Table of Contents

Preface

Acknowledgements

1 Introduction

1.1 Introduction

1.2 General approach

1.3 Prior knowledge

1.4 Example

1.5 Software

1.6 Data structure

1.7 Statistical notation

1.8 What’s new in the second edition?

2 Study design

2.1 Introduction

2.2 Observational longitudinal studies

2.2.1 Period and cohort effects

2.2.2 Other confounding effects

2.2.3 Example

2.3 Experimental (longitudinal) studies

3 Continuous outcome variables

3.1 Two measurements

3.1.1 Example

3.2 Non-parametric equivalent of the paired

*t*-test

3.2.1 Example

3.3 More than two measurements

3.3.1 The “univariate” approach: a numerical example

3.3.2 The shape of the relationship between an outcome variable and time

3.3.3 A numerical example

3.3.4 Example

3.4 The “univariate” or the “multivariate” approach?

3.5 Comparing groups

3.5.1 The “univariate” approach: a numerical example

3.5.2 Example

3.6 Comments

3.7 Post-hoc procedures

3.7.1 Example

3.8 Different contrasts

3.8.1 Example

3.9 Non-parametric equivalent of MANOVA for repeated measurements

3.9.1 Example

4 Continuous outcome variables — relationships with other variables

4.1 Introduction

4.2 “Traditional” methods

4.3 Example

4.4 Longitudinal methods

4.5 Generalized estimating equations

4.5.1 Introduction

4.5.2 Working correlation structures

4.5.3 Interpretation of the regression coefficients derived from GEE analysis

4.5.4 Example

4.5.4.1 Introduction

4.5.4.2 Results of a GEE analysis

4.5.4.3 Different correlation structures

4.6 Mixed model analysis

4.6.1 Introduction

4.6.2 Mixed models for longitudinal studies

4.6.3 Example

4.6.4 Comments

4.7 Comparison between GEE analysis and mixed model analysis

4.7.1 The “adjustment for covariance” approach

4.7.2 Extensions of mixed model analysis

4.7.3 Comments

5 The modeling of time

5.1 The development over time

5.2 Comparing groups

5.3 The adjustment for time

6 Other possibilities for modeling longitudinal data

6.1 Introduction

6.2 Alternative models

6.2.1 Time-lag model

6.2.2 Model of changes

6.2.3 Autoregressive model

6.2.4 Overview

6.2.5 Example

6.2.5.1 Introduction

6.2.5.2 Data structure for alternative models

6.2.5.3 GEE analysis

6.2.5.4 Mixed model analysis

6.3 Comments

6.4 Another example

7 Dichotomous outcome variables

7.1 Simple methods

7.1.1 Two measurements

7.1.2 More than two measurements

7.1.3 Comparing groups

7.1.4 Example

7.1.4.1 Introduction

7.1.4.2 Development over time

7.1.4.3 Comparing groups

7.2 Relationships with other variables

7.2.1 “Traditional” methods

7.2.2 Example

7.2.3 Sophisticated methods

7.2.4 Example

7.2.4.1 Generalized estimating equations

7.2.4.2 Mixed model analysis

7.2.5 Comparison between GEE analysis and mixed model analysis

7.2.6 Alternative models

7.2.7 Comments

8 Categorical and “count” outcome variables

8.1 Categorical outcome variables

8.1.1 Two measurements

8.1.2 More than two measurements

8.1.3 Comparing groups

8.1.4 Example

8.1.5 Relationship with other variables

8.1.5.1 “Traditional” methods

8.1.5.2 Example

8.1.5.3 Sophisticated methods

8.1.5.4 Example

8.2 “Count” outcome variables

8.2.1 Example

8.2.1.1 Introduction

8.2.1.2 GEE analysis

8.2.1.3 Mixed model analysis

8.2.2 Comparison between GEE analysis and mixed model analysis

8.3 Comments

9 Analysis of experimental studies

9.1 Introduction

9.2 Continuous outcome variables

9.2.1 Experimental models with only one follow-up measurement

9.2.1.1 Example

9.2.2 Experimental studies with more than one follow-up measurement

9.2.2.1 Simple analysis

9.2.2.2 Summary statistics

9.2.2.3 MANOVA for repeated measurements

9.2.2.4 MANOVA for repeated measurements adjusted for the baseline value

9.2.2.5 Sophisticated analysis

9.2.3 Conclusion

9.3 Dichotomous outcome variables

9.3.1 Introduction

9.3.2 Simple analysis

9.3.3 Sophisticated analysis

9.3.4 Other approaches

9.4 Comments

10 Missing data in longitudinal studies

10.1 Introduction

10.2 Ignorable or informative missing data?

10.3 Example

10.3.1 Generating datasets with missing data

10.3.2 Analysis of determinants for missing data

10.4 Analysis performed on datasets with missing data

10.4.1 Example

10.5 Imputation methods

10.5.1 Continuous outcome variables

10.5.1.1 Cross-sectional imputation methods

10.5.1.2 Longitudinal imputation methods

10.5.1.3 Comment

10.5.1.4 Multiple imputation

10.5.2 Dichotomous and categorical outcome variables

10.5.3 Example

10.5.3.1 Continuous outcome variables

10.5.3.2 Should multiple imputation be used in combination with a mixed model analysis?

10.5.3.3 Additional analyses

10.5.3.4 Dichotomous outcome variables

10.5.4 Comments

10.5.4.1 Alternative approaches

10.6 GEE analysis versus mixed model analysis regarding the analysis on datasets with missing data

10.7 Conclusions

11 Sample size calculations

11.1 Introduction

11.2 Example

12 Software for longitudinal data analysis

12.1 Introduction

12.2 GEE analysis with continuous outcome variables

12.2.1 Stata

12.2.2 SAS

12.2.3 R

12.2.4 SPSS

12.2.5 Overview

12.3 GEE analysis with dichotomous outcome variables

12.3.1 Stata

12.3.2 SAS

12.3.3 R

12.3.4 SPSS

12.3.5 Overview

12.4 Mixed model analysis with continuous outcome variables

12.4.1 Stata

12.4.2 SAS

12.4.3 R

12.4.4 SPSS

12.4.5 MLwiN

12.4.6 Overview

12.5 Mixed model analysis with dichotomous outcome variables

12.5.1 Introduction

12.5.2 Stata

12.5.3 SAS

12.5.4 R

12.5.5 SPSS

12.5.6 MLwiN

12.5.7 Overview

12.6 Categorical and “count” outcome variables

12.7 The “adjustment for covariance approach”

12.7.1 Example

13 One step further

13.1 Introduction

13.2 Outcome variables with upper or lower censoring

13.2.1 Introduction

13.2.2 Example

13.2.3 Remarks

13.3 Classification of subjects with different developmental trajectories

References

Index