This book is about the planning and analysis of a special kind of investigation: a case-control study. We use this term to cover a number of different designs. In the simplest form individuals with an outcome of interest, possibly rare, are observed and information about past experience is obtained. In addition corresponding data are obtained on suitable controls in the hope of explaining what influences the outcome. In this book we are largely concerned with binary outcomes, for example indicating disease diagnosis or death. Such studies are reasonably called retrospective as contrasted with prospective studies, in which one records explanatory features and then waits to see what outcome arises. In retrospective studies we are studying the causes of effects and in prospective studies we are studying the effects of causes. We also discuss some extensions of case-control studies to incorporate temporality, which may be more appropriately viewed as a form of prospective study. The key aspect of all these designs is that they involve a sample of the underlying population that motivates the study, in which individuals with certain outcomes are strongly over-represented.

While we shall concentrate on the many special issues raised by such studies, we begin with a brief survey of the general themes of statistical design and analysis. We use a terminology deriving in part from epidemiological applications although the ideas are of much broader relevance.

We start the general discussion by considering a population of study individuals, patients, say, assumed to be statistically independent.