Modelling Binary Data, Second Edition

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