• Division of Cancer Epidemiology and Genetics, National Cancer Institute, Executive Plaza South, Bethesda, Maryland, USA. lih5@mail.nih.gov

Case-control genome-wide association studies provide a vast amount of genetic information that may be used to investigate secondary phenotypes. We study the situation in which the primary disease is rare and the secondary phenotype and genetic markers are dichotomous. An analysis of the association between a genetic marker and the secondary phenotype based on controls only (CO) is valid, whereas standard methods that also use cases result in biased estimates and highly inflated type I error if there is an interaction between the secondary phenotype and the genetic marker on the risk of the primary disease. Here we present an adaptively weighted (AW) method that combines the case and control data to study the association, while reducing to the CO analysis if there is strong evidence of an interaction. The possibility of such an interaction and the misleading results for standard methods, but not for the AW or CO approaches, are illustrated by data from a case-control study of colorectal adenoma. Simulations and asymptotic theory indicate that the AW method can reduce the mean square error for estimation with a prespecified SNP and increase the power to discover a new association in a genome-wide study, compared to CO analysis. Further experience with genome-wide studies is needed to determine when methods that assume no interaction gain precision and power, thereby can be recommended, and when methods such as the AW or CO approaches are needed to guard against the possibility of nonzero interactions.