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Statistical Methods for Rates and Proportions, Third Edition 

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Comment from the Stata technical groupStatistical 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 chisquared 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 contentsView 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
2.3. Using the F Distribution2.2.2. A Fundamental Property of Confidence Intervals 2.4. Approximate Inference for a Single Proportion
2.4.1. Hypothesis Tests
2.5. Sample Size for a OneSample Study2.4.2. Confidence Intervals
2.5.1. Sample Size for Hypothesis Tests
2.6.* Standard Errors by the Delta Method2.5.2. Sample Size for Confidence Intervals 2.7.* Alternative Definitions of TwoSided PValues and Confidence Intervals
2.7.1. The Point Probability Method
Problems2.7.2. The Tail Probability Method 2.7.3. The Likelihood Ratio Method 2.7.4. Some Concluding Remarks 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. OneTailed versus TwoTailed 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: Crosssectional, Naturalistic, or Multinomial Sampling
6.1. Some Hypothetical Data
6.2. Measures of Association Derived from χ^{2} 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
6.7. Criticisms of the Odds Ratio6.6.2. Confidence Intervals 6.6.3.* A Confidence Interval Method to be Avoided 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 TwoPeriod Crossover Desig n 8.3. Factors Affecting Power in a Randomized Controlled Trial
8.3.1. The IntenttoTreat Principle
8.4. Alternatives to Simple Randomization8.3.2. Noninferiority and Equivalence Trials 8.3.3. Selection Trials 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
Problems9.6.2. 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 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
Problems10.9.2. Fixed and Random Effects Metaanalysis 10.9.3.* Tests of Odds Ratio Homogeneity in the Large Sparse Case 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
11.4. Polytomous Logistic Regression11.3.2. Multiple Binary Logistic Regression: Additive and Interactive Models 11.3.3. Generalized Likelihood Ratio Tests 11.3.4. LogLikelihood GoodnessofFit Tests and the Analysis of Information
11.4.1. An Example: The Double Dichotomy
Problems11.4.2. A General Framework for Multinomial Responses: The Exponential Family of Distributions 11.4.3.* General Logistic Regression References 12. Poisson Regression
12.1. Poisson Random Variables
12.2. Poisson Regression
12.2.1. Simple Poisson Regression
12.3.* Overdispersion12.2.2. Multiple Poisson Regression 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 MatchedSample Data
14.2. Conditional Logistic Regression
14.2.1. Matched CaseControl Studies: One Case Matched to One or More Controls
14.3. Extensions14.2.2. Matched Prospective Studies
14.3.1. Matched Studies with Varying Numbers of Cases and Controls
14.4. An Example14.3.2. Matched Studies with Polytomous Outcomes 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
15.5.* Extensions of Logistic Regression with Correlated Outcomes15.4.2. Inference for the Mantel–Haenszel Odds Ratio with Clustered Data
15.5.1. Generalized Estimating Equations
Problems15.5.2. 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 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
16.3. Data Missing At Random in Several 2 x 2 Tables16.2.2. Variance Estimation
16.3.1. Complete Record, Weighting, and Imputation Methods for the Mantel–Haenszel Estimator, and Variance Estimation by the Jackknife
16.4.* Logistic Regression When Covariates Are Missing at Random16.3.2. Multiple Imputation
16.4.1. Likelihood Approach
16.5.* Logistic Regression When Outcomes Are Missing at Random16.4.2. Imputation 16.4.3. Weighting 16.4.4. Models Conditioning on the Observation Indicator 16.4.5. Comparisons 16.4.6. Example 16.6.* Nonignorable Missingness
16.6.1. Inference under Nonignorable Missingness
16.7.* Nonmonotone Missingness16.6.2. Sensitivity Analysis 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 TwoTailed 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

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