The relative efficiencies of matched and independent sample designs for case-control studies

We have studied the asymptotic and small sample efficiencies of dependent (pair-matched or stratified) and independent samples as design techniques for case-control studies, and of matched, stratified, covariance-adjusted, and crude comparisons as methods of analysis. The asymptotic efficiencies of dependent sample designs relative to independent sample designs with adjustment were found to vary with the strengths of the relationships of disease with exposure and potential confounder: as the relationship with exposure increases, dependent samples lose efficiency; as the relationship with confounder increases, dependent samples gain efficiency. The relative efficiency also depends in a complicated manner on such other factors as the distribution of exposure and the strength of the exposure-confounder relationship. In the majority of situations examined, however, dependent samples were found to be somewhat more efficient than independent samples when confounding was present, while the reverse was true when confounding was absent. Results of small sample simulations do not differ importantly from the asymptotic results, except for pair-matching on a non-confounder, where the inefficiency of matching is greater in small samples.