Meta Analysis A Guide to Calibrating and Combining Statistical Evidence
, by Kulinskaya, Elena; Morgenthaler, Stephan; Staudte, Robert G.- ISBN: 9780470028643 | 0470028645
- Cover: Paperback
- Copyright: 4/14/2008
Professor S. Morgenthaler – Chair of Applied Statistics, Ecole Polytechnique Fédérale de Lausanne, Switzerland. Professor Morgenthaler was Assistant Professor at Yale University prior to moving to EPFL and has chaired various ISI committees.
Professor R. G. Staudte – Department of Statistical Science, La Trobe University, Melbourne. During his career at La Trobe he has served as Head of the Department of Statistical Science for five years and Head of the School of Mathematical and Statistical Sciences for two years. He was an Associate Editor for the Journal of Statistical Planning & Inference for 4 years, and is a member of the American Statistical Association, the Sigma Xi Scientific Research Society and the Statistical Society of Australia.
Preface | p. xiii |
The Methods | p. 1 |
What can the reader expect from this book? | p. 3 |
A calibration scale for evidence | p. 4 |
T-values and p-values | p. 4 |
How generally applicable is the calibration scale? | p. 6 |
Combining evidence | p. 7 |
The efficacy of glass ionomer versus resin sealants for prevention of caries | p. 8 |
The data p8 | |
Analysis for individual studies | p. 9 |
Combining the evidence: fixed effects model | p. 10 |
Combining the evidence: random effects model | p. 10 |
Measures of effect size for two populations | p. 11 |
Summary | p. 13 |
Independent measurements with known precision | p. 15 |
Evidence for one-sided alternatives | p. 15 |
Evidence for two-sided alternatives | p. 18 |
Examples | p. 19 |
Filling containers | p. 19 |
Stability of blood samples | p. 20 |
Blood alcohol testing | p. 20 |
Independent measurements with unknown precision | p. 23 |
Effects and standardized effects | p. 23 |
Paired comparisons | p. 26 |
Examples | p. 27 |
Daily energy intake compared to a fixed level | p. 27 |
Darwin's data on Zea mays | p. 28 |
Comparing treatment to control | p. 31 |
Equal unknown precision | p. 31 |
Differing unknown precision | p. 33 |
Examples | p. 35 |
Drop in systolic blood pressure | p. 35 |
Effect of psychotherapy on hospital length of stay | p. 37 |
Comparing K treatments | p. 39 |
Methodology | p. 39 |
Examples | p. 42 |
Characteristics of antibiotics | p. 42 |
Red cell folate levels | p. 43 |
Evaluating risks | p. 47 |
Methodology | p. 47 |
Examples | p. 49 |
Ultrasound and left-handedness | p. 49 |
Treatment of recurrent urinary tract infections | p. 49 |
Comparing risks | p. 51 |
Methodology | p. 51 |
Examples | p. 54 |
Treatment of recurrent urinary tract infections | p. 54 |
Diuretics in pregnancy and risk of pre-eclamsia | p. 54 |
Evaluating Poisson rates | p. 57 |
Methodology | p. 57 |
Example | p. 60 |
Deaths by horse-kicks | p. 60 |
Comparing Poisson rates | p. 63 |
Methodology | p. 64 |
Unconditional evidence | p. 64 |
Conditional evidence | p. 65 |
Example | p. 67 |
Vaccination for the prevention of tuberculosis | p. 67 |
Goodness-of-fit testing | p. 71 |
Methodology | p. 71 |
Example | p. 74 |
Bellbirds arriving to feed nestlings | p. 74 |
Evidence for heterogeneity of effects and transformed effects | p. 77 |
Methodology | p. 77 |
Fixed effects | p. 77 |
Random effects | p. 80 |
Examples | p. 81 |
Deaths by horse-kicks | p. 81 |
Drop in systolic blood pressure | p. 82 |
Effect of psychotherapy on hospital length of stay | p. 83 |
Diuretics in pregnancy and risk of pre-eclamsia | p. 84 |
Combining evidence: fixed standardized effects model | p. 85 |
Methodology | p. 86 |
Examples | p. 87 |
Deaths by horse-kicks | p. 87 |
Drop in systolic blood pressure | p. 88 |
Combining evidence: random standardized effects model | p. 91 |
Methodology | p. 91 |
Example | p. 94 |
Diuretics in pregnancy and risk of pre-eclamsia | p. 94 |
Meta-regression | p. 95 |
Methodology | p. 95 |
Commonly encountered situations | p. 98 |
Standardized difference of means | p. 98 |
Difference in risk (two binomial proportions) | p. 99 |
Log relative risk (two Poisson rates) | p. 99 |
Examples | p. 100 |
Effect of open education on student creativity | p. 100 |
Vaccination for the prevention of tuberculosis | p. 101 |
Accounting for publication bias | p. 105 |
The downside of publishing | p. 105 |
Examples | p. 107 |
Environmental tobacco smoke | p. 107 |
Depression prevention programs | p. 109 |
The Theory | p. 111 |
Calibrating evidence in a test | p. 113 |
Evidence for one-sided alternatives | p. 114 |
Desirable properties of one-sided evidence | p. 115 |
Connection of evidence to p-values | p. 115 |
Why the p-value is hard to understand | p. 116 |
Random p-value behavior | p. 118 |
Properties of the random p-value distribution | p. 118 |
Important consequences for interpreting p-values | p. 119 |
Publication bias | p. 119 |
Comparison with a Bayesian calibration | p. 121 |
Summary | p. 123 |
The basics of variance stabilizing transformations | p. 125 |
Standardizing the sample mean | p. 125 |
Variance stabilizing transformations | p. 126 |
Background material | p. 126 |
The Key Inferential Function | p. 127 |
Poisson model example | p. 128 |
Example of counts data | p. 129 |
A simple vst for the Poisson model | p. 129 |
A better vst for the Poisson model | p. 132 |
Achieving a desired expected evidence | p. 132 |
Confidence intervals | p. 132 |
Simulation study of coverage probabilities | p. 134 |
Two-sided evidence from one-sided evidence | p. 134 |
A vst based on the chi-squared statistic | p. 135 |
A vst based on doubling the p-value | p. 137 |
Summary | p. 138 |
One-sample binomial tests | p. 139 |
Variance stabilizing the risk estimator | p. 139 |
Confidence intervals for p | p. 140 |
Relative risk and odds ratio | p. 142 |
One-sample relative risk | p. 143 |
One-sample odds ratio | p. 144 |
Confidence intervals for small risks p | p. 145 |
Comparing intervals based on the log and arcsine transformations | p. 145 |
Confidence intervals for small p based on the Poisson approximation to the binomial | p. 146 |
Summary | p. 147 |
Two-sample binomial tests | p. 149 |
Evidence for a positive effect | p. 149 |
Variance stabilizing the risk difference | p. 149 |
Simulation studies | p. 151 |
Choosing sample sizes to achieve desired expected evidence | p. 151 |
Implications for the relative risk and odds ratio | p. 153 |
Confidence intervals for effect sizes | p. 153 |
Estimating the risk difference | p. 155 |
Relative risk and odds ratio | p. 155 |
Two-sample relative risk | p. 155 |
Two-sample odds ratio | p. 157 |
New confidence intervals for the RR and OR | p. 157 |
Recurrent urinary tract infections | p. 157 |
Summary | p. 158 |
Defining evidence in t-statistics | p. 159 |
Example | p. 159 |
Evidence in the Student t-statistic | p. 159 |
The Key Inferential Function for Student's model | p. 163 |
Corrected evidence | p. 165 |
Matching p-values | p. 166 |
Reducing bias | p. 167 |
A confidence interval for the standardized effect | p. 169 |
Simulation study of coverage probabilities | p. 170 |
Comparing evidence in t- and z-tests | p. 170 |
On substituting s for [sigma] in large samples | p. 170 |
Summary | p. 172 |
Two-sample comparisons | p. 175 |
Drop in systolic blood pressure | p. 175 |
Defining the standardized effect | p. 176 |
Evidence in the Welch statistic | p. 177 |
The Welch statistic | p. 177 |
Variance stabilizing the Welch t-statistic | p. 178 |
Choosing the sample size to obtain evidence | p. 179 |
Confidence intervals for [delta] | p. 179 |
Converting the evidence to confidence intervals | p. 179 |
Simulation studies | p. 180 |
Drop in systolic blood pressure (continued) | p. 181 |
Summary | p. 181 |
Evidence in the chi-squared statistic | p. 183 |
The noncentral chi-squared distribution | p. 183 |
A vst for the noncentral chi-squared statistic | p. 184 |
Deriving the vst | p. 184 |
The Key Inferential Function | p. 185 |
Simulation studies | p. 186 |
Bias in the evidence function | p. 186 |
Upper confidence bounds; confidence intervals | p. 187 |
Choosing the sample size | p. 190 |
Sample sizes for obtaining an expected evidence | p. 190 |
Sample size required to obtain a desired power | p. 192 |
Evidence for [lambda] > [lambda subscript 0] | p. 192 |
Summary | p. 193 |
Evidence in F-tests | p. 195 |
Variance stabilizing transformations for the noncentral F | p. 195 |
The evidence distribution | p. 199 |
The Key Inferential Function | p. 202 |
Refinements | p. 205 |
The random effects model | p. 205 |
Expected evidence in the balanced case | p. 207 |
Comparing evidence in REM and FEM | p. 208 |
Summary | p. 208 |
Evidence in Cochran's Q for heterogeneity of effects | p. 209 |
Cochran's Q: the fixed effects model | p. 210 |
Background material | p. 210 |
Evidence for heterogeneity of fixed effects | p. 212 |
Evidence for heterogeneity of transformed effects | p. 213 |
Simulation studies | p. 213 |
Cochran's Q: the random effects model | p. 216 |
Summary | p. 220 |
Combining evidence from K studies | p. 221 |
Background and preliminary steps | p. 221 |
Fixed standardized effects | p. 222 |
Fixed, and equal, standardized effects | p. 222 |
Fixed, but unequal, standardized effects | p. 223 |
Nuisance parameters | p. 223 |
Random transformed effects | p. 224 |
The random transformed effects model | p. 224 |
Evidence for a positive effect | p. 225 |
Confidence intervals for [kappa] and [delta]: K small | p. 226 |
Confidence intervals for [kappa] and [delta]: K large | p. 226 |
Simulation studies | p. 227 |
Example: drop in systolic blood pressure | p. 229 |
Inference for the fixed effects model | p. 231 |
Inference for the random effects model | p. 232 |
Summary | p. 232 |
Correcting for publication bias | p. 233 |
Publication bias | p. 233 |
The truncated normal distribution | p. 235 |
Bias correction based on censoring | p. 237 |
Summary | p. 240 |
Large-sample properties of variance stabilizing transformations | p. 241 |
Existence of the variance stabilizing transformation | p. 241 |
Tests and effect sizes | p. 242 |
Power and efficiency | p. 245 |
Summary | p. 249 |
Acknowledgements | p. 251 |
Bibliography | p. 253 |
Index | p. 257 |
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