Methodology for Genetic Studies of Twins and Families

502 Pages·1992·13.667 MB·English

by  Michael C. Neale, Lon R. Cardon (auth.)

Methodology for Genetic Studies
of Twins and Families
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Series D: Behavioural and Social Sciences· Vol. 67
Methodology for Genetic Studies
of Twins and Families
by
Michael C. Neale
Department of Human Genetics,
Medical College of Virginia,
Virginia Commonwealth University,
Richmond, Virginia, U.S.A.
and
Lon R. Cardon
Institute for Behavioral Genetics,
University of Colorado,
Boulder, Colorado, U.S.A.
Springer-Science+Business Media, B.V.
Based on NATO, NFWO and NIMH funded Workshops
taught in Leuven, Belgium (1987, 1989 and 1991)
and Boulder, Colorado, U.S.A. (1990)
ISBN 978-90-481-4179-1 ISBN 978-94-015-8018-2 (eBook)
DOI 10.1007/978-94-015-8018-2
Printed an acid-free paper
AII Rights Reserved
© 1992 Springer Science+Business Media Dordrecht
Originally published byKluwer Academic Publishers in 1992
Softcover reprint of the hardcover lst edition 1992
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical, including photo
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Contents
Preface xiii
List of Figures xvii
List of Tables xxi
Contributing Authors xxv
1 The Scope of Genetic Analyses 1
1.1 Introduction and General Aims 1
1.2 Heredity and Variation . . . . . 2
1.2.1 Variation ....... . 2
1.2.2 Graphing and Quantifying Familial Resemblance 5
1.2.3 Within Family Differences . . . . . . . . 7
1.3 Building and Fitting Models. . . . . . . . . . . 10
1.4 The Elements of a Model: Causes of Variation 11
1.4.1 Genetic Effects ........ . 12
1.4.2 Environmental Effects . . . . . 13
1.4.3 Genotype-Environment Effects 17
1.5 Relationships between Variables. . . . 23
1.5.1 The Contribution of Genes and Environment to the Correla-
tion between Variables. . . . . . . . . 24
1.5.2 Analyzing the Direction of Causation 25
1.5.3 Analyzing Developmental Change 26
1.6 The Context of our Approach . . . . . . . . 27
1.6.1 19th Century Origins ........ 27
1.6.2 Genetic, Factor, and Path Analysis . 29
1.6.3 Integration ofthe Biometrical and Path-Analytic Approaches 30
1.6.4 Development of Statistical Methods .............. 31
vi CONTENTS
2 Data Summary 35
2.1 Introduction. 35
2.2 Continuous Data Analysis . . . . . . . . . . . . . 35
2.2.1 Calculating Summary Statistics by Hand 36
2.2.2 Using PRELIS to Summarize Continuous Data 39
2.3 Ordinal Data Analysis . . . . . . . . . . . . . . . . 41
2.3.1 Univariate Normal Distribution of Liability . 42
2.3.2 Bivariate Normal Distribution of Liability .. 43
2.3.3 Testing the Normal Distribution Assumption 45
2.3.4 Terminology for Types of Correlation 49
2.3.5 Using PRELIS with Ordinal Data 49
2.4 Summary . . . . . . . . . . . . . . . . . . 52
3 Biometrical Genetics 55
3.1 Introduction and Description of Terminology 55
3.2 Breeding Experiments: Gametic Crosses . 57
3.3 Derivation of Expected Twin Covariances 60
3.3.1 Equal Gene Frequencies .. 60
3.3.2 Unequal Gene Frequencies . 63
3.4 Summary ............. . 69
4 Matrix Algebra 71
4.1 Matrix Notation ..... . 71
4.2 Matrix Algebra Operations 73
4.2.1 Binary Operations . 73
4.2.2 Unary Operations 75
4.3 Equations in Matrix Algebra 80
4.4 Applications of Matrix Algebra 82
4.4.1 Calculation of Covariance Matrix from Data Matrix 82
4.4.2 Transformations of Data Matrices 83
4.4.3 Further Operations and Applications . 84
4.5 Exercises ........ . 85
4.5.1 Binary operations 85
4.5.2 Unary operations. 86
5 Path Analysis and Structural Equations 87
5.1 Introduction ............ . 87
5.2 Conventions Used in Path Analysis 88
5.3 Assumptions of Path Analysis . . . 90
5.4 Tracing Rules of Path Analysis . . 91
5.4.1 Tracing Rules for Standardized Variables 91
5.4.2 Tracing Rules for Unstandardized Variables 92
5.5 Path Models for Linear Regression .... 93
5.6 Path Models for the Classical Twin Study . . . . . 98
CONTENTS VB
5.6.1 Path Coefficients Model: Example of Standardized Tracing
Rules ............................... 100
5.6.2 Variance Components Model: Example of Unstandardized
Tracing Rules . . . . . . . . . . . . 102
5.7 Identification of Models and Parameters . 104
5.8 Summary . . . . . . . . . . . . . . . . . . 107
6 LISREL Models and Methods 109
6.1 Introduction ..... · 109
6.2 The LISREL Model .... . · 110
6.3 Path Diagrams ........ . .112
6.3.1 Default Values for Parameter Matrices. .116
6.4 Submodels................... .117
6.4.1 Submodel 1: only x- and e-variables .. .118
6.4.2 Submodel 2: only y- and x-variables . . .118
6.4.3 Submodel 3A: only y-, TJ-, and e-variables · 119
6.4.4 Submodel 3B: only y- and TJ-variables .119
6.5 Twin Model Example ............ . .120
6.6 Practical Model Fitting .......... . · 122
6.6.1 Estimating Parameters ofthe Model · 122
6.6.2 Assessment of Fit. . . . . . . . . . . · 124
6.6.3 Tests of Hypotheses ........ . · 125
6.7 Problems with Analysis of Correlation Matrices .126
6.8 Multi-Sample Analysis . . . . . . . . . . . . . .129
7 Model Fitting Functions and Optimization 131
7.1 Introduction ................ . · 131
7.2 Fitting Models to Data ........... . · 132
7.3 Weighted Least Squares Fitting Functions .. · 134
7.3.1 Unweighted Least Squares Fitting Function (ULS) · 136
7.3.2 Generalized Least Squares (GLS) . · 137
7.3.3 Maximum Likelihood (ML) ....... . · 138
7.3.4 Fitting Functions Including Means ... . · 139
7.3.5 Weighted Least Squares (WLS) Revisited .139
7.3.6 Additional Fitting Functions: Modified ML, DWLS, and Fun-
ctions for Raw Data . . . . . . . . . . . . . . . . . . 141
7.3.7 Goodness of Fit and the Principle of Parsimony. . . 142
7.4 Optimization .... . . . . . . . . . . . . . 143
7.4.1 Introduction ............ . 143
7.4.2 Choice of Hessian Approximation. . 146
7.5 Summary . . . . . . . . . . . . . . . . . . . 147
viii CONTENTS
8 Univariate Analysis 149
8.1 Introduction ......... . .149
8.2 Body Mass Index in Twins . · .. 150
8.3 Basic Genetic Model . . . . . · .. 153
8.4 LISREL 7 Example: Path Coefficients Model · .. 156
8.4.1 Building a LISREL 7 script ..... . .157
8.4.2 Interpreting LISREL 7 Output . . . . . 163
8.5 LISREL 8 Example: The Variance Components Model. .166
8.5.1 Building a LISREL 8 Script .. .167
8.5.2 Interpreting LISREL 8 Output . 168
8.6 Interpreting Results of Model-fitting . .170
8.7 Testing the Equality of Means . . . . . · .. 172
8.8 Incorporating Data from Singleton Twins · .. 175
8.9 Conclusions: Genetic Analyses of BMI Data. .177
8.10 Fitting Genetic Models to Binary Data ... · .. 178
8.10.1 Major Depressive Disorder in Twins · .. 179
8.11 Model for Age-Correction of Twin Data .182
9 Power and Sample Size 189
9.1 Factors Contributing to Power ..................... 189
9.2 Steps in Power Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 190
9.2.1 Example: The Power of the Classical Twin Study to Detect
the Shared Environment . . . . 192
9.3 Loss of Power with Ordinal Data .. 194
9.4 Exercises ... .196
10 Social Interaction 199
10.1 Introduction to Recursive Models . .199
10.2 Background . . . . . . . . · .. 199
10.3 Sibling Interaction Model ..... . .201
10.4 Application to CBC Data . . . . . .203
10.5 Consequences for Variation and Covariation .205
10.5.1 Derivation of Expected Covariances .205
10.5.2 Numerical illustration ..... .208
11 Sex-limitation and G X E Interaction 211
11.1 Introduction .............. . .211
11.2 Sex-limitation Models ........ . .212
11.2.1 General Model for Sex-limitation .212
11.2.2 Restricted Models for Sex-limitation · .. 217
11.3 Sex-limitation in Body Mass Index . . · .. 220
11.4 Genotype x Environment Interaction ... . · .. 223
11.4.1 Models for G x E Interactions .. . .223
11.5 G x E Analysis of Marital Status and Depression. · .. 226
CONTENTS ix
12 Multivariate Analysis 231
12.1 Introduction ...................... . . 231
12.2 Phenotypic Factor Analysis . . . . . . . . . . . . . . .232
12.2.1 Exploratory and Confirmatory Factor Models .232
12.2.2 Building a Phenotypic Factor Model LISREL Script .233
12.2.3 Fitting a Phenotypic Factor Model .234
12.3 Simple Genetic Factor Models . . . . . . . . . . .237
12.3.1 Multivariate Genetic Factor Model ... .237
12.3.2 Fitting the Multivariate Genetic Model .238
12.3.3 Alternate Representation of the Multivariate Genetic Factor
Model. . . . . . . . . . . . . . . .243
12.3.4 Fitting a Second Genetic Factor ..... . 245
12.4 Multiple Genetic Factor Models. . . . . . . . . . . 248
12.4.1 Genetic and Environmental Correlations. . 248
12.4.2 Cholesky Decomposition . . . . . . . . . . . 249
12.4.3 Analyzing Genetic and Environmental Correlations . . 250
12.5 Common vs. Independent Pathway Genetic Models . . 253
12.5.1 Independent Pathway Model for Atopy. . 254
12.5.2 Common Pathway Model for Atopy ..... . 257
13 Direction of Causation 261
13.1 Introduction ..... . 261
13.2 Models for Data from Unrelated Individuals: Instrumental Variables
Method ....... . . . . . . . . . . . . . .263
13.3 Modeling Causation with Data from Twins . . . . . . . . . . 265
13.3.1 The Principle of the Method ............. . 265
13.3.2 LISREL Script for the Direction of Causation Model . 267
13.4 General Bivariate Models ............. . 269
13.5 Considerations in Causal Models . . . . . . . . . . 273
13.5.1 Data Simulation under the Causal Model . 273
13.5.2 Fitting False Models to Simulated Data . 276
13.5.3 Discussion of Simulation Exercise. . . 277
13.6 Application to Alcohol Data. . . . . . . . . . 279
13.7 Multivariate Direction of Causation Models . 285
13.8 Concluding Remarks . . . . . . . . . . . . . . 287
14 Repeated Measures 289
14.1 Introduction. . . . . . . . . . . . . . . . . . .. ......... . 289
14.2 Phenotypic Simplex Model ........... ......... . 290
14.2.1 Formulation of the Phenotypic Simplex Model in LISREL . 291
14.3 Genetic Simplex Model .................... . 296
14.3.1 LISREL Formulation of the Genetic Simplex Model . 296
14.3.2 Application to Longitudinal Data on Weight .... . 297
x CONTENTS
14.3.3 Application of Common Factor Model to Longitudinal Twin
Data. . . . . . . . . . . . . . . . . 301
14.4 Problems with Repeated Measures Data . 303
14.5 Discussion . . . . . . . . . . . . . . . . . . 303
15 Longitudinal Mean Trends 305
15.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 305
15.2 Genetic Analysis of Longitudinal Trends in Mean . . 305
15.2.1 Assumptions of the Model. . . . . . . . . . . 306
15.2.2 Building a LISREL Script for Longitudinal Means . 308
15.2.3 Application to data on weight. . 309
15.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
16 Observer Ratings 313
16.1 Introduction. . . . . . . . . . . . . 313
16.2 Models for Multiple Rating Data . 315
16.2.1 Rater Bias Model. . . 315
16.2.2 Psychometric Model . . 317
16.2.3 Biometric Model . . . . 318
16.2.4 Comparison of Models .320
16.3 Application to Data from the Child Behavior Checklist. · 321
16.3.1 Subjects and Methods .... . · 321
16.3.2 Results of Model-Fitting ... . .322
16.3.3 Discussion of CBC Application .324
17 Assortment and Cultural Transmission 329
17.1 Introduction to the Twin-Parent Design .329
17.2 Social Homogamy Model ........ . .330
17.2.1 LISREL Formulation of the Model · 331
17.3 Phenotypic Assortment Model. .334
17.3.1 Reverse Path Analysis ...... . .334
17.3.2 Parameter Constraints ...... . .336
17.3.3 LISREL 8 Specification of the Model. .337
17.3.4 Employing Constraints in LISREL . .343
17.3.5 Writing the Constraints in LISREL .. .345
17.4 Illustration of Twin-Parent Models . . . . . . .346
17.4.1 Phenotypic Assortment Model Results .346
17.4.2 Social Homogamy Model Results .348
17.5 Summary ................... . .350