Genetic association studies can be dichotomized into those that have population-based designs and those that have family-based designs. Population-based studies test for association between a phenotype and a genotype in a sample of unrelated individuals. These studies are susceptible to population stratification, i.e., systematic differences in allele frequencies between subpopulations in a population not due to a causal association with the phenotype of interest. Family-based studies test for association between a phenotype and a genotype in a sample of related individuals by assessing whether individuals with a given phenotype have a higher transmission ratio than would be expected by chance given their parents' (or other family members') genotypes and Mendel's laws. It is this ability to compare a person's genotype to his expected genotype based on Mendel's laws that makes family-based tests robust to population stratification. Family-based studies can also assess the evidence of association by examining allele frequencies across families in a somewhat similar fashion to what is done in population-based studies (although this evidence is not inherently robust to population stratification).
The use of the two independent sources of information available in family data is what makes the family-based association test (FBAT) screening method proposed by Steen et al. (2005)
so powerful. If we let x denote the offspring genotypes, y denote the offspring phenotypes, and P denote the parents' genotypes, the following relationship holds:
(x|y, P) represents the information used in the FBAT statistic; that is, the FBAT statistic conditions on the offspring phenotypes, y, and parents' genotypes, P, and only the offspring genotypes, x, are considered random variables. P
(y, P) represents the information used in Steen et al. (2005)
's screening approach, which first determines which SNPs will have the highest power to be detected if a true association exists in the given study and then applies FBAT only to those SNPs. In determining which SNPs have the highest power, only the offspring phenotypes, y, and parental genotypes, P are used. By applying the FBAT to only the SNPs in which a true association would most likely be detectable, the number of comparisons that must be adjusted for is reduced. The statistical validity of the screening method is due to the relationship in the formula above.
We propose a novel approach for family-based genetic association studies that also capitalizes on this relationship. However, instead of using one portion of the family data (i.e., x|y, P) to create a statistical test and the other independent portion (i.e., y, P) to screen SNPs, we take a Bayesian approach: we use one portion to calculate a Bayes factor and the other to calculate the prior odds of the null hypothesis. Our method capitalizes on both the between and within family information in a more intuitive and flexible manner than frequentist approaches. We construct a Bayes factor conditional on parental genotypes and offspring phenotypes and then use the information conditioned on to inform the prior odds of association for each marker. In this way we are able to combine evidence from the over-transmission of alleles within families with evidence based on the allele frequencies across the families into a posterior odds of no association.