Meta Analysis - Elena Kulinskaya

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Résumé :

Preface xiii

Part I The Methods 1

1 What can the reader expect from this book? 3

1.1 A calibration scale for evidence 4

1.1.1 T-values and p-values 4

1.1.2 How generally applicable is the calibration scale? 6

1.1.3 Combining evidence 7

1.2 The efficacy of glass ionomer versus resin sealants for prevention of caries 8

1.2.1 The data 8

1.2.2 Analysis for individual studies 9

1.2.3 Combining the evidence: fixed effects model 10

1.2.4 Combining the evidence: random effects model 10

1.3 Measures of effect size for two populations 11

1.4 Summary 13

2 Independent measurements with known precision 15

2.1 Evidence for one-sided alternatives 15

2.2 Evidence for two-sided alternatives 18

2.3 Examples 19

2.3.1 Filling containers 19

2.3.2 Stability of blood samples 20

2.3.3 Blood alcohol testing 20

3 Independent measurements with unknown precision 23

3.1 Effects and standardized effects 23

3.2 Paired comparisons 26

3.3 Examples 27

3.3.1 Daily energy intake compared to a fixed level 27

3.3.2 Darwin's data on Zea mays 28

4 Comparing treatment to control 31

4.1 Equal unknown precision 31

4.2 Differing unknown precision 33

4.3 Examples 35

4.3.1 Drop in systolic blood pressure 35

4.3.2 Effect of psychotherapy on hospital length of stay 37

5 Comparing K treatments 39

5.1 Methodology 39

5.2 Examples 42

5.2.1 Characteristics of antibiotics 42

5.2.2 Red cell folate levels 43

6 Evaluating risks 47

6.1 Methodology 47

6.2 Examples 49

6.2.1 Ultrasound and left-handedness 49

6.2.2 Treatment of recurrent urinary tract infections 49

7 Comparing risks 51

7.1 Methodology 51

7.2 Examples 54

7.2.1 Treatment of recurrent urinary tract infections 54

7.2.2 Diuretics in pregnancy and risk of pre-eclamsia 54

8 Evaluating Poisson rates 57

8.1 Methodology 57

8.2 Example 60

8.2.1 Deaths by horse-kicks 60

9 Comparing Poisson rates 63

9.1 Methodology 64

9.1.1 Unconditional evidence 64

9.1.2 Conditional evidence 65

9.2 Example 67

9.2.1 Vaccination for the prevention of tuberculosis 67

10 Goodness-of-fit testing 71

10.1 Methodology 71

10.2 Example 74

10.2.1 Bellbirds arriving to feed nestlings 74

11 Evidence for heterogeneity of effects and transformed effects 77

11.1 Methodology 77

11.1.1 Fixed effects 77

11.1.2 Random effects 80

11.2 Examples 81

11.2.1 Deaths by horse-kicks 81

11.2.2 Drop in systolic blood pressure 82

11.2.3 Effect of psychotherapy on hospital length of stay 83

11.2.4 Diuretics in pregnancy and risk of pre-eclamsia 84

12 Combining evidence: fixed standardized effects model 85

12.1 Methodology 86

12.2 Examples 87

12.2.1 Deaths by horse-kicks 87

12.2.2 Drop in systolic blood pressure 88

13 Combining evidence: random standardized effects model 91

13.1 Methodology 91

13.2 Example 94

13.2.1 Diuretics in pregnancy and risk of pre-eclamsia 94

14 Meta-regression 95

14.1 Methodology 95

14.2 Commonly encountered situations 98

14.2.1 Standardized difference of means 98

14.2.2 Difference in risk (two binomial proportions) 99

14.2.3 Log relative risk (two Poisson rates) 99

14.3 Examples 100

14.3.1 Effect of open education on student creativity 100

14.3.2 Vacc...

Sommaire:
confidence intervals 185

22.4 Choosing the sample size 188

22.4.1 Sample sizes for obtaining an expected evidence 188

22.4.2 Sample size required to obtain a desired power 190

> l 0 190

22.6 Summary 191

23 Evidence in F-tests 193

23.1 Variance stabilizing transformations for the noncentral F 193

23.2 The evidence distribution 197

23.3 The Key Inferential Function 200

23.3.1 Refinements 203

23.4 The random effects model 203

23.4.1 Expected evidence in the balanced case 205

23.4.2 Comparing evidence in REM and FEM 206

23.5 Summary 206

24 Evidence in Cochran's Q for heterogeneity of effects 207

24.1 Cochran's Q: the fixed effects model 208

24.1.1 Background material 208

24.1.2 Evidence for heterogeneity of fixed effects 210

24.1.3 Evidence for heterogeneity of transformed effects 211

24.2 Simulation studies 211

24.3 Cochran's Q: the random effects model 214

24.4 Summary 218

25 Combining evidence from K studies 219

25.1 Background and preliminary steps 219

25.2 Fixed standardized effects 220

25.2.1 Fixed, and equal, standardized effects 220

25.2.2 Fixed, but unequal, standardized effects 221

25.2.3 Nuisance parameters 221

25.3 Random transformed effects 222

25.3.1 The random transformed effects model 222

25.3.2 Evidence for a positive effect 223

25.3.3 Confidence intervals for k and ?: K small 224

25.3.4 Confidence intervals for k and ?: K large 224

25.3.5 Simulation studies 225

25.4 Example: drop in systolic blood pressure 227

25.4.1 Inference for the fixed effects model 229

25.4.2 Inference for the random effects model 230

25.5 Summary 230

26 Correcting for publication bias 231

26.1 Publication bias 231

26.2 The truncated normal distribution 233

26.3 Bias correction based on censoring 235

26.4 Summary 238

27 Large-sample properties of variance stabilizing transformations 239

27.1 Existence of the variance stabilizing transformation 239

27.2 Tests and effect sizes 240

27.3 Power and efficiency 243

27.4 Summary 247

References 249

Index 253