The design of case-control studies: the influence of confounding and interaction effects.

This paper considers quantitatively the extent to which the interaction or confounding effects of covariates may influence the design of case-control studies with particular reference to sample requirements and the role of matching. For the most part, attention is confined to a dichotomous exposure variable, and a single dichotomous covariate. Adjustment for confounding variables appears to have little effect on the power of a study unless they are strongly (odds ratio of 5 or more) related to both the disease and the exposure of interest, and only in similar circumstances will matching be of appreciable value. Matching also makes only a small improvement in the power to detect interaction effects, except under fairly extreme conditions. Both to control confounding and to detect interaction, the effect of matching may sometimes be to reduce the power of a study. The difference in power between matched and unmatched studies diminishes rapidly as the control-to-case ratio is increased. The implications of interaction effects for sample size requirements are more important. If one aim of a study is to detect interactions, the size of the study will have to be at least four times larger than if attention were confined to detecting main effects of the same magnitude. These conclusions are based on a quantitative evaluation of a wide range of possible situations.