Global tests for linkage

Abstract

To test for global linkage along a genome or in a chromosomal region, the maximum over the marker locations of mean alleles shared identical by descent of affected relative pairs, Z(max), can be used. Feingold et al. (1993) derived a Gaussian approximation to the distribution of the Z(max). As an alternative we propose to sum over the observed marker locations along the chromosomal region of interest. Two test statistics can be derived. (1) The likelihood ratio statistic (LR) and (2) the corresponding score statistic. The score statistic appears to be the average mean IBD over all available marker locations. The null distribution of the LR and score tests are asymptotically a 50: 50 mixture of chi-square distributions of null and one degree of freedom and a normal distribution, respectively.We compared empirically the type I error and power of these two new test statistics and Z(max) along a chromosome and in a candidate region. Two models were considered, namely (1) one disease locus and (2) two disease loci. The new test statistics appeared to have reasonable type I error. Along the chromosome, for both models we concluded that for very small effect sizes, the score test has slightly more power than the other test statistics. For large effect sizes, the likelihood ratio statistic was comparable to and sometimes performed better than Z(max) and both test statistics performed much better than the score test. For candidate regions of about 30 cM, all test statistics were comparable when only one disease-locus existed and the score and likelihood ratio statistics had somewhat better power than Z(max) when two disease loci existed.