Statistics in Medicine

Front Cover

Statistics in Medicine, Second Edition

Copyright Page

Contents

Foreword to the Second Edition

Foreword to the First Edition

Acknowledgments

Databases

Part I: A Study Course of Fundamentals

Chapter 1. Data, Notation, and Some Basic Terms

1.1. About This Book

1.2. Stages of Scientific Knowledge

1.3. Quantification and Accuracy

1.4. Data Types

1.5. Notation (or Symbols)

1.6. Samples, Populations, and Randomness

Chapter 2. Distribution

2.1. Frequency Distributions

2.2. Relative Frequencies and Probabilities

2.3. Characteristics of a Distribution

2.4. What Is Typical?

2.5. The Spread About the Typical

2.6. The Shape

2.7. Statistical Inference

2.8. Distributions Commonly Used in Statistics

2.9. Standard Error of the Mean

2.10. Joint Distributions of Two Variables

Chapter 3. Summary Statistics

3.1. Numerical Summaries, One Variable

3.2. Numerical Summaries, Two Variables

3.3. Pictorial Summaries, One Variable

3.4. Pictorial Summaries, Two Variables

3.5. Good Graphing Practices

Chapter 4. Confidence Intervals and Probability

4.1. Overview

4.2. The Normal Distribution

4.3. Confidence Interval on an Observation from an Individual Patient

4.4. Concept of a Confidence Interval on a Descriptive Statistic

4.5. Confidence Interval on a Mean, Known Standard Deviation

4.6. The t Distribution

4.7. Confidence Interval on a Mean, Estimated Standard Deviation

4.8. The Chi-square Distribution

4.9. Confidence Interval on a Variance or Standard Deviation

4.10. Other Frequently Seen Confidence Intevals and Probabilities

Chapter 5. Hypothesis Testing: Concept and Practice

5.1. Hypotheses in Inference

5.2. Error Probabilities

5.3. Two Policies of Testing

5.4. Organizing Data for Inference

5.5. Evolving a Way to Answer Your Data Question

Chapter 6. Statistical Testing, Risks, and Odds in Medical Decisions

6.1. Overview

6.2. Categorical Data: Basics

6.3. Categorical Data: Tests on 2 x 2 Tables

6.4. Categorical Data: Risks and Odds

6.5. Rank Data: Basics

6.6. Rank Data: The Rank-Sum Test to Compare Two Samples

6.7. Continuous Data: Basics of Means

6.8. Continuous Data: Normal ( z ) and t Tests to Compare Two Sample Means

6.9. Other Tests of Hypotheses

Chapter 7. Sample Size Required for a Study

7.1. Overview

7.2. Is the Estimate of Minimum Required Sample Size Adequate?

7.3. Sample Size in Means Testing

7.4. Minimum Sample Size Estimation for a Test of Two Means

7.5. Other Situations in Which Minimum Sample Size Estimation Is Used

Chapter 8. Statistical Prediction

8.1. What Is a "Model"?

8.2. Straight-Line Models

8.3. What Is "Regression" (and Its Relation to Correlation)?

8.4. Assessing and Predicting Relationships by Regression

8.5. Other Questions That Can Be Answered by Regression

8.6. Clinical Decisions and Outcomes Analysis

Chapter 9. Epidemiology

9.1. The Nature of Epidemiology

9.2. Some Key Stages in the History of Epidemiology

9.3. Concept of Disease Transmission

9.4. Descriptive Measures

9.5. Types of Epidemiologic Studies

9.6. An Informal Approach to Public Health Problems

9.7. Analysis of Survival and Causal Factors

Chapter 10. Reading Medical Articles

10.1. Assessing Medical Information from an Article

10.2. Keep in Mind How a Study Is Constructed

10.3. Study Types

10.4. Sampling Bias

10.5. Statistical Aspects Where Articles May Fall Short

10.6. Evolving Terms: Meta-analysis, Multivariable Analysis, and Others

10.7. Selection of Statistical Tests to Use in a Study

Answers to Chapter Exercise, Part I

Part II: A Reference Guide

Chapter 11. Using the Reference Guide

11.1. How to Use This Guide

11.2. Basic Concepts Needed to Use This Guide

Chapter 12. Planning Medical Studies

12.1. The Science Underlying Clinical Decision Making

12.2. The Objective of Statistics

12.3. Concepts in Study Design

12.4. Sampling Schemes

12.5. How to Randomize a Sample

12.6. How to Plan and Conduct a Study

12.7. Mechanisms to Improve Your Study Plan

12.8. How to Manage Data

12.9. Setting Up a Test Within a Study

12.10. Choosing the Right Test

12.11. Statistical Ethics in Medical Studies

Chapter 13. Finding Probabilities or Error

13.1. Introduction

13.2. The Normal Distribution

13.3. The t Distribution

13.4. The Chi-square Distribution

13.5. The F Distribution

13.6. The Binomial Distribution

13.7. The Poisson Distribution

Chapter 14. Confidence Intervals

14.1. Overview

14.2. Confidence Interval on a Mean, Known Standard Deviation

14.3. Confidence Interval on a Mean, Estimated Standard Deviation

14.4. Confidence Interval on a Variance or Standard Deviation

14.5. Confidence Interval on a Proportion

14.6. Confidence Interval on a Correlation Coefficient

Chapter 15. Tests on Categorical Data

15.1. Categorical Data Summary

15.2. 2 x 2 Tables: Contingency Tests

15.3. r x c Tables: Contingency Tests

15.4. Risks and Odds in Medical Decisions

15.5. 2 x 2 Tables: Tests of Association

15.6. Tests of Proportion

15.7. Tests of a Small Proportion (Close to Zero)

15.8. Matched Pair Test (McNemar's Test)

Chapter 16. Test on Ranked Data

16.1. Basics of Ranks

16.2. Single or Paired Small Samples: The Signed-Rank Test

16.3. Two Small Samples: The Rank-Sum Test

16.4 Three or More Independent Samples: The Kruskal–Wallis Test

16.5. Three or More Matched Samples: The Friedman Test

16.6. Single Large Samples: Normal Approximation to Signed-Rank Test

16.7. Two Large Samples: Normal Approximation to Rank-Sum Test

Chapter 17. Tests on Means of Continuous Data

17.1. Summary of Means Testing

17.2. Normal ( z ) and t Tests for Single or Paired Means

17.3. Post Hoc Confidence and Power

17.4. Normal ( z ) and t Tests for Two Means

17.5. Three or More Means: One-Way Analysis of Variance

Chapter 18. Multifactor Tests on Means of Continuous Data

18.1. Concepts of Elperimental Design

18.2. Two-Factor Analysis of Variance

18.3. Repeated-Measures Analysis of Variance

18.4. Analysis of Covariance

18.5. Three- and Higher-Factor Analysis of Variance

18.6. More Specialized Designs and Techniques

Chapter 19. Tests on Variances of Continuous Data

19.1. Basics of Tests on Variability

19.2. Single Samples

19.3. Two Samples

19.4. Three or More Samples

Chapter 20. Tests on the Distribution Shape of Continuous Data

20.1. Objectives of Tests on Distributions

20.2. Test of Normality of a Distribution

20.3. Test of Equality of Two Distributions

Chapter 21. Equivalence Testing

21.1. Concepts and Terms

21.2. Basics Underlying Equivalence Testing

21.3. Methods for Nonsuperiority Testing

21.4. Methods for Equivalence Testing

Chapter 22. Sample Size Required in a Study

22.1. Overview

22.2. Relation of Sample Size Calculated to Sample Size Needed

22.3. Sample Size for Tests on Means

22.4. Sample Size for Confidence Intervals on Means

22.5. Sample Size for Tests on Rates (Proportions)

22.6. Sample Size for a Confidence Interval on a Rate (Proportion)

22.7. Sample Size for Significance of a Correlation Coefficient

22.8. Sample Size for Tests on Ranked Data

22.9. Sample Size for Tests on Variances, Anaslysis of Variance, and Regression

Chapter 23. Modeling and Clinical Decisions

23.1. Overview of Modeling

23.2. Straight-Line Models

23.3. Curved Models

23.4. Constants of Fit for Any Model

23.5. Multiple-Variable Models

23.6. Clinical Decision Based on Recursive Partitioning

23.7. Number Needed to Treat or to Benefit

23.8. Clinical Decision Based on Measures of Effectiveness: Outcomes Analysis

Chapter 24. Regression and Correlation Methods

24.1. Regression Concepts and Assumptions

24.2. Correlation Concepts and Assumptions

24.3. Simple Regression

24.4. Correlation Coefficients

24.5. Tests and Confidence Intervals on Regression Parameters

24.6. Tests and Confidence Intervals on Correlation Coefficients

24.7. Curved Regression

24.8. Multiple Regression

24.9. Types of Regression

24.10. Logistic Regression

Chapter 25. Survival and Time-Series Analysis

25.1. Time-Dependent Data

25.2. Survival Curves: Estimation

25.3. Survival Curves: Testing

25.4. Sequential Analysis

25.5. Time Series: Detecting Patterns

25.6. Time-Series Data: Testing

Chapter 26. Methods You Might Meet, But Not Every Day

26.1. Overview

26.2. Analysis of Variance Issues

26.3. Regression Issues

26.4. Multivariate Methods

26.5. Nonparametric Tests

26.6. Imputation of Missing Data

26.7. Resampling Methods

26.8. Agreement Measures and Correlation

26.9. Bonferroni "Correction"

26.10. Logit and Probit

26.11. Adjusting for Outliers

26.12. Curve Fitting to Data

26.13. Tests of Normality

Chapter Summaries

References and Data Sources

Tables of Probability Distributions

I. Normal Distribution

II. t Distribution

III. Chi-square Distribution, Right Tail

IV. Chi-square Distribution, Left Tail

V. F Distribution

VI. Binomial Distribution

VII. Poisson Distribution

VIII. Signed-Rank Probabilities

IX. Rank-Sum U Probabilities

Symbol Index

Subject Index