Search
   >> Home >> Bookstore >> Biostatistics and epidemiology >> Statistical Methods for Rates and Proportions, Third Edition

Statistical Methods for Rates and Proportions, Third Edition

Authors:
Joseph L. Fleiss, Bruce Levin, and Myunghee Cho Paik
Publisher: Wiley
Copyright: 2003
ISBN-13: 978-0-471-52629-2
Pages: 760; hardcover
Price: $114.50

Comment from the Stata technical group

Statistical Methods for Rates and Proportions covers a wide variety of methods for analyzing categorical data, with the emphasis and examples drawn from clinical medicine, epidemiology, psychiatry, psychopathology, and public health. The book is aimed at researchers and students who have at least a year’s course in applied statistics, including a thorough grounding in chi-squared tests and correlation. The mathematical background is restricted to high school algebra.

This book has the look and feel of a textbook, complete with examples used to demonstrate methods and motivate questions and exercises (with selected answers) at the end of each chapter. A bibliography is provided at the end of each chapter, providing a valuable desk reference for those interested in probing a topic in more depth.

Covered topics include statistical inference for one proportion, significance in a fourfold table, sample sizes, randomization, comparative studies, randomized controlled trials, logistic and Poisson regression, regression models for matched samples, correlated binary data, missing data, measuring interrater agreement, and standardization of rates.


Table of contents

Preface
Preface to the Second Edition
Preface to the First Edition
1. An Introduction to Applied Probability
1.1. Notation and Definitions
1.2. The Rule of Total Probability
1.3. The Evaluation of a Screening Test
1.4. Biases Resulting from the Study of Selected Samples
Problems
References
2. Statistical Inference for a Single Proportion
2.1. Exact Inference for a Single Proportion: Hypothesis Tests
2.2. Exact Inference for a Single Proportion: Interval Estimation
2.2.1. Definition of an Exact Confidence Interval
2.2.2. A Fundamental Property of Confidence Intervals
2.3. Using the F Distribution
2.4. Approximate Inference for a Single Proportion
2.4.1. Hypothesis Tests
2.4.2. Confidence Intervals
2.5. Sample Size for a One-Sample Study
2.5.1. Sample Size for Hypothesis Tests
2.5.2. Sample Size for Confidence Intervals
2.6.* Standard Errors by the Delta Method
2.7.* Alternative Definitions of Two-Sided P-Values and Confidence Intervals
2.7.1. The Point Probability Method
2.7.2. The Tail Probability Method
2.7.3. The Likelihood Ratio Method
2.7.4. Some Concluding Remarks
Problems
References
3. Assessing Significance in a Fourfold Table
3.1. Methods for Generating a Fourfold Table
3.2. "Exact" Analysis of a Fourfold Table
3.3. Yates' Correction for Continuity
3.4. One-Tailed versus Two-Tailed Tests
3.5. A Simple Confidence Interval for the Difference between Two Independent Proportions
3.6. An Alternative Critical Ratio Test
Problems
References
4. Determining Sample Sizes Needed to Detect a Difference between Two Proportions
4.1. Specifying a Difference Worth Detecting
4.2. The Mathematics of Sample Size Determination
4.3. Using the Sample Size Tables
4.4. Unequal Sample Sizes
4.5. Some Additional Uses of the Tables
4.6. Some Additional Comments
Problems
References
5. How to Randomize
5.1. Selecting a Simple Random Sample
5.2. Randomization in a Clinical Trial
5.3. Variations on Simple Randomization
References
6. Comparative Studies: Cross-sectional, Naturalistic, or Multinomial Sampling
6.1. Some Hypothetical Data
6.2. Measures of Association Derived from χ2
6.3. The Odds Ratio and Its Logarithm
6.4. Exact Inference for an Odds Ratio: Hypothesis Tests
6.5. Exact Inference for an Odds Ratio: Confidence Intervals
6.6. Approximate Inference for an Odds Ratio
6.6.1. Hypothesis Tests
6.6.2. Confidence Intervals
6.6.3.* A Confidence Interval Method to be Avoided
6.7. Criticisms of the Odds Ratio
6.8. Attributable Risk
6.9.* Standard Errors for Measures of Association
Problems
References
7. Comparative Studies: Prospective and Retrospective Sampling
7.1. Prospective Studies
7.2. Retrospective Studies
7.3. Estimating Attributable Risk from Retrospective Studies
7.4. The Retrospective Approach versus the Prospective Approach
Problems
References
8. Randomized Controlled Trials
8.1. The Simple Comparative Trial
8.2. The Two-Period Crossover Desig
n 8.3. Factors Affecting Power in a Randomized Controlled Trial
8.3.1. The Intent-to-Treat Principle
8.3.2. Noninferiority and Equivalence Trials
8.3.3. Selection Trials
8.4. Alternatives to Simple Randomization
Problems
References
9. The Comparison of Proportions from Several Independent Samples
9.1. The Comparison of m Proportions
9.2. Gradient in Proportions: Samples Quantitatively Ordered
9.3. Gradient in Proportions: Samples Qualitatively Ordered
9.4. Ridit Analysis
9.5.* Logit Models for Qualitatively Ordered Outcomes
9.6.* The Effect of Randomness in True Proportions
9.6.1. Estimation of the Marginal Mean Proportion
9.6.2. An Example
9.6.3. General Empirical Bayes Estimation of Posterior Odds, and a Test of Homogeneity of Proportions in the Large Sparse Case
9.6.4 Parametric Models
Problems
References
10. Combining Evidence from Fourfold Tables
10.1. The Construction and Interpretation for Some Chi Squared Tests
10.2. Combining the Logarithms of Odds Ratios
10.3.* Exact Inference for a Common Odds Ratio
10.4. Approximate Inference for a Common Odds Ratio
10.5. The Mantel–Haenszel Method
10.6. A Comparison of the Three Procedures
10.7. Alternatives to Matching
10.8. Methods to be Avoided
10.9. Related Matters
10.9.1. Potential Confounding and Operational Nonconfounding
10.9.2. Fixed and Random Effects Meta-analysis
10.9.3.* Tests of Odds Ratio Homogeneity in the Large Sparse Case
Problems
References
11. Logistic Regression
11.1. Introduction
11.2. The Log Odds Transformation Revisited
11.3. A Closer Look at Some Logistic Regression Models
11.3.1. Simple Binary Logistic Regression
11.3.2. Multiple Binary Logistic Regression: Additive and Interactive Models
11.3.3. Generalized Likelihood Ratio Tests
11.3.4. Log-Likelihood Goodness-of-Fit Tests and the Analysis of Information
11.4. Polytomous Logistic Regression
11.4.1. An Example: The Double Dichotomy
11.4.2. A General Framework for Multinomial Responses: The Exponential Family of Distributions
11.4.3.* General Logistic Regression
Problems
References
12. Poisson Regression
12.1. Poisson Random Variables
12.2. Poisson Regression
12.2.1. Simple Poisson Regression
12.2.2. Multiple Poisson Regression
12.3.* Overdispersion
Problems
References
13. The Analysis of Data from Matched Samples
13.1. Matched Pairs: Dichotomous Outcome
13.2. Matched Pairs: Polytomous Outcome
13.3. Multiple Matched Controls per Case
13.4. The Comparison of Matched Samples with m Distinct Types
13.5. Sample Size Determination for Matched Samples
13.6. Advantages and Disadvantages of Matching
Problems
References
14. Regression Models for Matched Samples
14.1. Direct and Indirect Parametric Modeling of Matched-Sample Data
14.2. Conditional Logistic Regression
14.2.1. Matched Case-Control Studies: One Case Matched to One or More Controls
14.2.2. Matched Prospective Studies
14.3. Extensions
14.3.1. Matched Studies with Varying Numbers of Cases and Controls
14.3.2. Matched Studies with Polytomous Outcomes
14.4. An Example
14.5. Other Issues
Problems
References
15. Analysis of Correlated Binary Data
15.1. Inference for a Single Proportion
15.2. Inference for Two Proportions
15.3. Design Considerations
15.4. 2 x 2 x 2 Tables
15.4.1. Hypothesis Testing
15.4.2. Inference for the Mantel–Haenszel Odds Ratio with Clustered Data
15.5.* Extensions of Logistic Regression with Correlated Outcomes
15.5.1. Generalized Estimating Equations
15.5.2. Random Effects Models
15.5.3. Summarizing by Individual or by Time
15.5.4. Models Conditioning on Previous Outcomes
15.5.5. Multivariate Binary Distributions
Problems
References
16. Missing Data
16.1. Three Types of Nonresponse Mechanism
16.2. Data Missing at Random in a 2 x 2 Table
16.2.1. Point Estimation
16.2.2. Variance Estimation
16.3. Data Missing At Random in Several 2 x 2 Tables
16.3.1. Complete Record, Weighting, and Imputation Methods for the Mantel–Haenszel Estimator, and Variance Estimation by the Jackknife
16.3.2. Multiple Imputation
16.4.* Logistic Regression When Covariates Are Missing at Random
16.4.1. Likelihood Approach
16.4.2. Imputation
16.4.3. Weighting
16.4.4. Models Conditioning on the Observation Indicator
16.4.5. Comparisons
16.4.6. Example
16.5.* Logistic Regression When Outcomes Are Missing at Random
16.6.* Nonignorable Missingness
16.6.1. Inference under Nonignorable Missingness
16.6.2. Sensitivity Analysis
16.7.* Nonmonotone Missingness
Problems
References
17. Misclassification: Effects, Control, and Adjustment
17.1. An Example of the Effects of Misclassification
17.2. The Algebra of Misclassification
17.3. The Algebra of Misclassification: Both Variables in Error
17.4. Statistical Control for Error
17.5. Probabilistic Control for Error
17.6. Experimental Control of Error
17.7.* Misclassification in Logistic Regression Models
Problems
References
18. The Measurement of Interrater Agreement
18.1. The Same Pair of Raters per Subject
18.2. Weighted Kappa
18.3. Multiple Ratings per Subject with Difference Raters
18.4. Further Applications
18.5.* Interrater Agreement as Association in a Multivariate Binary Vector
Problems
References
19. The Standardization of Rates
19.1. Reasons for and Warnings against Standardization
19.2. Two Types of Standardization: Direct and Indirect
19.3. Indirect Standardization
19.4. A Feature of Indirect Standardization
19.5. Direct Standardization
19.6. Some Other Summary Indices
19.7. Adjustment for Two Factors
Problems
References
Appendix A. Numerical Tables
A.1. Critical Values of the Normal Distribution
A.2. Critical Values of the Chi Squared Distribution
A.3. Percentage Points of the F Distribution
A.4. Sample Sizes per Group for a Two-Tailed Test of Two Proportions
A.5. 20,000 Random Digits
A.6. Natural Logarithms of x(ln x)
A.7. Percentage Points of Bartholomew’s Test for Order When m=3 Proportions Are Compared
A.8. Percentage Points of Bartholomew’s Test for Order When Up to m=4 Proportions Are Compared
A.9. Percentage Points of Bartholomew’s Test for Order When Up to m=12 Proportions Based on Equal Sample Sizes Are Compared
A.10. The Logit Transformation
Appendix B. The Basic Theory of Maximum Likelihood Estimation
Appendix C. Answers to Selected Problems
Author Index
Subject Index
The Stata Blog: Not Elsewhere Classified Find us on Facebook Follow us on Twitter LinkedIn Google+ Watch us on YouTube