Selecting Controls for Assessing Interaction in Nested Case-control Studies

Background: Two methods for selecting controls in nested case-control studies — matching on X and counter matching on X — are compared when interest is in interaction between a risk factor X measured in the full cohort and another risk factor Z measured only in the case-control sample. This is important because matching provides efficiency gains relative to random sampling when X is uncommon and the interaction is positive (greater than multiplicative), whereas counter matching is generally efficient compared to random sampling. Methods: Matching and counter matching were compared to each other and to random sampling of controls for dichotomous X and Z. Comparison was by simulation, using as an example a published study of radiation and other risk factors for breast cancer in the Japanese atomic-bomb survivors, and by asymptotic relative efficiency calculations for a wide range of parameters specifying the prevalence of X and Z as well as the levels of correlation and interaction between them. Focus was on analyses utilizing general models for the joint risk of X and Z. Results: Counter-matching performed better than matching or random sampling in terms of efficiency for inference about interaction in the case of a rare risk factor X and uncorrelated risk factor Z. Further, more general, efficiency calculations demonstrated that counter-matching is generally efficient relative to matched case-control designs for studying interaction. Conclusions: Because counter-matched designs may be analyzed using standard statistical methods and allow investigation of confounding of the effect of X, whereas matched designs require a non-standard approach when fitting general risk models and do not allow investigating the adjusted risk of X, it is concluded that counter-matching on X can be a superior alternative to matching on X in nested case-control studies of interaction when X is known at the time of case-control sampling.