Consider a sample of unrelated individuals, phenotyped for a normally distributed trait, and typed for rare variants in a gene or small genomic region. Let ni denote the number of rare variants for which the ith individual has been successfully genotyped, and let ri denote the number of these variants at which they carry at least one copy of the minor allele. We can model the phenotype, yi, of the ith individual in a linear regression framework, given by yi = E[yi]+ɛi, where ɛi,σE), and
