Statistical Reasoning in Medicine (eBook)

Preface 6
Acknowledgments 8
Contents 10
Introduction 16
Prologue 20
Europe’s Emergence from the Middle Ages 20
Absolutism 22
Refusing to be Counted 23
No Need for Probability 24
Intellectual Triumph: The Industrial Revolution 25
Reasoning from a Sample 26
Political Arithmetic 27
The Role of Religion in Political Arithmetic 27
Probability and the Return to Order 29
“Let Others Thrash It Out!” 30
Early Experimental Design 30
Agricultural Articulations 31
Fisher, Gosset, and Modern Experimental Design 32
References 33
The Basis of Statistical Reasoning in Medicine 35
1.1 What Is Statistical Reasoning? 35
1.2 Statistical Reasoning 40
1.3 Generalizations to Populations 47
References 53
Search Versus Research 54
2.1 Introduction 54
2.2 Catalina’s Dilemma 54
2.3 Exploratory Analysis and Random Research 57
2.4 Gender–Salary Problem Revisited 59
2.5 Exploratory Versus Confirmatory 61
2.6 Exploration and MRFIT 63
2.7 Exploration in the ELITE Trials 64
2.8 Necessity of Exploratory Analyses 65
2.9 Prospective Plans and “Calling Your Shot” 67
2.10 Tight Protocols 72
2.11 Design Manuscripts 73
2.12 Concordant Versus Discordant Research 74
2.13 Conclusions 76
References 77
A Hypothesis-Testing Primer 80
3.1 Introduction 80
3.2 The Rubric of Hypothesis Testing 81
3.3 The Normal Distribution and Its Estimators 82
3.4 Using the Normal Distribution 83
3.5 The Null Hypothesis: State of the Science 87
3.6 Type II Error and Power 93
3.7 Balancing Alpha and Beta 97
3.8 Reducing Alpha and Beta: The Sample Size 98
3.9 Two-Sided Testing 100
3.10 Sampling Error Containment 103
3.11 Confidence Intervals 104
3.12 Hypothesis Testing in Intervention Studies 106
3.13 Community Responsibility 106
Mistaken Identity: P-values in Epidemiology 108
4.1 Mistaken Identity 108
4.2 Detective Work 108
4.3 Experimental Versus Observational Studies 109
4.4 Determining Causation 112
4.5 Clinical Significance Without P- Values 115
4.6 Tools of the Epidemiologist 117
4.7 Fenfluramines 125
4.8 Design Considerations 126
4.9 Solid Structures from Imperfect Bricks 127
4.10 Drawing Inferences in Epidemiology 128
4.11 Study counting: The ceteris paribus fallacy 129
4.12 Critiquing Experimental Designs 130
4.13 Conclusions 130
References 131
Shrine Worship 133
5.1 Introduction 133
5.2 The Nightmare 133
5.3 P- value Bashing 134
5.4 Epidemiology and Biostatistics 134
5.5 The Initial Schism 136
5.6 Appearance of Statistical Significance 138
5.7 The P- value Love Affair in Healthcare 142
5.8 Use and Abuse of P- values 143
5.9 Proper Research Interpretation 147
References 149
P-values, Power, and Efficacy 152
6.1 Introduction 152
6.2 P- values and Strength of Evidence 152
6.3 Power 156
6.4 No Way Out? 158
6.5 Sample Size Computations 159
6.6. Non-statistical Considerations 160
6.7 The “Good Enough for Them” Approach 162
6.8 Efficacy Seduction 162
6.9 Number Needed To Treat 165
6.10 Absolute versus Relative Risk 166
6.11 Matching Statistical with Clinical Significance 168
6.12 Power for Smaller Efficacy Levels 170
6.13 Conclusions 171
References 171
Scientific Reasoning, P-values, and the Court 172
7.1 Introduction 172
7.2 Blood Pressure and Deception: The Frye Test 173
7.3 Rule 402 174
7.4 The Daubert Rulings 175
7.5 The Havner Ruling 176
7.6 Relative Risk and the Supreme Court 178
7.7 P- values, Confidence Intervals, and the Courts 179
7.8 Conclusions 180
References 180
One-Sided Versus Two-Sided Testing 181
8.1 Introduction 181
8.2 Attraction of One-Sided Testing 181
8.3 Belief Versus Knowledge in Healthcare 181
8.4 Belief Systems and Research Design 182
8.5 Statistical Versus Ethical Optimization 183
8.6 “Blinded by the Light”: CAST 184
8.7 LRC Results 187
8.8 Sample Size Issues 188
8.9 Hoping for the Best, Preparing for the Worst 189
8.10. Symmetrics versus Ethics 190
8.11 Conclusions 193
References 194
Multiple Testing and Combined Endpoints 195
9.1 Introduction 195
9.2 Definition of Multiple Analyses 196
9.3 Efficiency Versus Parsimony 196
9.4 Hypothesis Testing in Multiple Analyses 198
9.5 Familywise Error 200
9.7 The Bonferroni Inequality 200
9.8 Is Tight Control of the FWER Necessary? 202
9.9 Alternative Approaches 204
9.10 Analysis Triage 205
9.11 Combined Endpoints 208
9.12 Why Use Combined Endpoints 208
9.13 Combined Endpoint Construction 210
9.14 Measuring Combined Endpoints 213
9.15 Conclusions 215
References 216
Subgroup Analyses 218
10.1 Bona Fide Gems or Fool’s Gold 218
10.2 What Are Subgroups? 218
10.3 The Amlopidine Controversy 219
10.4 Definitions 221
10.5 Interpretation Difficulties 221
10.6 Stratified Randomization 229
10.7 Proper Versus Improper Subgroups 230
10.8 “Intention-to-Treat” Versus “As Treated” 231
10.9 Effect Domination Principle 232
10.10 Confirmatory Subgroup Analyses 233
10.11 Assessment of Subgroup Effects 234
10.12 Data Dredging — Caveat Emptor 237
10.13 Conclusions 237
References 238
P-values and Regression Analyses 241
11.1 The New Meaning of Regression 241
11.2 Assumptions in Regression Analysis 242
11.3 Model Estimation 243
11.4 Variance Partitioning 245
11.5 Enter Dichotomous Explainer Variables 248
11.6 The Meaning of “Adjustment” 249
11.7 Super Fits 251
11.8 Pearls of Great Price 253
11.9 Effect Modifiers and Alpha Allocation 254
11.10 Conclusions 259
Bayesian Analysis: Posterior P-values 261
12.1 An Arbitrary Process 261
12.2 The Frequentists 262
12.3 The Bayesian Philosophy 267
12.4 Feasibility of Prior Distributions 275
12.5 The Loss Function 277
12.6 Example of Bayesian Estimation 277
12.7 Bayesians and P- values 278
12.8 Bayes Testing: Asthma Prevalence 279
12.9 Conclusions 283
References 284
Conclusions: Good Servants but Bad Masters 285
Standard Normal Probabilities Probabilities Probabilities 290
Sample Size Primer 294
B.1 General Discussion of Sample Size 294
B.2 Derivation of Sample Size 296
B.3 Example 299
B.4 Continuous Outcomes 300
References 304
Daubert and Rule 702 Factors 305
C.1 The Daubert Factors 305
C.2 The 702 Factors 305
Index 307