Statistics in Medicine

Dedication 1 Dedication 2 Foreword to the Third Edition Foreword to the Second Edition Foreword to the First Edition Acknowledgments Databases How to Use This Book Chapter 1. Planning Studies 1.1 Organizing a Study 1.2 Stages of Scientific Knowledge 1.3 Science Underlying Clinical Decision Making 1.4 Why Do We Need Statistics? 1.5 Concepts in Study Design 1.6 Study Types 1.7 Convergence with Sample Size 1.8 Sampling Schemes 1.9 Sampling Bias 1.10 How to Randomize a Sample 1.11 How to Plan and Conduct a Study 1.12 Mechanisms to Improve your Study Plan 1.13 Reading Medical Articles 1.14 Where Articles May Fall Short 1.15 Writing Medical Articles 1.16 Statistical Ethics in Medical Studies Appendix to Chapter 1 Chapter 2. Planning Analysis 2.1 What is in this Chapter 2.2 Notation (or Symbols) 2.3 Quantification and Accuracy 2.4 Data Types 2.5 Multivariable Concepts 2.6 How to Manage Data 2.7 A First Step Guide to Descriptive Statistics 2.8 Setting Up a Test Within a Study 2.9 Choosing the Right Test 2.10 A First Step Guide to Tests of Rates or Averages 2.11 A First Step Guide to Tests of Variability 2.12 A First Step Guide to Tests of Distributions Appendix to Chapter 2 Chapter 3. Probability and Relative Frequency 3.1 Probability Concepts 3.2 Probability and Relative Frequency 3.3 Graphing Relative Frequency 3.4 Continuous Random Variables 3.5 Frequency Distributions for Continuous Variables 3.6 Probability Estimates from Continuous Distributions 3.7 Probability as Area under the Curve Chapter 4. Distributions 4.1 Characteristics of a Distribution 4.2 Greek Versus Roman Letters 4.3 What is Typical 4.4 The Spread about the Typical 4.5 The Shape 4.6 Statistical Inference 4.7 Distributions Commonly Used in Statistics 4.8 Standard Error of the Mean 4.9 Joint Distributions of Two Variables Chapter 5. Descriptive Statistics 5.1 Numerical Descriptors, One Variable 5.2 Numerical Descriptors, Two Variables 5.3 Pictorial Descriptors, One Variable 5.4 Pictorial Descriptors, multiple Variables 5.5 Good Graphing Practices Chapter 6. Finding Probabilities 6.1 Probability and Area Under the Curve 6.2 The Normal Distribution 6.3 The t Distribution 6.4 The Chi-Square Distribution 6.5 The F Distribution 6.6 The Binomial Distribution 6.7 The Poisson Distribution Chapter 7. Confidence Intervals 7.1 Overview 7.2 Confidence Interval on an Observation from an Individual Patient 7.3 Concept of a Confidence Interval on a Descriptive Statistic 7.4 Confidence Interval on a Mean, Known Standard Deviation 7.5 Confidence Interval on a Mean, Estimated Standard Deviation 7.6 Confidence Interval on a Proportion 7.7 Confidence Interval on a Median 7.8 Confidence Interval on a Variance or Standard Deviation 7.9 Confidence Interval on a Correlation Coefficient Chapter 8. Hypothesis Testing 8.1 Hypotheses in Inference 8.2 Error Probabilities 8.3 Two Policies of Testing 8.4 Organizing Data for Inference 8.5 Evolving a Way to Answer Your Data Question Chapter 9. Tests on Categorical Data 9.1 Categorical Data Basics 9.2 Tests on Categorical Data: 2 × 2 Tables 9.3 The Chi-Square Test of Contingency 9.4 Fisher’s Exact Test of Contingency 9.5 Tests on r × c Contingency Tables 9.6 Tests of Proportion 9.7 Tests of Rare Events (Proportions Close to Zero) 9.8 Mcnemar’s test: Matched Pair Test of a 2 × 2 Table 9.9 Cochran’s Q: Matched Pair Test of a 2 × r Table Chapter 10. Risks, Odds, and ROC Curves 10.1 Categorical Data: Risks and Odds 10.2 Receiver Operating Characteristic Curves 10.3 Comparing Two ROC Curves 10.4 The Log Odds Ratio Test of Association 10.5 Confidence Interval on the Odds Ratio Chapter 11. Tests on Ranked Data 11.1 Rank Data: Basics 11.2 Single or Paired Sample(s), Ranked Outcomes: The Signed-Rank Test 11.3 Large Sample Single or Paired Ranked Outcomes 11.4 Two Independent Samples, Ranked Outcomes: The Rank-Sum Test 11.5 Two Large Independent samples, Ranked Outcomes 11.6 Multiple Independent Samples, Ranked Outcomes: The Kruskal–Wallis Test 11.7 Multiple Matched Samples, Ranked Outcomes: The Friedman Test 11.8 Ranked Independent Samples, Two Outcomes: Royston’s Ptrend Test 11.9 Ranked Independent Samples, Multiple Categorical or Ranked Outcomes: Cusick’s Nptrend Test 11.10 Ranked Matched Samples, Ranked Outcomes: Page’s L Test Chapter 12. Tests on Means of Continuous Data 12.1 Basics of Means Testing 12.2 Normal (z) and t Tests for Single or Paired Means 12.3 Two Sample Means Tests 12.4 Testing Three or More Means: One-Factor ANOVA 12.5 ANOVA Trend Test Chapter 13. Multi-Factor ANOVA and ANCOVA 13.1 Concepts of Experimental Design 13.2 Two-Factor ANOVA 13.3 Repeated Measures ANOVA 13.4 Analysis of Covariance (ANCOVA) 13.5 Three-and-Higher-Factor ANOVA 13.6 More Specialized Designs and Techniques Chapter 14. Tests on Variability and Distributions 14.1 Basics of Tests on Variability 14.2 Testing Variability on a Single Sample 14.3 Testing Variability Between Two Samples 14.4 Testing Variability among Three or more Samples 14.5 Basics on Tests of Distributions 14.6 Test of Normality of a Distribution 14.7 Test of Equality of Two Distributions Chapter 15. Managing Results of Analysis 15.1 Interpreting Results 15.2 Significance in Interpretation 15.3 Post Hoc Confidence and Power 15.4 Multiple Tests and Significance 15.5 Interim Analysis 15.6 Bootstrapping: When You Can’t Increase Your Sample Size 15.7 Resampling and Simulation 15.8 Bland–Altman Plots Chapter 16. Equivalence Testing 16.1 Concepts and Terms 16.2 Basics Underlying Equivalence Testing 16.3 Methods for Non-Inferiority Testing 16.4 Methods for Equivalence Testing Chapter 17. Bayesian Statistics 17.1 What is Bayesian Statistics 17.2 Bayesian Concepts 17.3 Describing and Testing Means 17.4 On Parameters other than Means 17.5 Describing and Testing a Rate (Proportion) 17.6 Conclusion Chapter 18. Sample Size Estimation and Meta-Analysis 18.1 Issues in Sample Size Considerations 18.2 Is the Sample Size Estimate Adequate? 18.3 The Concept of Power Analysis 18.4 Sample Size Methods in this Chapter 18.5 Test on One Mean (Normal Distribution) 18.6 Test on Two Means (Normal Distribution) 18.7 Test When Distributions are Non-Normal or Unknown 18.8 Test with No Objective Prior Data 18.9 Confidence Intervals on Means 18.10 Test of One Proportion (One Rate) 18.11 Test of Two Proportions (Two Rates) 18.12 Confidence Intervals on Proportions (On Rates) 18.13 Test on a Correlation Coefficient 18.14 Tests on Ranked Data 18.15 Variance Tests, Anova, and Regression 18.16 Equivalence Tests 18.17 Meta-Analysis Chapter 19. Modeling Concepts and Methods 19.1 What is a “Model”? 19.2 Straight-Line Models 19.3 Curved Models 19.4 Constants of Fit for any Model 19.5 Multiple-Variable Models 19.6 Building Models: Measures of Effectiveness 19.7 Outcomes Analysis Chapter 20. Clinical Decisions Based on Models 20.1 Introduction 20.2 Clinical Decision Based on Recursive Partitioning 20.3 Number Needed to Treat or Benefit 20.4 Basics of Matrices 20.5 Markov Chain Modeling 20.6 Simulation and Monte Carlo Sampling 20.7 Markov Chain Monte Carlo: Evolving Models 20.8 Markov Chain Monte Carlo: Stationary Models 20.9 Cost Effectiveness Chapter 21. Regression and Correlation 21.1 Introduction 21.2 Regression Concepts and Assumptions 21.3 Simple Regression 21.4 Assessing Regression: Tests and Confidence Intervals 21.5 Deming Regression 21.6 Types of Regression 21.7 Correlation Concepts and Assumptions 21.8 Correlation Coefficients 21.9 Correlation as Related to Regression 21.10 Assessing Correlation: Tests and Confidence Intervals 21.11 Interpretation of Small-But-Significant Correlations Chapter 22. Multiple and Curvilinear Regression 22.1 Concepts 22.2 Multiple Regression 22.3 Curvilinear Regression Chapter 23. Survival, Logistic Regression, and Cox Regression 23.1 Survival Concepts 23.2 Survival Estimation and Kaplan–Meier Curves 23.3 Survival Testing: The Log Rank Test 23.4 Survival Prediction: Logistic Regression 23.5 Survival Time Prediction: Cox Regression Chapter 24. Sequential Analysis and Time Series 24.1 Introduction 24.2 Sequential Analysis 24.3 Time-Series: Detecting Patterns 24.4 Time-Series Data: Testing Patterns Chapter 25. Epidemiology 25.1 The Nature of Epidemiology 25.2 Some Key Stages in the History of Epidemiology 25.3 Concept of Disease Transmission 25.4 Descriptive Measures 25.5 Types of Epidemiologic Studies 25.6 An Informal Approach to Public Health Problems 25.7 The Analysis of Survival and Causal Factors Chapter 26. Measuring Association and Agreement 26.1 What are Association and Agreement? 26.2 Contingency as Association 26.3 Correlation as Association 26.4 Contingency as Agreement 26.5 Correlation as Agreement 26.6 Agreement Among Ratings: Kappa 26.7 Agreement Among Multiple Rankers 26.8 Reliability 26.9 Intra-Class Correlation Chapter 27. Questionnaires and Surveys 27.1 Introduction 27.2 Surveys 27.3 Questionnaires Chapter 28. Methods You Might Meet, But Not Every Day 28.1 Overview 28.2 Analysis of Variance Issues 28.3 Regression Issues 28.4 Rates and Proportions Issues 28.5 Multivariate Methods 28.6 Further Non-Parametric Tests 28.7 Imputation of Missing Data 28.8 Frailty Models in Survival Analysis 28.9 Bonferroni “Correction” 28.10 Logit and Probit 28.11 Adjusting for Outliers 28.12 Curve Fitting to Data 28.13 Another Test of Normality 28.14 Data Mining Answers to Chapter Exercises Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Tables of Probability Distributions Symbol Index Statistical Subject Index Medical Subject Index