Statistics in Medicine (eBook)

Front Cover 1
Statistics in Medicine, Second Edition 4
Copyright Page 5
Contents 10
Foreword to the Second Edition 18
Foreword to the First Edition 20
Acknowledgments 22
Databases 24
Part I: A Study Course of Fundamentals 44
Chapter 1. Data, Notation, and Some Basic Terms 46
1.1. About This Book 46
1.2. Stages of Scientific Knowledge 48
1.3. Quantification and Accuracy 49
1.4. Data Types 50
1.5. Notation (or Symbols) 52
1.6. Samples, Populations, and Randomness 54
Chapter 2. Distribution 58
2.1. Frequency Distributions 58
2.2. Relative Frequencies and Probabilities 60
2.3. Characteristics of a Distribution 61
2.4. What Is Typical? 61
2.5. The Spread About the Typical 62
2.6. The Shape 64
2.7. Statistical Inference 66
2.8. Distributions Commonly Used in Statistics 68
2.9. Standard Error of the Mean 75
2.10. Joint Distributions of Two Variables 76
Chapter 3. Summary Statistics 80
3.1. Numerical Summaries, One Variable 80
3.2. Numerical Summaries, Two Variables 84
3.3. Pictorial Summaries, One Variable 86
3.4. Pictorial Summaries, Two Variables 94
3.5. Good Graphing Practices 97
Chapter 4. Confidence Intervals and Probability 100
4.1. Overview 100
4.2. The Normal Distribution 101
4.3. Confidence Interval on an Observation from an Individual Patient 104
4.4. Concept of a Confidence Interval on a Descriptive Statistic 104
4.5. Confidence Interval on a Mean, Known Standard Deviation 106
4.6. The t Distribution 107
4.7. Confidence Interval on a Mean, Estimated Standard Deviation 109
4.8. The Chi-square Distribution 111
4.9. Confidence Interval on a Variance or Standard Deviation 113
4.10. Other Frequently Seen Confidence Intevals and Probabilities 115
Chapter 5. Hypothesis Testing: Concept and Practice 118
5.1. Hypotheses in Inference 118
5.2. Error Probabilities 124
5.3. Two Policies of Testing 127
5.4. Organizing Data for Inference 128
5.5. Evolving a Way to Answer Your Data Question 131
Chapter 6. Statistical Testing, Risks, and Odds in Medical Decisions 136
6.1. Overview 136
6.2. Categorical Data: Basics 137
6.3. Categorical Data: Tests on 2 x 2 Tables 139
6.4. Categorical Data: Risks and Odds 144
6.5. Rank Data: Basics 148
6.6. Rank Data: The Rank-Sum Test to Compare Two Samples 149
6.7. Continuous Data: Basics of Means 151
6.8. Continuous Data: Normal ( z ) and t Tests to Compare Two Sample Means 153
6.9. Other Tests of Hypotheses 156
Chapter 7. Sample Size Required for a Study 158
7.1. Overview 158
7.2. Is the Estimate of Minimum Required Sample Size Adequate? 161
7.3. Sample Size in Means Testing 162
7.4. Minimum Sample Size Estimation for a Test of Two Means 164
7.5. Other Situations in Which Minimum Sample Size Estimation Is Used 165
Chapter 8. Statistical Prediction 168
8.1. What Is a "Model"? 168
8.2. Straight-Line Models 169
8.3. What Is "Regression" (and Its Relation to Correlation)? 171
8.4. Assessing and Predicting Relationships by Regression 173
8.5. Other Questions That Can Be Answered by Regression 175
8.6. Clinical Decisions and Outcomes Analysis 176
Chapter 9. Epidemiology 180
9.1. The Nature of Epidemiology 180
9.2. Some Key Stages in the History of Epidemiology 181
9.3. Concept of Disease Transmission 181
9.4. Descriptive Measures 182
9.5. Types of Epidemiologic Studies 185
9.6. An Informal Approach to Public Health Problems 187
9.7. Analysis of Survival and Causal Factors 188
Chapter 10. Reading Medical Articles 196
10.1. Assessing Medical Information from an Article 196
10.2. Keep in Mind How a Study Is Constructed 197
10.3. Study Types 198
10.4. Sampling Bias 200
10.5. Statistical Aspects Where Articles May Fall Short 201
10.6. Evolving Terms: Meta-analysis, Multivariable Analysis, and Others 203
10.7. Selection of Statistical Tests to Use in a Study 206
Answers to Chapter Exercise, Part I 208
Part II: A Reference Guide 228
Chapter 11. Using the Reference Guide 230
11.1. How to Use This Guide 230
11.2. Basic Concepts Needed to Use This Guide 231
Chapter 12. Planning Medical Studies 238
12.1. The Science Underlying Clinical Decision Making 238
12.2. The Objective of Statistics 239
12.3. Concepts in Study Design 241
12.4. Sampling Schemes 241
12.5. How to Randomize a Sample 242
12.6. How to Plan and Conduct a Study 244
12.7. Mechanisms to Improve Your Study Plan 245
12.8. How to Manage Data 247
12.9. Setting Up a Test Within a Study 248
12.10. Choosing the Right Test 249
12.11. Statistical Ethics in Medical Studies 251
Chapter 13. Finding Probabilities or Error 256
13.1. Introduction 256
13.2. The Normal Distribution 256
13.3. The t Distribution 258
13.4. The Chi-square Distribution 260
13.5. The F Distribution 262
13.6. The Binomial Distribution 264
13.7. The Poisson Distribution 267
Chapter 14. Confidence Intervals 270
14.1. Overview 270
14.2. Confidence Interval on a Mean, Known Standard Deviation 272
14.3. Confidence Interval on a Mean, Estimated Standard Deviation 274
14.4. Confidence Interval on a Variance or Standard Deviation 276
14.5. Confidence Interval on a Proportion 278
14.6. Confidence Interval on a Correlation Coefficient 280
Chapter 15. Tests on Categorical Data 284
15.1. Categorical Data Summary 284
15.2. 2 x 2 Tables: Contingency Tests 286
15.3. r x c Tables: Contingency Tests 290
15.4. Risks and Odds in Medical Decisions 294
15.5. 2 x 2 Tables: Tests of Association 304
15.6. Tests of Proportion 307
15.7. Tests of a Small Proportion (Close to Zero) 313
15.8. Matched Pair Test (McNemar's Test) 317
Chapter 16. Test on Ranked Data 324
16.1. Basics of Ranks 324
16.2. Single or Paired Small Samples: The Signed-Rank Test 325
16.3. Two Small Samples: The Rank-Sum Test 328
16.4 Three or More Independent Samples: The Kruskal–Wallis Test 330
16.5. Three or More Matched Samples: The Friedman Test 334
16.6. Single Large Samples: Normal Approximation to Signed-Rank Test 337
16.7. Two Large Samples: Normal Approximation to Rank-Sum Test 340
Chapter 17. Tests on Means of Continuous Data 348
17.1. Summary of Means Testing 348
17.2. Normal ( z ) and t Tests for Single or Paired Means 349
17.3. Post Hoc Confidence and Power 353
17.4. Normal ( z ) and t Tests for Two Means 354
17.5. Three or More Means: One-Way Analysis of Variance 362
Chapter 18. Multifactor Tests on Means of Continuous Data 374
18.1. Concepts of Elperimental Design 374
18.2. Two-Factor Analysis of Variance 376
18.3. Repeated-Measures Analysis of Variance 383
18.4. Analysis of Covariance 389
18.5. Three- and Higher-Factor Analysis of Variance 392
18.6. More Specialized Designs and Techniques 394
Chapter 19. Tests on Variances of Continuous Data 398
19.1. Basics of Tests on Variability 398
19.2. Single Samples 399
19.3. Two Samples 402
19.4. Three or More Samples 405
Chapter 20. Tests on the Distribution Shape of Continuous Data 412
20.1. Objectives of Tests on Distributions 412
20.2. Test of Normality of a Distribution 413
20.3. Test of Equality of Two Distributions 422
Chapter 21. Equivalence Testing 430
21.1. Concepts and Terms 430
21.2. Basics Underlying Equivalence Testing 431
21.3. Methods for Nonsuperiority Testing 432
21.4. Methods for Equivalence Testing 436
Chapter 22. Sample Size Required in a Study 440
22.1. Overview 440
22.2. Relation of Sample Size Calculated to Sample Size Needed 442
22.3. Sample Size for Tests on Means 442
22.4. Sample Size for Confidence Intervals on Means 449
22.5. Sample Size for Tests on Rates (Proportions) 450
22.6. Sample Size for a Confidence Interval on a Rate (Proportion) 454
22.7. Sample Size for Significance of a Correlation Coefficient 456
22.8. Sample Size for Tests on Ranked Data 458
22.9. Sample Size for Tests on Variances, Anaslysis of Variance, and Regression 459
Chapter 23. Modeling and Clinical Decisions 462
23.1. Overview of Modeling 462
23.2. Straight-Line Models 464
23.3. Curved Models 464
23.4. Constants of Fit for Any Model 469
23.5. Multiple-Variable Models 473
23.6. Clinical Decision Based on Recursive Partitioning 476
23.7. Number Needed to Treat or to Benefit 480
23.8. Clinical Decision Based on Measures of Effectiveness: Outcomes Analysis 484
Chapter 24. Regression and Correlation Methods 490
24.1. Regression Concepts and Assumptions 490
24.2. Correlation Concepts and Assumptions 493
24.3. Simple Regression 495
24.4. Correlation Coefficients 497
24.5. Tests and Confidence Intervals on Regression Parameters 500
24.6. Tests and Confidence Intervals on Correlation Coefficients 507
24.7. Curved Regression 511
24.8. Multiple Regression 516
24.9. Types of Regression 521
24.10. Logistic Regression 523
Chapter 25. Survival and Time-Series Analysis 530
25.1. Time-Dependent Data 530
25.2. Survival Curves: Estimation 530
25.3. Survival Curves: Testing 535
25.4. Sequential Analysis 537
25.5. Time Series: Detecting Patterns 546
25.6. Time-Series Data: Testing 554
Chapter 26. Methods You Might Meet, But Not Every Day 564
26.1. Overview 564
26.2. Analysis of Variance Issues 564
26.3. Regression Issues 565
26.4. Multivariate Methods 565
26.5. Nonparametric Tests 567
26.6. Imputation of Missing Data 568
26.7. Resampling Methods 568
26.8. Agreement Measures and Correlation 569
26.9. Bonferroni "Correction" 570
26.10. Logit and Probit 570
26.11. Adjusting for Outliers 571
26.12. Curve Fitting to Data 571
26.13. Tests of Normality 572
Chapter Summaries 574
References and Data Sources 624
Tables of Probability Distributions 629
I. Normal Distribution 630
II. t Distribution 631
III. Chi-square Distribution, Right Tail 632
IV. Chi-square Distribution, Left Tail 633
V. F Distribution 634
VI. Binomial Distribution 635
VII. Poisson Distribution 639
VIII. Signed-Rank Probabilities 642
IX. Rank-Sum U Probabilities 643
Symbol Index 646
Subject Index 650