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Longitudinal data analysis, spring 2009

What's new

The last lecture will be on Tuesday (April 28). We will review topics on missing data and any other questions that may have risen.

The 2nd course exam will take place on Tuesday, May 5, at 10 a.m. - 1 p.m. The exam will cover the lectures 8-17, the corresponding chapters/sections in the book, and exercises
6-10. You can find a more detailed list of contents of the exam below.

Exercise 10 (Friday, April 24) http://www.rni.helsinki.fi/~kja/exercise10.pdf
http://www.rni.helsinki.fi/~kja/simulbinary.R

Lecture 18 (Tuesday, April 21). We continue with
reading the article by Lindsey and Lambert (see Lecture 17).
Read sections 3, 4, 6 and 8 in particular. In addition, the
exam will be agreed upon. The options for its date are
Tuesday (April 28), the probably preferred Tuesday (May 5), or Thursday (May 7).

Answers to exercise 9
http://www.rni.helsinki.fi/~kja/answers9.pdf

Answers to exercise 8 http://www.rni.helsinki.fi/~kja/answers8.pdf

Exercise 9 (Friday, April 17) http://www.rni.helsinki.fi/~kja/exercise9.pdf

http://www.rni.helsinki.fi/~kja/simulpoisson.R

Answers to exercise 7. http://www.rni.helsinki.fi/~kja/answers7.pdf

Lecture 17 (Tuesday, April 6). Time dependent covariates (Chapters 12.1 and 12.3. In addition, the article "Lindsey & Lambert: On the appropriateness of marginal models for repeated measurements in clunical trials; Stat Med 17, 447-469 (1998)" will be discussed.)
http://www.rni.helsinki.fi/~kja/luento17.pdf

Lecture 16 (Tuesday, March 31). Sample size (Chapter 2).
http://www.rni.helsinki.fi/~kja/samplesize.pdf
http://www.rni.helsinki.fi/~kja/Otoskoosta.pdf

The will be a computer class exercise at 10-12 a.m. on
Friday , April 3.

Lecture 15 (Friday, March 20)http://www.rni.helsinki.fi/~kja/luento15E.pdf

Exercise 6 (Friday, Marc 20) http://www.rni.helsinki.fi/~kja/exercise6.pdf

Lecture 14 (Tuesday, March 17). http://www.rni.helsinki.fi/~kja/luento14E.pdf

Lecture 13 (Friday, March 13). The 1st exam is corrected
and will be returned. In addition, we start the chapter on transition models. http://www.rni.helsinki.fi/~kja/luento13E.pdf

Answers to exercise 5 http://www.rni.helsinki.fi/~kja/answers5.pdf

Answers to exercise 4 http://www.rni.helsinki.fi/~kja/answers4.pdf

12. Lecture (Friday, Feb 27) http://www.rni.helsinki.fi/~kja/luento12E.pdf

Exercise 5 (Friday, Feb 27) http://www.rni.helsinki.fi/~kja/exercise5.pdf

Lecturer

Kari Auranen

Scope

8 cu.

Type

Advanced studies

Prerequisites & Course description

Prerequisites: basic skills in linear algebra and general statistics are required. The course on Generalized linear models is helpful but not necessary background information.

Course description: In longitudinal studies repeated measurements are taken from the
same individual over time. This makes it possible to separate changes in the outcome
varibale over time (or age) from those between individuals. The course will concentrate
on general concepts in longitudinal data analysis, different ways of modelling longitudinal
data. The applications will be mostly from medicine and epidemiology but the statistical models are generic in the sense that they find applications in many different fields where
repeated measurements are required. Some class exercises are done with the statistical
software R.

Lectures

The lectures will be held on Tuesdays (10-12 a.m. C 323) and Fridays (10-12 a.m., D123)
The first lecture will be on Tuesday, January 20 (10-12 a.m., C323).

The last lecture will be in May, 2009.

Easter holiday 9.-15.4.

Course contents & Lecture summaries

Lecture summaries will appear on the course home page (i.e., here) during the course.

The preliminary plan of the course contents:

1. Characteristics of longitudinal data
2. Exploratory data analysis
3. Robust estimation of the covariance structure
4. Parametric modelling of the covariance
5. Estimation of individual parameters
6. Generalized linear modeld for longitudinal data
7. Marginal models
8. Random effects models
9. Transition models
10. Missing data in longitudinal studies

Lecture summaries

1. Introduction http://www.rni.helsinki.fi/~kja/luento1E.pdf
2. Exploring longitudinal data http://www.rni.helsinki.fi/~kja/luento2E.pdf
3. Linear models for longitudinal data http://www.rni.helsinki.fi/~kja/luento3E.pdf
4. Models of correlation structure (Chapter 5, 1st part)http://www.rni.helsinki.fi/~kja/luento4E.pdf
5. Fitting linear models (Chapter 5, 2nd part) http://www.rni.helsinki.fi/~kja/luento5E.pdf
6. Fitting linear models (continues)
7. Introduction to generalized linear models for longitudinal data (Chapter 7) http://www.rni.helsinki.fi/~kja/luento7E.pdf
8. Marginal models, 1st part http://www.rni.helsinki.fi/~kja/luento8E.pdf
9. Marginal models, 2nd part (Chapters 8.1 and 8.2) http://www.rni.helsinki.fi/~kja/luento9E.pdf
10. Marginal models, 3rd part (Chapters 8.3 and 8.4; Corrected version, 4.45 p.m., Feb 20) http://www.rni.helsinki.fi/~kja/luento10E.pdf
11. Random effects models, 1st part (Chapters 9.1, 9.2.1 and 9.3.1) http://www.rni.helsinki.fi/~kja/luento11E.pdf
12. Random effects models, 2nd part http://www.rni.helsinki.fi/~kja/luento12E.pdf
13. Transition models http://www.rni.helsinki.fi/~kja/luento13E.pdf
14. Missing values in longitudinal data (Chapters 13.1,13.2,13.3., 13.7) http://www.rni.helsinki.fi/~kja/luento14E.pdf
15. Missing values in LDA, part 2 (Chapters 13.1,13.4, 13.5)
http://www.rni.helsinki.fi/~kja/luento15E.pdf
16. Sample size (Chapter 2)
http://www.rni.helsinki.fi/~kja/samplesize.pdf
http://www.rni.helsinki.fi/~kja/Otoskoosta.pdf
17. Time dependent covariates (Chapter 12.1 and 12.3)
http://www.rni.helsinki.fi/~kja/luento17.pdf

Exams

The first course exam will be on Tuesday, March 10, at 10 a.m. - 1 p.m.

The exam will be on Tuesday, March 10, 10 a.m - 1 p.m. The place is lecture room C323 (this is the regular place for the Tuesday lectures).The exam covers the following chapters in the book (see also information about the lectures and exercises included in the exam at the bottom).

  • Chapter 1
    • sections from 1.1. to 1.5.
    • In section 1.2., please read the introduction to different data sets as far as it explains general aspects about modelling longitundinal data.You can pay more attention to the data sets that have been dealt with in the lectures and/or exercises. These are explained in Example 1.1. (CD4+ count),Example 1.4. (protein content in cow milk),and Example 1.6. (epileptic seizures). There is also a familiar data set in Example 3.1. (growth of pigs)
  • Chapter 3
    • sections 3.1 to 3.5
  • Chapter 4
    • sections 4.1, 4.2, 4.3 (until mid-page 60),
    • sections 4.4, 4.5 (except the development
      of REML equations on page 67)
    • section 4.6
  • Chapter 5:
    • sections 5.1, 5.2, 5.3
    • Example 5.1. from section 5.4,
    • section 5.5
  • Chapter 7
  • In addition, exercises 1, 2, 3, 4 and 5.1 and 5.2., as well as lectures 1- 7.
  • In summary, the area of the exam covers the general
    linear model, i.e., linear models with covariance structure
    to account for within-unit correlation in repeated measurements.
    In addition, Chapter 7 introduces generalized linear
    models with correlation structure among repeated
    measurements.
  • In exam you can answer either in Finnish or in English.

The 2nd course exam will take place on Tuesday, May 5, at 10 a.m. - 1 p.m. The exam will cover the chapters in the book
as listed below, lectures 8-17, and exercises 6-10.

  • Chapter 8
    • sections 8.1., 8.2., Example 8.1 from section 8.4., section 8.4. and Example 8.5
  • Chapter 9
    • sections 9.1., 9.2., Example 9.1 from section 9.3.
    • sections 9.3.2 and 9.3.3, Example 9.3.
    • section 9.4.
  • Chapter 10
    • sections 10.1., 10.2, 10.3 (up to Example 10.3.1 which is not included)
  • Chapter 12
    • section 12.1.
  • Chapter 13
    • sections 13.1 - 13.7 (up to Exampe 13.3. which is not included)

 

Bibliography

Diggle, Heagerty, Liang, Zeger: Analysis of longitudinal data, Oxford University Press, 2002.

Registration at the first lecture

Exercises

There are 2 hours of class exercises each week. Some of the exercises will require the use of the R program. The exercise class takes place on Fridays, 12-14 p.m. (D123)

1. Exercise 1 http://www.rni.helsinki.fi/~kja/exercise1.pdf
http://www.rni.helsinki.fi/~kja/cd4.dat
Answers to exercise 1 http://www.rni.helsinki.fi/~kja/vastaus1E.pdf
2. Exercise 2 http://www.rni.helsinki.fi/~kja/exercise2.pdf
http://www.rni.helsinki.fi/~kja/bindata1.dat
Answers to exercise 2 http://www.rni.helsinki.fi/~kja/vastaus2E.pdf
http://www.rni.helsinki.fi/~kja/lorelogram.R
3. Exercise 3 http://www.rni.helsinki.fi/~kja/exercise3.pdf
The data http://www.rni.helsinki.fi/~kja/pigsdata.dat
The weight matrix http://www.rni.helsinki.fi/~kja/pigsW
The data in a broad format http://www.rni.helsinki.fi/~kja/pigdatbroad
An R function to create block diagonal matrices http://www.rni.helsinki.fi/~kja/blockd
Answers to exercise 3 http://www.rni.helsinki.fi/~kja/answers3.pdf
4. Exercise 4 http://www.rni.helsinki.fi/~kja/exercise4.pdf
The data http://www.rni.helsinki.fi/~kja/cowdata
Hints to exercise 4/4: http://www.rni.helsinki.fi/~kja/cow_instructions
Answers to exercise 4 http://www.rni.helsinki.fi/~kja/answers4.pdf
5. Exercise 5 http://www.rni.helsinki.fi/~kja/exercise5.pdf
Answers to exercise 5 http://www.rni.helsinki.fi/~kja/answers5.pdf
6. Exercise 6 http://www.rni.helsinki.fi/~kja/exercise6.pdf

7. Exercise 7 http://www.rni.helsinki.fi/~kja/exercise7.pdf
http://www.rni.helsinki.fi/~kja/variogram
http://www.rni.helsinki.fi/~kja/answers7.pdf

8. Exercise 8 http://www.rni.helsinki.fi/~kja/exercise8.pdf
Seizures.dat http://www.rni.helsinki.fi/~kja/seizures.dat
Crossdata.dathttp://www.rni.helsinki.fi/~kja/crossdata.dat
http://www.rni.helsinki.fi/~kja/answers8.pdf

9. Exercise 9 http://www.rni.helsinki.fi/~kja/exercise9.pdf
http://www.rni.helsinki.fi/~kja/answers9.pdf
http://www.rni.helsinki.fi/~kja/simulpoisson.R

10. Exercise 10 http://www.rni.helsinki.fi/~kja/exercise10.pdf
http://www.rni.helsinki.fi/~kja/simulbinary.R

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