Relative Efficiency of Haplotype Frequency Estimation in Sibships and Nuclear Families Compared to Unrelated Individuals

Abstract

The problem of estimating haplotype frequencies from unphased single nucleotide polymorphism (SNP) genotype data in sibships with and without parents is considered. We focus on the Fisher information of the haplotype frequencies of the parents in order to correctly deal with the dependence of haplotypes within sibships. We compare these Fisher information matrices with those obtained for unrelated individuals and study the relative efficiency of sibships with and without parents compared to unrelated individuals in estimating haplotype frequencies. Crudely summarizing, the second sib contributes half the information of the first, except for rare haplotypes, when the second sib counts almost as one. We argue that the relative efficiencies can also be used to correct for dependence in the calculation of standard errors after initially ignoring the dependence in the estimation phase.