Estimation of Pairwise Relationships in the Presence of Genotyping Errors

Abstract

To the Editor: Boehnke and Cox (Boehnke and Cox, 1997Boehnke M Cox NJ Accurate inference of relationships in sib-pair linkage studies.Am J Hum Genet. 1997; 61: 423-429Abstract Full Text PDF PubMed Scopus (238) Google Scholar) described a likelihood method for the inference of pairwise relationships from data for a genome scan. This tool is useful for verification of the relationships in a linkage study, to identify pedigree errors, which, if undetected, could reduce the power to detect genes. While they showed that the method is robust for genotyping errors when the relationships full sibs, half sibs, and unrelated are inferred, a single genotyping error will lead to zero likelihood for the relationships MZ twins and parent/offspring. A simple modification of the method eliminates this problem and thus allows the accurate inference of the relationships MZ twins and parent/offspring, even in the presence of genotyping errors. The crucial calculation in the method of Boehnke and Cox (Boehnke and Cox, 1997Boehnke M Cox NJ Accurate inference of relationships in sib-pair linkage studies.Am J Hum Genet. 1997; 61: 423-429Abstract Full Text PDF PubMed Scopus (238) Google Scholar), with regard to genotyping errors, is P(Xk|Ik=i), the probability that two individuals have genotypes Xk=(Xk1, Xk2) at locus k, given that they share i alleles identical by descent at the locus. To simplify the notation, let Pi(x)=P(Xk=x|Ik=i). When two individuals share no alleles identical by state at a locus, P1(x)=p2(x)=0, which results in a zero likelihood for relationships such as MZ twins and parent/offspring. If we allow Pi(x)>0 for all possible x, this problem is eliminated. In the calculation of the likelihood for a putative relationship, we propose to replace the values for pi(x) used by Boehnke and Cox (Boehnke and Cox, 1997Boehnke M Cox NJ Accurate inference of relationships in sib-pair linkage studies.Am J Hum Genet. 1997; 61: 423-429Abstract Full Text PDF PubMed Scopus (238) Google Scholar) with the following: p0*(x)=p0(x) ,p1*(x)=(1-ɛ)p1(x)+ɛp0(x) ,p2*(x)=(1-ɛ)p2(x)+ɛp0(x) , where ε denotes twice the approximate genotyping error rate. To test this idea, we performed a computer simulation. By use of the 366 autosomal markers in Weber screening set version 9 (Yuan et al. Yuan et al., 1997Yuan B Vaske D Weber JL Beck J Sheffied VC Improved set of short-tandem-repeat polymorphisms for screening the human genome.Am J Hum Genet. 1997; 60: 459-460PubMed Google Scholar), 10,000 relative pairs were simulated for each of five relationships: MZ twins, parent/offspring, full sibs, half sibs, and unrelated. The sex-averaged map locations were taken from the study by Broman et al. (Broman et al., 1998Broman KW Murray JC Sheffield VC White RL Weber JL Comprehensive human genetic maps: individual and sex-specific variation in recombination.Am J Hum Genet. 1998; 63: 861-869Abstract Full Text Full Text PDF PubMed Scopus (892) Google Scholar); allele frequencies were estimated by use of eight of the CEPH families. The intermarker spacings were 9.4±3.6 cM; the marker heterozygosities were .78±.06. Genotypes were simulated by use of an error rate of 2%. For each relative pair, the likelihood for the five relationships were calculated by use of ɛ=.02, .04, and .08. For the values of ε considered, all five relationships were classified correctly in all 10,000 replicates. Thus, our proposal is successful in extending Boehnke and Cox's (Boehnke and Cox, 1997Boehnke M Cox NJ Accurate inference of relationships in sib-pair linkage studies.Am J Hum Genet. 1997; 61: 423-429Abstract Full Text PDF PubMed Scopus (238) Google Scholar) method to the inference of MZ twins and parent/offspring pairs, in the presence of genotyping errors.