A note on a conditional-likelihood approach for family-based association studies of candidate genes

The family-based association study design is a variation of the case-control study design, where unaffected family members instead of unrelated subjects are sampled as controls. This variation is useful in assessing the effects of candidate genes on disease, because it avoids false associations caused by admixture of populations. A complication of this design is that because of an inherited genotypic correlation among family members, the genotypic distributions between cases and relative controls may be distorted by the ascertainment criteria of families, which could involve not only cases and relative controls, but also other relatives. Analyzing such data naively may lead to biased estimates of relative risk. In this note, we will discuss the consistency of a conditional-likelihood approach. We show analytically that maximum conditional-likelihood estimators are consistent for the true relative risks, if genotypes for family members are exchangeable under the sampling process, for example, sibling clusters. Besides being straightforward conceptually and computationally, this approach is robust to ascertainment bias and naturally accommodates genetic heterogeneity across families.