Elementary bayesian biostatistics
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla.
Chapman & Hall/CRC
2008
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| Schriftenreihe: | Chapman & Hall/CRC biostatistics series
21 |
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| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
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| 100 | 1 | |a Moyé, Lemuel A. |d 1952- |e Verfasser |0 (DE-588)122260651 |4 aut | |
| 245 | 1 | 0 | |a Elementary bayesian biostatistics |c Lemuel A. Moyé |
| 264 | 1 | |a Boca Raton, Fla. |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a XXI, 377 S. |b graph. Darst. |c 24 cm. + 1 CD-ROM (4 3/4 in.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Chapman & Hall/CRC biostatistics series |v 21 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Bayes, Teoría de decisión estadística de | |
| 650 | 4 | |a Biometría | |
| 650 | 4 | |a Medicina - Investigación - Métodos estadísticos | |
| 830 | 0 | |a Chapman & Hall/CRC biostatistics series |v 21 |w (DE-604)BV023097394 |9 21 | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip0722/2007027670.html |3 Table of contents only | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018764912 | ||
Datensatz im Suchindex
| _version_ | 1804140890138083328 |
|---|---|
| adam_text | Contents
Contents ix
Preface xv
Acknowledgments xvii
Introduction xix
Prologue Opening Salvos 1
Old Conflicts, New Wars /
Bayes Quiet Bombshell 1
Trapped in a Bottle 4
Unleased! 7
Holy Grail. 13
Attack of the Frequentists 14
Total War. 18
Fighting Back 19
The Health Care Love Affair with P-Values 21
Circling Two Suns 23
References 24
1. Basic Probability and Bayes Theorem 29
1.1 Probability s Role 29
1.2 Objective and Subjective Probability 30
1.3 Relative Frequency and Collections of Events 30
Example 1.1. Probability as Relative Frequency 31
1.4 Counting and Combinatorics 31
Example 1.2. Language Translator for the Clinic 33
1.5 Simple Rules in Probability 34
1.5.1 Combinations of Events 35
1.5.2 Joint Occurrences 35
1.5.3 Mutual Exclusivity 35
1.5.4 Independence 36
1.5.5 Dependence 37
1.5.6 Unions of Events 39
1.5.7 Complements 40
1.5.8 Probabilities and the Differential Effect of Gender: CARE 40
1.6 Law of Total Probability and Bayes Theorem 42
Example 1.3: Cause of Death 44
Example 1.4: Market Share 47
Example 1.5: Sensitivity and Specificity 49
ix
x Elementary Bayes Biostatistics
References 54
2. Compounding and the Law of Total Probability 57
2.1 Introduction 57
2.2 The Law of Total Probability: Compounding 58
2.2.1 The Role of Compounding in Bayes Procedures 59
2.3 Proportions and the Binomial Distribution 60
Example 2.1 61
2.4 Negative Binomial Distribution 68
Example 2.2 69
2.5 The Poisson Process 71
Example 2.3 72
Example 2.4 73
2.5.1 Compound Poisson Process 76
Example 2.5: Cold Checks 77
2.6 The Uniform Distribution 78
2.6.1 Measuring Probability 78
2.6.2 Probability as Area 80
2.6.3 Compounding with the Uniform Distribution 82
2.7 Exponential Distribution 84
Example 2.6 85
Problems 88
References 89
3. Intermediate Compounding and Prior Distributions 91
3.1 Compounding and Prior Distributions 91
3.2 Epidemiology 101 92
3.2.1 The Orange Juice or the Bee 92
3.3 Computing Distributions of Deaths 94
Example 3.1 94
3.4 The Gamma Distribution andER Arrivals 97
Example 3.2 99
3.4.1 Compound Gamma and Negative Binomial Distributions 103
Example 3.3: Storm Warnings 103
Example 3.4: Substance Abuse Rehabilitation 105
3.6 The Normal Distribution 109
3.6.1 Why Is the Normal Distribution Normally Used? 110
Example 3.5: Generating Central Tendency Ill
3.6.2 Using the Normal Distribution 113
3.6.3.1 Simplifying Transformations 113
Example 3.6 115
3.6.3. Compounding the Normal Distribution 115
Example 3.7 115
Problems 116
References 118
4. Completing Your First Bayesian Computations 119
4.1 Compounding and Bayes Procedures 119
Contents xi
4.2 Introduction to a Simple Bayes Procedure 120
Example 4.1 120
4.3. Including a Continuous Conditional Distribution 123
Example 4.2: Hepatitis Sera Production 124
4.4. Workingwith Continuous Conditional Distributions 128
Example 4.3: Astrocytomas 128
4.5. Continuous Conditional and Prior Distributions 131
Example 4.4: Testing for Diabetes Mellitus 131
Example 4.5: Clinical Trial Compliance 136
Problems 140
Reference 144
5. When Worlds Collide 145
5.7 Introduction 145
Reference 161
6. Developing Prior Probability 163
6.1 Introduction 163
6.2 Prior Knowledge and Subjective Belief 163
6.3 The Counterintuitive Prior 165
Example 6.1 166
6.4. Prior Information from Different Investigators 171
Example 6.2 171
6.5 Meta Analysis and Prior Distributions 174
Example 6.3 175
6.6 Priors and Clinical Trials 177
6.6.1 Difficulties in Estimating the Underlying Event Rate 178
6.6.2 Difficulties in Estimating a Study Intervention s Effectiveness 179
6.6.2.1 UKPDS 179
6.6.2.2 CAST 180
6.6.2.3 Wavering Prior Opinions 181
6.6.2.4 Conclusions on Nonintuitive Priors 183
6.7 Conclusions 187
Problems 187
References 188
7. Using Posterior Distributions: Loss and Risk 191
7.1 Introduction 191
7.2 The Role of Loss and Risk. 191
7.3 Decision Theory Dichotomous Loss 192
Example 7.1: Loss Functions and Hypothesis Testing 194
Example 7.2: Discrete Loss Functions and HDL Levels 197
7.4 Generalized Discrete Loss Functions 198
Example 7.3: Multiple Discrete Loss Functions: Alzheimer s Disease 198
7.5 Continuous Loss Functions 202
7.5.1 Linear Loss 202
Example 7.4: West Nile Virus Infection Rates 202
7.5.2 Weighted Linear Loss 203
Example 7.5: Reactive Airway Disease 205
xii Elementary Bayes Biostatistics
7.5.3 Square Error Loss 208
Example 7.6: Modeling Drug Approval Activity 209
7.6 The Need for Realistic Loss Functions 212
Example 7.7: Loss Function for Blood Sugar Measurement 212
Problems 214
References 216
8. Putting It All Together 217
8.1 Introduction 217
8.2 Illustration 1: Stroke Treatment 217
8.2.1 Background 217
8.2.2 Parameterization of the Problem 219
8.2.3 The Prior Distribution 219
8.2.4 Conditional Distribution 221
8.2.5 Loss Functions 222
8.2.6 Identifying the Posterior Distribution 222
8.3 Illustration 2: Adverse Event Rates 225
8.3.1 Background 225
8.3.2 Statement of the Problem 226
8.3.3 Constructing the Prior Distribution 227
8.3.4 Conditional Distribution 230
8.3.5 Loss Function 230
8.3.6 Constructing the Posterior Distribution 230
8.4 Conclusions 233
References 234
9. Bayesian Sample Size 235
9.1 Introduction 235
9.2 The Real Purpose of Sample Size Discussions 235
9.3. Hybrid Bayesian-Frequentist Sample Sizes 236
9.3.1 One-Sample Test on a Proportion 236
9.3.1.1 Providing a Probability Distribution for 9 237
Example 9.1: Leg Amputations in Diabetes Mellitus 238
9.3.2 Two Sample Computation 241
Example 9.2: Clinical Trial Sample Size 243
9.4 Complete Bayesian Sample Size Computations 245
Example 9.3: Parkinson s Disease 246
9.5 Conclusions 250
Problems 252
References 253
10. Predictive Power and Adaptive Procedures 255
10.1 Introduction 255
10.2 Predictive Power 255
10.2.1 The Importance of Monitoring Clinical Trials 255
10.2.2. Test Statistic Trajectories 256
10.2.3 Brownian Motion and Conditional Power 257
10.2.4 An Example of a Bayes Monitoring Rule 260
10.2.5 Comments on Predictive Value 263
Contents xiii
10.3 Adaptive Bayes Procedures 263
10.3.1 Introduction 264
10.3.2 Acute Pancreatitis 265
10.3.3 Some Implications of Adaptive Bayes Procedures 267
10.3.4 Setting the Allocation Ratio 268
10.3.5 Anti-Obesity Therapy 268
10.4 Conclusions 272
References 272
11. Is My Problem a Bayes Problem? 275
11.1 Introduction 275
11.2 Unidimensional versus Multidimensional Problems 276
11.3 Ovulation Timing 277
11.3.1 Introduction 277
11.3.2 Framework of the Problem 279
11.3.3 Setting the Loss Function 279
11.3.4 Prior Probabilities of 0 280
11.3.5 Conditional Distribution 282
11.3.6 Building the Posterior Distribution 285
11.3.7 Results 285
11.3.8 Commentary 291
11.4 Building Community Intuition 292
References 295
12. Conclusions and Commentary 297
12.1 Validity of the Key Ingredients 298
12.1.1 The Likelihood Principle 298
12.1.2 Prior Information 300
12.1.3 Loss Function 302
12.2 Dark Clouds 302
12.3 Recommendations 304
Step 1. Take a strong stand for disciplined research methodology 304
Step 2. Fix the miss-translation 304
Step 3. Show us something new 305
Step 4. Develop realistic prior distributions and loss functions 305
Step 5. Actively incorporate counterintuitive prior information 305
Step 6. Banish discussion of improper priors from clinical research 305
Step 7. Develop good Bayesian primers for clinical investigators 306
References 306
Appendices 311
Index 373
|
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| discipline | Medizin |
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| indexdate | 2024-07-09T22:07:10Z |
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| isbn | 9781584887249 |
| language | English |
| lccn | 2007027670 |
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| physical | XXI, 377 S. graph. Darst. 24 cm. + 1 CD-ROM (4 3/4 in.) |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Chapman & Hall/CRC |
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| series | Chapman & Hall/CRC biostatistics series |
| series2 | Chapman & Hall/CRC biostatistics series |
| spelling | Moyé, Lemuel A. 1952- Verfasser (DE-588)122260651 aut Elementary bayesian biostatistics Lemuel A. Moyé Boca Raton, Fla. Chapman & Hall/CRC 2008 XXI, 377 S. graph. Darst. 24 cm. + 1 CD-ROM (4 3/4 in.) txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC biostatistics series 21 Includes bibliographical references and index Bayes, Teoría de decisión estadística de Biometría Medicina - Investigación - Métodos estadísticos Chapman & Hall/CRC biostatistics series 21 (DE-604)BV023097394 21 http://www.loc.gov/catdir/toc/ecip0722/2007027670.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018764912&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moyé, Lemuel A. 1952- Elementary bayesian biostatistics Chapman & Hall/CRC biostatistics series Bayes, Teoría de decisión estadística de Biometría Medicina - Investigación - Métodos estadísticos |
| title | Elementary bayesian biostatistics |
| title_auth | Elementary bayesian biostatistics |
| title_exact_search | Elementary bayesian biostatistics |
| title_full | Elementary bayesian biostatistics Lemuel A. Moyé |
| title_fullStr | Elementary bayesian biostatistics Lemuel A. Moyé |
| title_full_unstemmed | Elementary bayesian biostatistics Lemuel A. Moyé |
| title_short | Elementary bayesian biostatistics |
| title_sort | elementary bayesian biostatistics |
| topic | Bayes, Teoría de decisión estadística de Biometría Medicina - Investigación - Métodos estadísticos |
| topic_facet | Bayes, Teoría de decisión estadística de Biometría Medicina - Investigación - Métodos estadísticos |
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