Variance estimators for attributable fraction estimates consistent in both large strata and sparse data

A number of variance formulae for the attributable fraction have been presented, but none is consistent in sparse data, such as found in individually matched case-control studies. This paper employs Mantel-Haenszel estimation to derive variance estimators for attributable fractions that are dually consistent, that is, consistent in both sparse data and large strata. The method may also be applied using conditional maximum likelihood. Extensions of these estimators to situations involving effect modification and preventive exposures are also derived. Examples of applications to individually matched case-control studies are given.