Modelling Binary Data (Hardback): (Chapman & Hall/CRC Texts in Statistical Science)

Data are said to be binary when each observation falls into one of two categories, such as alive or dead, positive or negative, defective or non-defective and success or failure. In this book, it is shown how data of this type can be analyzed using a modelling approach. It is designed to meet the need of a textbook of an intermediate level which dwells on the practical aspects of modelling binary data, which incorporates recent work on checking the adequacy of fitted models and which shows how modern computational facilities can be exploited. The book begins with a description of a number of studies in which binary data have been collected. These data sets, and others, are then used to illustrate the techniques that are presented in the subsequent chapters. The majority of the examples are drawn from the agricultural, biological and medical sciences. Following this, a number of standard statistical procedures based on binomial distribution are described. The book then introduces the modelling approach, with particular emphasis on the linear logistic model, and covers the analysis of binary data from biological assays and other applications. Further topics discussed include model checking diagnostics, models for overdispersed data, analyzing data from cohort and case-control studies and statistical software packages. Suggestions for further reading are included in each chapter. The book is aimed at statisticians in the pharmaceutical industry and those engaged in agricultural, biological, industrial and medical research, who need to analyze binary data.

Table of Contents:
Part 1 Introduction: some examples; the scope of this book; use of statistical software. Part 2 Statistical inference for binary data: the binomial distribution; inference about the success probability; comparison of two proportions; comparison of two or more proportions. Part 3 Models for binary and binomial data: statistical modelling; linear models; methods of estimation; fitting linear models to binary data; models for binary response data; the linear logistic model; fitting the linear logistic model to binomial data; goodness of fit of a logistic model; comparing linear logistic models; linear trends in proportions; comparing stimulus-response relationships; non-convergence and over-fitting; a further example on model selection; predicting a binary response probability. Part 4 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. Part 5 Definition of residuals; checking the form of the linear predictor; checking the adequacy of the link function; identification of outlying observations; indentification of influential observations; checking the assumption of a binomial distribution; model checking for binary data; a further example on the use of diagnostics. Part 6 Overdispersion: potential causes of overdispersion; modelling variability in response probabilities; modelling correlation between binary responses; modelling overdispersed data; the special case of equal n2; the beta-binomial model; random effects in a linear logistic model; summary and recommendations; a further example. Part 7 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; a matched case-control studies; a matched case-control study on sudden infant death syndrome. Part 8 Some additional topics: analysis of proportions and percentages; analysis of rates; analysis of binary data from cross-over trials; random effects modelling; modelling errors in the measurement of explanatory variables; analysis of binary time series; multivariate binary data; experimental design. Part 9 Computer software for modelling binary data: statistical packages for modelling binary data; computer-based analyses of example data sets; using packages to perform some non-standard analyses; summary of the relative merits of packages for modelling binary data. Appendices: Tables of the logistic and probit transformations; algorithm for fitting the linear logistic model; glim macros used in modelling binary data.