A hybrid design: case-parent triads supplemented by control-mother dyads.

Hybrid designs arose from an effort to combine the benefits of family-based and population-based study designs. A recently proposed hybrid approach augments case-parent triads with population-based control-parent triads, genotyping everyone except the control offspring. Including parents of controls substantially improves statistical efficiency for testing and estimating both offspring and maternal genetic relative risk parameters relative to using case-parent triads alone. Moreover, it allows testing of required assumptions. Nevertheless, control fathers can be hard to recruit, whereas control offspring and their mothers may be readily available. Consequently, we propose an alternative hybrid design where offspring-mother pairs, instead of parents, serve as population-based controls. We compare the power of our proposed method with several competitors and show that it performs well in various scenarios, though it is slightly less powerful than the hybrid design that uses control parents. We describe approaches for checking whether population stratification will bias inferences that use controls and whether the mating-symmetry assumption holds. Surprisingly, if mating symmetry is violated, even though mating-type parameters cannot be directly estimated using control-mother dyads alone, and maternal effects cannot be estimated using case-parent triads alone, combining both sources of data allows estimation of all the parameters. This hybrid design can also be used to study environmental influences on disease risk and gene-by-environment interactions.