• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.1-17
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• 2008

The ordinary least squares regression method of Haseman and Elston(1972) is most widely used in genetic linkage studies for continuous traits of sib pairs. Kruglyak and Lander(1995) suggested a statistic which appears to be a nonparametric counterpart to the Haseman and Elston(1972)'s regression method, but in fact these two methods are quite different. In this paper the relationships between these two methods are described and will be compared by simulation studies. One of the characteristics of the sib-pair linkage study is that the explanatory variable has only three different values and thus dependent variable is heavily replicated in each value of the explanatory variable. We propose a weighted least squares regression method which is more appropriate to this situation and the efficiency of the weighted regression in genetic linkage study was explored with normal and non-normal simulated continuous traits data. Simulation studies demonstrated that the weighted regression is more powerful than other tests.

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.19-33
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• 2008

Linear regression method, proposed by Haseman and Elston(1972), for detecting linkage to a quantitative trait of sib pairs is a linkage testing method for a single locus and a single trait. However, multivariate methods for detecting linkage are needed, when information from each of several traits that are affected by the same major gene are available on each individual. Amos et al. (1990) extended the regression method of Haseman and Elston(1972) to incorporate observations of two or more traits by estimating the principal component linear function that results in the strongest correlation between the squared pair differences in the trait measurements and identity by descent at a marker locus. But, it is impossible to control the probability of type I errors with this method at present, since the exact distribution of the statistic that they use is yet unknown. In this paper, we propose a multivariate nonparametric trend test for detecting linkage to multiple traits. We compared with a simulation study the efficiencies of multivariate nonparametric trend test with those of the method developed by Amos et al. (1990) for quantitative traits data. For multivariate nonparametric trend test, the results of the simulation study reveal that the Type I error rates are close to the predetermined significance levels, and have in general high powers.