Morris Nathan J, Elston Robert, Stein Catherine M
Case Western Reserve University, USA.
Stat Appl Genet Mol Biol. 2009;8(1):Article 39. doi: 10.2202/1544-6115.1456. Epub 2009 Sep 17.
The asymptotic distribution of the multivariate variance component linkage analysis likelihood ratio test has provoked some contradictory accounts in the literature. In this paper we confirm that some previous results are not correct by deriving the asymptotic distribution in one special case. It is shown that this special case is a good approximation to the distribution in many situations. We also introduce a new approach to simulating from the asymptotic distribution of the likelihood ratio test statistic in constrained testing problems. It is shown that this method is very efficient for small p-values, and is applicable even when the constraints are not convex. The method is related to a multivariate integration problem. We illustrate how the approach can be applied to multivariate linkage analysis in a simulation study. Some more philosophical issues relating to one-sided tests in variance components linkage analysis are discussed.
多变量方差分量连锁分析似然比检验的渐近分布在文献中引发了一些相互矛盾的说法。在本文中，我们通过推导一种特殊情况下的渐近分布，证实了之前的一些结果是不正确的。结果表明，这种特殊情况在许多情况下是对分布的良好近似。我们还引入了一种新方法，用于在约束检验问题中从似然比检验统计量的渐近分布进行模拟。结果表明，该方法对于小p值非常有效，并且即使在约束不凸的情况下也适用。该方法与一个多变量积分问题相关。我们在模拟研究中说明了该方法如何应用于多变量连锁分析。还讨论了与方差分量连锁分析中的单侧检验相关的一些更具哲学性的问题。
