Abstract
Variance component analysis provides an efficient method for performing linkage analysis for quantitative traits. However, type I error of variance components-based likelihood ratio testing may be affected when phenotypic data are non-normally distributed (especially with high values of kurtosis). This results in inflated LOD scores when the normality assumption does not hold. Even though different solutions have been proposed to deal with this problem with univariate phenotypes, little work has been done in the multivariate case. We present an empirical approach to adjust the inflated LOD scores obtained from a bivariate phenotype that violates the assumption of normality.Using the Collaborative Study on the Genetics of Alcoholism data available for the Genetic Analysis Workshop 14, we show how bivariate linkage analysis with leptokurtotic traits gives an inflated type I error. We perform a novel correction that achieves acceptable levels of type I error.
Highlights
Variance component methods are very well suited to normally distributed phenotypes
In this work we investigate four questions: First, can we find a robust LOD score approximately proportional to the LOD score under model misspecification with the bivariate phenotype? Second, will the proportionality be between the two degrees of freedom (2-df) LOD scores or between the equivalent one degree of freedom (1-df) LOD scores? Third, what is the lower boundary of the number of replicates required to achieve a good approximation of the slope? Lastly, which smoothing constant is most appropriate for use with the phenotypes of the Collaborative Study on the Genetics of Alcoholism (COGA) data?
The plots in the first column are derived from the 2-df LOD scores; those in the second column are derived from the 1-df LOD scores
Summary
Variance component methods are very well suited to normally distributed phenotypes. When the phenotype under study is not normal, these methods tend to increase the type I error [1]. A robust LOD score correction has been developed to solve this problem for univariate phenotypes [2,3]. This approach takes advantage of a remarkable result: the distribution of the likelihood ratio statistic under model misspecification is equal to a constant times a χ12 variate [4]. A robust alternative to the likelihood ratio statistic is: ΛR = kΛ and the analogous robust LOD score is: LODR = kLOD. The problem simplifies to the search for the constant of proportionality k
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