A score test for linkage using identity by descent data from sibships

• 成果类型: Article
• 署名作者: Dudoit, S; Speed, TP
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 943-986
• 关键词: sib-pair linkage; disease susceptibility genes; genetically complex traits; affected relative pairs; quantitative trait; nuclear families; loci; strategies; models; probability

摘要

We consider score tests of the null hypothesis H-0: theta = 1/2 against the alternative hypothesis H-1: 0 less than or equal to theta < 1/2, based upon counts multinomially distributed with parameters n and rho(theta, pi)(1xm) = pi(1xm)T(theta)(mxm), where T(theta) is a transition matrix with T(0) = I, the identity matrix, and T(1/2) = (1,..., 1)(T)(alpha(1),...,alpha(m)). This type of testing problem arises in human genetics when testing the null hypothesis of no linkage between a marker and a disease susceptibility gene, using identity by descent data from families with affected members. In important cases in this genetic context, the score test is independent of the nuisance parameter pi and based on a widely used test statistic in linkage analysis. The proof of this result involves embedding the states of the multinomial distribution into a continuous-time Markov chain with infinitesimal generator Q. The second largest eigenvalue of Q and its multiplicity are key in determining the form of the score statistic. We relate Q to the adjacency matrix of a quotient graph in order to derive its eigenvalues and eigenvectors.