Affected sib pair tests in inbred populations

The affected-sib-pair (ASP) method for detecting linkage between a disease locus and marker loci was first established 50 years ago, and since then numerous modifications have been made. We modify two identity-by-state (IBS) test statistics of Lange (Lange, 1986a, 1986b) to allow for inbreeding in the population. We evaluate the power and false positive rates of the modified tests under three disease models, using simulated data. Before estimating false positive rates, we demonstrate that IBS tests are tests of both linkage and linkage disequilibrium between marker and disease loci. Therefore, the null hypothesis of IBS tests should be no linkage and no LD. When the population inbreeding coefficient is large, the false positive rates of Lange's tests become much larger than the nominal value, while those of our modified tests remain close to the nominal value. To estimate power with a controlled false positive rate, we choose the cutoff values based on simulated datasets under the null hypothesis, so that both Lange's tests and the modified tests generate same false positive rate. The powers of Lange's z-test and our modified z-test are very close and do not change much with increasing inbreeding. The power of the modified chi-square test also stays stable when the inbreeding coefficient increases. However, the power of Lange's chi-square test increases with increasing inbreeding, and is larger than that of our modified chi-square test for large inbreeding coefficients. The power is high under a recessive disease model for both Lange's tests and the modified tests, though the power is low for additive and dominant disease models. Allowing for inbreeding is therefore appropriate, at least for diseases known to be recessive.