emphasis on the part on competing risks. We went more quickly through the parts on the illness-death model and the general model within the resulting Aalen-Johansen estimator. The main goal was to give an intuitive understanding of the formulas, and otherwise to reefer to the book. For the practical use of the methods with R, it is referred to the tutorials on competing risks and the illness-death models given under `Computing' (see exercises for next week). We then started to go through Slides 10 on nonparametric tests, including the logrank test. We covered pages 1-16 which give the theoretical basis for the methods, ending with a hand-calculation example from ASAUR. We will have a look at the last pages, 17-32, next week, but without going too much into detail. We went through exercises ABG 3.8 and ASAUR 3.1-3.2 which were part of the exercises for this lecture. The lecture was recorded and can be found by login to Canvas.
Week 7 (17.02): We started by going through an "extract" of the first pages of Slides 8, complementing and explaining the presentation from last week. Then we continued with the original Slides 8. These slides are based on Chapter 3.2 in ABG and give the theoretical basis for the Kaplan-Meier estimator. After having gone through the main ideas of exercise 2.12 in ABG, we started going through Slides 9 on multistate models (page 1-12 were considered). These slides include competing risks, which we in fact also looked at in connection with the multiplicative model in Slides 7. The lecture was recorded and can be found by login to Canvas.
Week 6 (10.02): We started by going through a summary ("extract") from last lecture, with slides given here. At the end of these slides, we went through Rebolledo's central limit theorem for martingales and applied it to the Nelson-Aalen estimator. The presentation here is somewhat polished as compared to the treatment in Slides 6, but is essentially equivalent. We continued by Slides 7 which present various applications of the Nelson-Aalen estimator (Chapter 3.1 in ABG). We then started to go thorugh Slides 8 (page 1-6 today) which gives the theoretical basis for the Kaplan-Meier estimator. We also had a brief look at exercises E.1.1 and E.1.2. Two polls were held: One resulting in a favor of continuing to record lectures, and one resulting in a majority for going through some of the exercises in the Wednesday lectures. The lecture was recorded and can be found by login to Canvas.
Week 5 (03.02): We started by going through a summary from last lecture (the last part of Slides 5). This summary is found here. Then we continued with Slides 6 from page11. These slides end with a first treatment of the Nelson-Aalen estimator from Chapter 3, including the estimate of variance and the asymptotic distribution. There was not enough time to go through the asymptotics, so we will take the last pages of Slides 6 next week. The lecture was recorded and can be found in Canvas.
Week 4 (27.01): We finished Slides 5 (which cover sections 2.1 and 2.2.1-2.2.4 in ABG) by going through 33-51 (continuous time martingales). We started by going through the four page summary of pages 1-32 (discrete time martingales), which is found here. We then went over to Slides 6 on counting processes, which are the main tools of this course. Slides 6 cover sections 1.4, 2.2.5-2.2.6, and 2.3 in ABG. The slides end with a first look at the Nelson-Aalen estimator from Chapter 3. On January 27.01 we went through pages 1-10 out of 33 pages, so we continue next week on page 11 of Slides 6. The lecture was recorded and can be found in Canvas.
Week 3 (20.01): We went quickly through the informal introduction of the Kaplan-Meier and Nelson-Aalen estimators in Slides 4. This was for motivation for the rest of the course, while the theoretical treatment including standard errors confidence intervals etc will come later (Chapter 3). The main part of today's lecture was will to go through pages 1-32 of Slides 5, which covers the theory of martingales from Chapter 2 in ABG. We will complete the coverage of Slides 5 next week. NOTE: The following pages of Slides 5 are not important for the rest of the course, and were considered rather quickly in the lectures: pages 21-22 and 25-30. They were included in the slides because they give a more complete introduction, and because they are included in Chapter 2 of ABG. The book ASAUR is not relevant for today's topics.
Week 2 (13.01) We went through Slides 1-3 and just the start of Slides 4. In ABG (main book): Reading list: ABG 1.1, 1.2, 1.5. Supplementary reading: ASAUR (Applied Survival Analysis Using R) : 1.3, 1.4, 2.1-2.4.