The power of linkage analysis of a disease-related endophenotype using asymmetrically ascertained sib pairs

A linkage study of a qualitative disease endophenotype in a sample of sib pairs, consisting of one disease affected proband and one sibling is considered. The linkage statistic compares marker allele sharing with the proband in siblings with an abnormal endophenotype to siblings with the normal endophenotype. Expressions for the distribution of this linkage statistic, in terms of the recombination fraction are derived and (1) the genetic parameter values (allele frequency and endophenotype and disease penetrance) and (2) the abnormal endophenotype rates in the population and in classes of relatives of disease affected probands. It is then shown that when either the disease or the abnormal endophenotype has additive penetrance, the expressions simplify to a monotonic function of the difference between abnormal endophenotype rates in siblings and in the population. Thought disorder is considered as a putative schizophrenia endophenotype. Forty sets of genetic parameter values that correspond to the known prevalence values for thought disorder in schizophrenic patients, siblings of schizophrenics and the general population are evaluated. For these genetic parameter values, numerical results show that the test statistic has>70% power (α = 0.0001) in general with a sample of 200 or more proband-sibling pairs to detect the linkage between a marker (θ = 0.01), and a locus pleiotropic for schizophrenia and thought disorder.