Modelling binary data

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 bkExact 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.