Preface
xiii
1 Introduction
1
2 Various Measures of Effect Size 13
2.1 Effect Size Based on Means 13
2.2 Effect Size Based on Proportions 17
2.3 Effect Size Based on Coef揻椀攀渀琀 and Odds Ratio 19
2.4 Effect Size Based on Correlation 22
3 Combining Independent Tests 25
3.1 Introduction
25
3.2 Description of Combined Tests 27
4 Methods of Combining Effect Sizes 35
5 Inference about a Common Mean of Several Univariate Normal
Populations
43
5.1 Results on Common Mean Estimation 45
5.1.1 Small-Sample Comparison of GD with Other
Estimators
45
5.1.2 Properties of GD
48
5.2 Asymptotic Comparison of Some Estimates of Common Mean
for k = 2 Populations
52
5.3 Con擻攀渀挀攀 Intervals for the Common Mean 54
5.3.1 Approximate Con擻攀渀挀攀 Intervals 55
5.3.2 Exact Con擻攀渀挀攀 Intervals 56
5.4 Applications
59
Appendix: Theory of Fisher’s Method 60
6 Tests of Homogeneity in Meta-Analysis 63
6.1 Model and Test Statistics 64
6.2 An Exact Test of Homogeneity 67
6.3 Applications 68
7 One-Way Random Effects Model 73
7.1 Introduction 73
7.2 Homogeneous Error Variances 76
7.2.1 Test for σ2a = 0 76
7.2.2 Approximate Tests for H0 : σ2a = δ > 0 andCon擻攀渀挀攀 Intervals for σ2a 77
7.2.3 Exact Test and Con擻攀渀挀攀 Interval for σ2a Based on a Generalized P-value Approach 81
7.2.4 Tests and Con擻攀渀挀攀 Intervals for 85
7.3 Heterogeneous Error Variances 85
7.3.1 Tests for H0 : σ2a= 0 85
7.3.2 Tests for H0 : σ2a = δ > 0 85
7.3.3 Nonnegative Estimation of σ2a and Con擻攀渀挀攀 Intervals 87
7.3.4 Inference about 93
8 Combining Controlled Trials with Normal Outcomes 97
8.1 Difference of Means 98
8.1.1 Approximate Con擻攀渀挀攀 Intervals for the Common Mean Difference 100
8.1.2 Exact Con擻攀渀挀攀 Intervals for the Common Mean Difference 100
8.1.3 Testing Homogeneity 102
8.1.4 Analysis in the Random Effects Model 103
8.2 Standardized Difference of Means 107
8.3 Ratio of Means 110
9 Combining Controlled Trials with Discrete Outcomes 113
9.1 Binary Data 116
9.1.1 Effect Size Estimates 116
9.1.2 Homogeneity Tests 118
9.1.3 Binomial-Normal Hierarchical Models in Meta-Analysis 118
9.1.4 An Example for Combining Results from Controlled Clinical Trials 120
9.1.5 An Example for Combining Results from Observational Studies 121
9.2 Ordinal Data 122
9.2.1 Proportional Odds Model 123
9.2.2 Agresti’s α 124
9.2.3 An Example of Combining Results from Controlled
Clinical Trials 124
10 Meta-Regression 127
10.1 Model with One Covariate 128
10.2 Model with More Than One Covariate 132
10.3 Further Extensions and Applications 136
11 Multivariate Meta-Analysis 139
11.1 Combining Multiple Dependent Variables from a Single Study 141
11.2 Modeling Multivariate Effect Sizes 143
11.2.1 Multiple-Endpoint Studies 144
11.2.2 Multiple-Treatment studies 149
12 Bayesian Meta-Analysis 155
12.1 A General Bayesian Model for Meta-Analysis under Normality 156
12.2 Further Examples of Bayesian Analyses 159
12.3 A Uni旻搀 Bayesian Approach to Meta-Analysis 164
12.4 Further Results on Bayesian Meta-Analysis 167
13 Publication Bias 171
14 Recovery of Interblock Information 179
14.1 Notation and Test Statistics 180
14.2 BIBD with Fixed Treatment Effects 183
14.2.1 Combined Tests When b > v 184
14.2.2 Combined Tests When b = v 187
14.2.3 A Numerical Example 188
15 Combination of Polls 191
15.1 Formulation of the Problem 192
15.2 Meta-Analysis of Polls 196
15.2.1 Estimation of θ 196
15.2.2 Con擻攀渀挀攀 Interval for θ 198
15.2.3 Hypothesis Testing for θ 200
16 Vote Counting Procedures 203
17 Computational Aspects 213
17.1 Extracting Summary Statistics 213
17.2 Combining Tests 214
17.3 Generalized P-values 215
17.4 Combining Effect Sizes 217
17.4.1 Graphics 218
17.4.2 Sample Program in R 218
17.4.3 Sample Program in SAS 220
18 Data Sets 225
18.1 Validity Studies 225
18.2 Effects of Teacher Expectance on Pupil IQ 226
18.3 Dentifrice Data 227
18.4 Effectiveness of Amlodipine on Work Capacity 228
18.5 Effectiveness of Cisapride on the Treatment of Nonulcer Dyspepsia 229
18.6 Second-hand Smoking 230
18.7 Effectiveness of Misoprostol in Preventing Gastrointestinal Damage 230
18.8 Prevention of Tuberculosis 230