A permutation test for the robust sib-pair linkage method

The robust sib-pair method introduced by Haseman & Elston (1972) is one of the most widely circulated allele-sharing methods for linkage analysis. The procedure evaluates linkage by significance testing of a regression coefficient and, hence, a standard t-test has traditionally been applied despite known violations of the statistical assumptions underlying the test. We present a permutation based reference distribution for the estimate of the regression coefficient that is motivated by genetic principles rather than by standard regression testing procedures. The permutation test approximates Mendelian co-segregation under the null hypothesis of no linkage, making it a very natural approach. Theory and simulations show that the conventional t-test approximates the permutation test quite well, even when dependent sib pairs are used for analysis. These results thus indirectly address concerns over the t-test. To illustrate the permutation test using real data we applied the procedure to two lipoprotein systems that have been well characterized.