Cover image for Nonparametric analysis of longitudinal data in factorial experiments
Title:
Nonparametric analysis of longitudinal data in factorial experiments
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Series:
Wiley series in probability and statistics
Publication Information:
New York, NY : J. Wiley, 2002
ISBN:
9780471441663

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30000004826149 QA278.8 B78 2002 Open Access Book Book
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Summary

Summary

The authoritative reference on nonparametric methods for evaluating longitudinal data in factorial designs

Broadening the range of techniques that can be used to evaluate longitudinal data, Nonparametric Analysis of Longitudinal Data in Factorial Experiments presents nonparametric methods of evaluation that supplement the generalized linear models approach. Emphasizing the practical application of these methods in statistical procedures, this book provides a unified approach for the analysis of factorial designs involving longitudinal data that is appropriate for metric data, count data, ordered categorical data, and dichotomous data.

Topics covered include nonparametric models, effects and hypotheses in experimental design, estimators for relative effects, experiments for one and several groups of subjects, multifactorial experiments, dependent replications, and experiments with numerous time points. The basic mathematical principles for the methods introduced here are described in theory, consistent with the book's minimal math requirements. Simple approximations for small data sets are provided, as well as ample chapter exercises to test skills, an appendix that includes original data for the examples used throughout the book, and downloadable SAS-IML macros for implementing the more extensive calculations. All applications are designed to be useful in many fields.

Generously supplemented with more than 110 graphs and tables, Nonparametric Analysis of Longitudinal Data in Factorial Experiments is an essential reference for statisticians and biometricians, researchers in clinical trials, psychological studies, and in the fields of forestry, agriculture, sociology, ecology, and biology, as well as graduate students in statistics and biostatistics.


Author Notes

EDGAR BRUNNER is Head of the Department of Medical Statistics at the University of Gottingen, Germany.

SEBASTIAN DOMHOF is Assistant Professor in the Department of Medical Statistics at the University of Gottingen, Germany.

FRANK LANGER is a Statistician at Lilly Deutschland GmbH, Bad Homburg, Germany.


Table of Contents

Prefacep. xi
Acknowledgmentsp. xv
1 Introductionp. 1
1.1 Motivationp. 1
1.2 Overview of This Bookp. 2
1.3 Examplesp. 4
1.3.1 Panic Disorder Study Ip. 4
1.3.2 Panic Disorder Study IIp. 5
1.3.3 Solling Spruce Forest Roof Projectp. 6
1.3.4 Water-Maze Testp. 8
1.3.5 [alpha]-Amylase Studyp. 9
1.3.6 Cortisol Concentration in Plasmap. 10
1.3.7 Plasma-Renin Activityp. 12
1.3.8 [gamma]-GT Studyp. 13
1.3.9 Stem-Cell Concentrate Studyp. 14
1.3.10 Shoulder Tip Pain Studyp. 15
1.3.11 Body-Weight Evolution of Wistar Ratsp. 17
1.3.12 PCT-Concentration Studyp. 17
1.3.13 Postoperative Edemap. 18
1.3.14 Removal of Cardioplegical Solution (HTK Study)p. 19
2 Modelsp. 21
2.1 Nonparametric Modelsp. 21
2.1.1 Historical Developmentp. 21
2.1.2 Definition of the Modelp. 22
2.1.3 Notationp. 24
2.1.4 Examples and Specific Designsp. 25
2.2 Covariance Structuresp. 32
3 Effects and Hypothesesp. 35
3.1 Nonparametric Effectsp. 35
3.1.1 Relative Summary Effectsp. 35
3.1.2 Relative Marginal Effectsp. 38
3.2 Nonparametric Hypothesesp. 40
3.2.1 Hypotheses on the Distribution Functionsp. 40
3.2.2 Hypotheses on Relative Effectsp. 42
4 Estimators for Relative Effectsp. 45
4.1 The (Normalized) Empirical Distribution Functionp. 45
4.2 Ranksp. 47
4.3 Estimation of Relative Treatment Effectsp. 52
4.4 Asymptotic Distributions of the Estimatorsp. 55
4.4.1 Relative Marginal Effectsp. 55
4.4.2 Relative Summary Effectsp. 58
4.5 Confidence Intervalsp. 60
4.6 Graphical Representation of the Resultsp. 62
4.6.1 Metric Datap. 63
4.6.2 Ordered Categorical Datap. 64
Problemsp. 65
5 Test Statisticsp. 67
5.1 Statistics for Normal Distributionsp. 67
5.2 Wald-Type Statistic (WTS)p. 69
5.3 Hotelling's T[superscript 2] Statisticp. 70
5.4 ANOVA-Type Statistic (ATS)p. 71
5.5 Comparison of the Statistics Q[subscript n], Z[subscript R] and F[subscript n]p. 73
5.6 Statistics for Patterned Alternativesp. 75
5.7 Consistency of Statisticsp. 75
5.8 Comparison with the Rank Transform (RT) Methodp. 80
6 Softwarep. 83
6.1 Special SAS Macrosp. 83
6.2 SAS Standard Proceduresp. 84
7 Experiments for One Group of Subjectsp. 87
7.1 Two Time Pointsp. 87
7.1.1 The Hypothesis H[superscript F subscript 0] : F[subscript 1] = F[subscript 2]p. 88
7.1.2 The Wilcoxon Signed Rank Testp. 90
7.1.3 The Nonparametric Behrens-Fisher Situationp. 92
7.1.4 Confidence Intervalsp. 93
7.1.5 Application to the Stem-Cell Concentrate Study Datap. 94
7.2 More than Two Time Pointsp. 95
7.2.1 Models and Hypothesesp. 95
7.2.2 Global Alternativesp. 98
7.2.3 Confidence Intervalsp. 98
7.2.4 Examplesp. 99
7.2.5 Patterned Alternativesp. 102
7.2.6 Application to the Data from the Panic Disorder Study Ip. 103
7.2.7 Application to the Data from the [alpha]-Amylase Studyp. 104
7.2.8 Missing Valuesp. 105
7.2.9 Singular Covariance Matricesp. 107
7.3 Softwarep. 110
7.3.1 Instructions on the Use of the Macro LD_F1p. 110
7.3.2 Instructions on the Use of the Macro LD_CIp. 113
7.3.3 SAS Standard Proceduresp. 114
Problemsp. 117
8 Experiments for Several Groups of Subjectsp. 119
8.1 Two Groups and Two Time Pointsp. 120
8.1.1 Nonparametric Effects and Hypothesesp. 120
8.1.2 Statisticsp. 121
8.1.3 Application to the Stem-Cell Concentrate Datap. 124
8.2 The Two-Period Cross-Over Designp. 128
8.3 Several Groups and Several Time Pointsp. 130
8.3.1 Technical Formulation of Hypothesesp. 131
8.3.2 Interpretation of the Nonparametric Hypothesesp. 133
8.3.3 Group Effectsp. 134
8.3.4 Time Effectsp. 137
8.3.5 Interactionsp. 140
8.3.6 Missing Values and Singular Covariance Matricesp. 143
8.3.7 Examplesp. 144
8.4 Methods for Summary Effectsp. 152
8.4.1 Effects, Hypotheses and Statisticsp. 152
8.4.2 Application to the PRA Studyp. 153
8.5 Softwarep. 157
8.5.1 Instructions on the Use of the Macro F1_LD_F1p. 157
8.5.2 Instructions on the Use of the Macro LD_CIp. 165
8.5.3 Instruction on the Use of the Macro OWLp. 166
8.5.4 SAS Standard Proceduresp. 168
Problemsp. 171
9 Dependent Replicationsp. 175
9.1 Modelsp. 175
9.2 Examplesp. 178
9.3 Softwarep. 183
9.3.1 SAS Macrosp. 183
9.3.2 SAS Standard Proceduresp. 184
Problemsp. 184
10 Multifactorial Experimentsp. 187
10.1 Introductionp. 187
10.2 Examplesp. 188
10.2.1 F2-LD-F1p. 188
10.2.2 LD-F2p. 188
10.2.3 F1-LD-F2p. 189
10.3 General Techniquesp. 189
10.4 Analysis of Some Examplesp. 190
10.5 Macros for Multifactorial Experimentsp. 195
10.5.1 Instructions on the Use of the Macro F2_LD_F1p. 195
10.5.2 Instructions on the Use of the Macro LD_F2p. 199
10.5.3 Instructions on the Use of the Macro F1_LD_F2p. 202
10.5.4 Instructions on the Use of the Macro LD_CIp. 206
10.6 SAS Standard Proceduresp. 206
10.6.1 F2-LD-F1p. 207
10.6.2 LD-F2p. 208
Problemsp. 210
11 Numerous Time Pointsp. 211
11.1 General Discussionp. 211
11.2 Reduction of the Designp. 212
11.3 Examplesp. 213
11.3.1 Body-Weight Evolution of Wistar Ratsp. 213
11.3.2 Cortisol Concentration in Plasmap. 215
Problemsp. 217
Referencesp. 219
Appendix A Original Datap. 225
A.1 Panic Disorder Study Ip. 225
A.2 Panic Disorder Study IIp. 226
A.3 SO[subscript 4]-Concentrationp. 227
A.4 Vitality of Treetopsp. 230
A.5 Water-Maze Testp. 231
A.6 [alpha]-Amylase Studyp. 232
A.7 Cortisol Concentration in Plasmap. 233
A.8 Plasma-Renin Activity in Serump. 236
A.9 [gamma]-GT Studyp. 238
A.10 Stem-Cell Concentrate Studyp. 239
A.11 Shoulder Tip Pain Studyp. 241
A.12 Body-Weight Evolution of Wistar Ratsp. 242
A.13 Postoperative Edemap. 244
A.14 PCT-Concentration Studyp. 246
A.15 HTK Studyp. 248
Appendix B Results from the SAS Macrosp. 249
B.1 Confidence-Intervals for the [alpha]-Amylase Studyp. 249
B.2 Confidence-Intervals for the Shoulder Tip Pain Studyp. 250
B.3 Confidence-Intervals for the Plasma-Renin Studyp. 251
Glossaryp. 253
Indexp. 257