where Vd = (v1, v2, ..., v2n - 1, v2n) is the inheritance vector [5] of a sibship at locus d, v2j - 1 = 1 or 2, and v2j = 3 or 4 to indicate the origins of the inherited alleles for j = 1, 2, ..., n. Ud1 and Ud2 represent the genetic frailties due to part of the genome on the two chromosomes of the father at locus d. Ud3 and Ud4 represent the same, though for the mother. The random frailty term, Up, takes into account possible genetic contributions to shared familial effects. Gamma distributions were used to model the frailties and retrospective likelihood ratio tests were constructed for linkage analysis [3]. After linkage evidence is established by the linkage analysis [3], we used an association test in the presence of linkage as proposed by Zhong and Li [4] that examines the putative association between the disease and the testing allele at a candidate chromosomal locus in the linked region. Because we use age-at-onset as the outcome, the association test is based on the proportional hazards model.
