An analytical study is conducted of the properties of statistical tests to detect linkage between a disease locus and a very polymorphic marker locus when data on sib pairs are available. In most instances the most powerful test is the test based on the mean number of marker alleles shared identical by descent by the two members of a sib pair, and the most efficient sampling strategy is almost always to sample only pairs with both sibs affected. We show it is valid to use the information from all possible sib pairs as though they came from separate families when data on sibships of size three or larger are available, though more power may be obtained if different weights are given to the different sibship sizes.
A statistical model that uses an iterative maximum likelihood estimation procedure is proposed for measuring and testing the association between polymorphic genetic markers and quantitative traits in human pedigrees, after adjusting for covariates such as age and sex. The model allows the quantitative trait to have a familial correlation structure among the individuals in the sample and to follow one of a broad class of skewed or kurtotic underlying distributions. The use of the model is illustrated, and the results are compared to those using models that assume normality without any transformation and do not incorporate familial correlations.
A more powerful robust test for linkage is developed from the methodology of Haseman and Elston [Behav Genet 2(1):3-19, 1972]. This new robust test uses weighted least-squares (WLS) methods to detect linkage between a quantitative trait and a polymorphic marker. For comparison, the characteristics of a test for linakge that uses known trait genotypes for the parents are also studied. Sample sizes needed to detect linkage, calculated using asymptotic results, are compared for 1) the usual Haseman-Elston method, 2) the WLS method, and 3) the method that uses parental trait genotype data. The WLS method needs at most twice the number of sib pairs as does the method that uses information on the trait genotypes of the parents. The small sample properties of the Haseman-Elston (H-E) and WLS tests are investigated by simulation. The power calculations for the H-E method are found to be accurate. The power of the WLS method is overestimated when fewer than 300 sib pairs are studied, but the WLS method is nonetheless more powerful than the usual H-E method. In samples of fewer than 300 sib pairs, the WLS test tends to be anticonservative. Treating all sib pairs from sibships of size 3 or 5 as independent does not increase the significance of the tests.
The robust method for detecting linkage developed by Haseman and Elston [The investigation of linkage between a quantitative trait and a marker locus. Behav Genet 2:3-19, 1972] for data from sib pairs is extended to any type of noninbred relative pair. The regression of the squared relative-pair trait difference on the estimated proportion of genes identical by descent (i.b.d.) at a marker locus is shown to depend upon the recombination fraction between the two loci; the regression coefficient is negative if the trait and marker loci are linked. A test for linkage based on data from any informative type of relative pair can thus be obtained by testing that this regression coefficient is less than zero. Formulae for the asymptotic power of such tests for linkage based upon independent relative pairs are developed. Results are also given for the special case in which the proportion of genes shared i.b.d. for relative pairs is known. Finally, a general algorithm is described that will incorporate all available pedigree data to calculate an estimate of the proportion of genes that a relative pair shares i.b.d. at a marker locus.
Serum dopamine-beta-hydroxylase (DBH) levels and 30 polymorphic markers were determined on 178 individuals of the HGAR 29 family, ascertained through six probands who had clinical and electrocardiographic evidence of myocardial infarction. Individuals in this pedigree with a history of heart attack had significantly lower levels of DBH, but this difference was partly confounded with age differences. Pedigree segregation analysis showed evidence of a codominant gene for DBH segregating in the family. Linkage analysis between the putative DBH locus and 30 polymorphic marker loci, assuming a codominant model, yielded a largest lod score of 0.53, with ABO at 20% recombination. Adding this to the lod scores obtained by Elston et al [1979] and Goldin et al [1982], we obtain combined lod scores of 2.49 and 2.50 at 0.0 and 10% recombination respectively.
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