Statistical studies on genetic linkage analysis based on affected sibships

The sib-pair approach is widely used in studies to determine whether there is genetic linkage between a disease susceptibility locus and a marker locus. Sib-pairs from different families are categorized according to whether they share 0, 1 or 2 alleles identical by descent (IBD). Several robust tests were established in literature based on the proportions of the sib-pairs in these three categories. However, in all these tests, sib-pairs are assumed to be independent and noninbred. We examine how family relatedness and inbreeding affect the statistical properties of these tests.; It is possible that some sib-pairs in the population are related. We show that despite this relatedness, the null distribution of the commonly used test statistics remains the same. Hence, the type I error will not be affected. The power of the tests, however, is affected due to the change of the distribution in the presence of linkage.; When there exist sib-pairs from consanguineous (relatives) mating, the IBD sharing probabilities of the three categories deviate from the values 1/4, 1/2 and 1/4 in the case of random mating. We obtain the distributions of IBD sharing of affected sib-pairs under the null (no linkage between the marker and disease loci) and the alternative of linkage.; The effect of inbreeding on the IBD configurations of sib-triples is also investigated. In this situation, one more possible configuration is observed than in the case of no inbreeding. The null probabilities of all five configurations are obtained for common types of consanguineous matings in human populations. The posterior probability of inbreeding is estimated based on samples and prior surveys of inbreeding. A contamination model is proposed to incorporate inbreeding and an efficient score test is obtained.