INTRODUCTION

Some Examples

The Scope of this Book

Use of Statistical Software

STATISTICAL INFERENCE FOR BINARY DATA

The Binomial Distribution

Inference about the Success Probability

Comparison of Two Proportions

Comparison of Two or More Proportions

MODELS FOR BINARY AND BINOMIAL DATA

Statistical Modelling

Linear Models

Methods of Estimation

Fitting Linear Models to Binomial Data

Models for Binomial Response Data

The Linear Logistic Model

Fitting the Linear Logistic Model to Binomial Data

Goodness of Fit of a Linear Logistic Model

Comparing Linear Logistic Models

Linear Trend in Proportions

Comparing Stimulus-Response Relationships

Non-Convergence and Overfitting

Some other Goodness of Fit Statistics

Strategy for Model Selection

Predicting a Binary Response Probability

BIOASSAY AND SOME OTHER APPLICATIONS

The Tolerance Distribution

Estimating an Effective Dose

Relative Potency

Natural Response

Non-Linear Logistic Regression Models

Applications of the Complementary Log-Log Model

MODEL CHECKING

Definition of Residuals

Checking the Form of the Linear Predictor

Checking the Adequacy of the Link Function

Identification of Outlying Observations

Identification of Influential Observations

Checking the Assumption of a Binomial Distribution

Model Checking for Binary Data

Summary and Recommendations

OVERDISPERSION

Potential Causes of Overdispersion

Modelling Variability in Response Probabilities

Modelling Correlation Between Binary Responses

Modelling Overdispersed Data

A Model with a Constant Scale Parameter

The Beta-Binomial Model

Discussion

MODELLING DATA FROM EPIDEMIOLOGICAL STUDIES

Basic Designs for Aetiological Studies

Measures of Association Between Disease and Exposure

Confounding and Interaction

The Linear Logistic Model for Data from Cohort Studies

Interpreting the Parameters in a Linear Logistic Model

The Linear Logistic Model for Data from Case-Control Studies

Matched Case-Control Studies

MIXED MODELS FOR BINARY DATA

Fixed and Random Effects

Mixed Models for Binary Data

Multilevel Modelling

Mixed Models for Longitudinal Data Analysis

Mixed Models in Meta-Analysis

Modelling Overdispersion Using Mixed Models

EXACT METHODS

Comparison of Two Proportions Using an Exact Test

Exact Logistic Regression for a Single Parameter

Exact Hypothesis Tests

Exact Confidence Limits for bk

Exact Logistic Regression for a Set of Parameters

Some Examples

Discussion

SOME ADDITIONAL TOPICS

Ordered Categorical Data

Analysis of Proportions and Percentages

Analysis of Rates

Analysis of Binary Time Series

Modelling Errors in the Measurement of Explanatory Variables

Multivariate Binary Data

Analysis of Binary Data from Cross-Over Trials

Experimental Design

COMPUTER SOFTWARE FOR MODELLING BINARY DATA

Statistical Packages for Modelling Binary Data

Interpretation of Computer Output

Using Packages to Perform Some Non-Standard Analyses

Appendix A: Values of logit(p) and probit(p)

Appendix B: Some Derivations

Appendix C: Additional Data Sets

References

Index of Examples

Index