Asymptotic bias and efficiency in case-control studies of candidate genes and gene-environment interactions: basic family designs.

Case-control designs that use population controls are compared with those that use controls selected from their relatives (i.e., siblings, cousins, or "pseudosibs" based on parental alleles) for estimating the effect of candidate genes and gene-environment interactions. The authors first evaluate the asymptotic bias in relative risk estimates resulting from using population controls when there is confounding due to population stratification. Using siblings or pseudosibs as controls completely addresses this issue, whereas cousins provide only partial protection from population stratification. Next, they show that the conventional conditional likelihood for matched case-control studies can give asymptotically biased effect estimates when applied to the pseudosib approach; the asymptotic bias is toward the null and disappears with disease rarity. They show how to reparameterize the pseudosib likelihood so this approach gives consistent effect estimates. They then show that the designs using population or pseudosib controls are generally the most efficient for estimating the main effect of a candidate gene, followed in efficiency by the design using cousins. Finally, they show that the design using sibling controls can be quite efficient when studying gene-environment interactions. In addition to asymptotic bias and efficiency issues, family-based designs might benefit from a higher motivation to participate among cases' relatives, but these designs have the disadvantage that many potential cases will be excluded from study by having no available controls.