Properties of the transmission-disequilibrium test in the presence of inbreeding

Family-based association tests such as the transmission-disequilibrium test (TDT), which compare alleles transmitted and non-transmitted from parents to affected offspring, are widely used to detect the role of genetic risk factors in diseases. These methods have the advantage of being robust to population stratification and are thus believed to be valid whatever the population context. In different studies of the statistical properties of the TDT, parents of affected offspring are typically assumed to be neither inbred nor related. In many human populations, however, this assumption is false and parental alleles are then no longer independent. It is thus of interest to determine whether the TDT is a valid test of linkage and association in the presence of inbreeding. We present a method to derive the expected value of the TDT statistic under different disease models and for any relationship between the parents of affected offspring. Using this method, we show that in the presence of inbreeding, the TDT is still a valid test for linkage but not for association. The power of the test to detect linkage may, however, be increased in the presence of inbreeding under different modes of inheritance.