The design of case‐control studies: The effect of confounding on sample size requirements

Abstract

This paper considers the extent to which confounding effects of covariates, which are not controlled for by matching in the design, may influence the sample size necessary for case‐control studies. The quantitative calculations are performed for an age‐matched case‐control study on lung cancer and air pollution, and are based on different evaluation methods. For illustrative purposes attention is confined to a dichotomous risk factor and a single dichotomous covariate. By using the numerical values of a pilot study investigating lung cancer and air pollution, it turns out that the sample size required for detecting a relative risk as close as 1.15 to 1 is only slightly influenced by the strength of the association between confounder and risk factor for reasonable variations around our empirical values. On the other hand, sample size considerably increases with increasing relative risk of a confounder even when the association remains small. The sample size required for an individually matched analysis practically equals that for an age‐stratified analysis when the relative risk of the covariate is one. With a relative risk greater than one, however, the size for a matched analysis exceeds that for a stratified analysis and the ratio between them increases with increasing relative risk.