Covariance analysis for case-control studies with small blocks

Medical and epidemiological studies often employ a blocked design in order to control for some types of variation. For example, environmental and, to some extent, genetic factors may be controlled by blocking on sibs. The most common situation is one in which a subject in one group is blocked with one or more subjects in another. Additional factors may be considered as covariates in the analysis. Conditional likelihood methods give rise to consistent estimators of the parameters of the log-linear model. These estimators are generalized, and cases where there are small numbers of subjects in each group or where there are more than two groups are discussed. The resulting models can be considered as special cases of the general-linear model, and therefore the analyses can often be carried out with existing computer programs. The methods are illustrated by use of data from a case-control study in which each block contains one case and four controls.