• The cornerstone of the analysis of case-control studies is that the ratio of the odds of a binary outcome Y given exposure X = 1 to that given X = 0 is the same as the ratio of the odds where the roles of Y and X are reversed. This result means that prospective odds ratios can be estimated from retrospective case-control data.

• For binary exposure X and outcome Y there are both exact and large-sample methods for estimating odds ratios from case-control studies.

• Methods for the estimation of odds ratios for binary exposures extend to categorical exposures and allow the combination of estimates across strata. The latter enables control for confounding and background variables.

• For binary exposure X and outcome Y, the probabilities of X given Y and of Y given X can be formulated using two different logistic regression models. However, the two models give rise to the same estimates of odds ratios under maximum likelihood estimation.

• Rate ratios can be estimated from a case-control study if ‘time’ is incorporated correctly into the sampling of individuals; a simple possibility is to perform case-control sampling within short time bands and then to combine the results.

Preliminaries

Many central issues involved in the analysis of case-control data are illustrated by the simplest special case, namely that of a binary explanatory variable or risk factor and a binary outcome or response.