Score test for mapping quantitative-trait loci with sibships of arbitrary size when the dominance effect is not negligible

Robust score statistics for QTL linkage analysis

The traditional variance components approach for quantitative trait locus (QTL) linkage analysis is sensitive to violations of normality and fails for selected sampling schemes. Recently, a number of new methods have been developed for QTL mapping in humans. Most of the new methods are based on score statistics or regression-based statistics and are expected to be relatively robust to non-normality of the trait distribution and also to selected sampling, at least in terms of type I error. Whereas the theoretical development of these statistics is more or less complete, some practical issues concerning their implementation still need to be addressed. Here we study some of these issues such as the choice of denominator variance estimates, weighting of pedigrees, effect of parameter misspecification, effect of non-normality of the trait distribution, and effect of incorporating dominance. We present a comprehensive discussion of the theoretical properties of various denominator variance estimates and of the weighting issue and then perform simulation studies for nuclear families to compare the methods in terms of power and robustness. Based on our analytical and simulation results, we provide general guidelines regarding the choice of appropriate QTL mapping statistics in practical situations.

A unified framework for linkage and association analysis of quantitative traits

We give a unified treatment of the statistical foundations of population based association mapping and of family based linkage mapping of quantitative traits in humans. A central ingredient in the unification involves the efficient score statistic. The discussion focuses on generalized linear models with an additional illustration of the Cox (proportional hazards) model for age of onset data. We give analytic expressions for noncentrality parameters and show how they give qualitative insight into the loss of power that occurs if the scientist's assumed genetic model differs from nature's "true" genetic model. Issues to be studied in detail in the future development of this approach are discussed.

Widespread Evidence for Non-Additive Genetic Variation in Cloninger’s and Eysenck’s Personality Dimensions using a Twin Plus Sibling Design

Studies using the classical twin design often conclude that most genetic variation underlying personality is additive in nature. However, studies analyzing only twins are very limited in their ability to detect non-additive genetic variation and are unable to detect sources of variation unique to twins, which can mask non-additive genetic variation. The current study assessed 9672 MZ and DZ twin individuals and 3241 of their siblings to investigate the environmental and genetic architecture underlying eight dimensions of personality: four from Eysenck's Personality Questionnaire and four from Cloninger's Temperament and Character Inventory. Broad-sense heritability estimates from best-fitting models were two to three times greater than the narrow-sense heritability estimates for Harm Avoidance, Novelty Seeking, Reward Dependence, Persistence, Extraversion, and Neuroticism. This genetic non-additivity could be due to dominance, additive-by-additive epistasis, or to additive genetic effects combined with higher-order epistasis. Environmental effects unique to twins were detected for both Lie and Psychoticism but accounted for little overall variation. Our results illustrate the increased sensitivity afforded by extending the classical twin design to include siblings, and may provide clues to the evolutionary origins of genetic variation underlying personality.

Power and robustness of linkage tests for quantitative traits in general pedigrees

There are numerous statistical methods for quantitative trait linkage analysis in human studies. An ideal such method would have high power to detect genetic loci contributing to the trait, would be robust to non-normality in the phenotype distribution, would be appropriate for general pedigrees, would allow the incorporation of environmental covariates, and would be appropriate in the presence of selective sampling. We recently described a general framework for quantitative trait linkage analysis, based on generalized estimating equations, for which many current methods are special cases. This procedure is appropriate for general pedigrees and easily accommodates environmental covariates. In this report, we use computer simulations to investigate the power and robustness of a variety of linkage test statistics built upon our general framework. We also propose two novel test statistics that take account of higher moments of the phenotype distribution, in order to accommodate non-normality. These new linkage tests are shown to have high power and to be robust to non-normality. While we have not yet examined the performance of our procedures in the context of selective sampling via computer simulations, the proposed tests satisfy all of the other qualities of an ideal quantitative trait linkage analysis method.

Mapping quantitative trait loci using multiple phenotypes in general pedigrees

The use of correlated phenotypes may dramatically increase the power to detect the underlying quantitative trait loci (QTLs). Current approaches for multiple phenotypes include regression-based methods, the multivariate variance of components method, factor analysis and structural equations. Issues with these methods include: 1) They are computation intensive and are subject to problems of optimization algorithms; 2) Existing claims on the asymptotic distribution of the likelihood ratio statistic for the multivariate variance of components method are contradictory and erroneous; 3) The dimension reduction of the parameter space under the null hypothesis, a phenomenon that is unique to multivariate analyses, makes the asymptotic distribution of the likelihood ratio statistic more complicated than expected. In this article, three cases of varying complexity are considered. For each case, the efficient score statistic, which is asympotically equivalent to the likelihood ratio statistic, is derived, so is its asymptotic distribution [correction]. These methods are straightforward to calculate. Finite-sample properties of these score statistics are studied through extensive simulations. These score statistics are for use with general pedigrees.

Score test for detecting linkage to complex traits in selected samples

We present a unified approach to selection and linkage analysis of selected samples, for both quantitative and dichotomous complex traits. It is based on the score test for the variance attributable to the trait locus and applies to general pedigrees. The method is equivalent to regressing excess IBD sharing on a function of the traits. It is shown that when population parameters for the trait are known, such inversion does not entail any loss of information. For dichotomous traits, pairs of pedigree members of different phenotypic nature (e.g., affected sib pairs and discordant sib pairs) can easily be combined as well as populations with different trait prevalences.

Score tests for epistasis models on quantitative traits using general pedigree data

Efficient score tests for a two-locus model for quantitative traits are proposed for general pedigrees. Two search strategies, simultaneous search and conditional search, are considered. These tests are attractive alternatives to the likelihood ratio test for their asymptotic equivalency to their respective likelihood ratio tests and efficiency in computation. The finite-sample properties of these tests are investigated through simulations. Extensions to more complicated models and to other search strategies are discussed.

Recent advances in human quantitative-trait-locus mapping: comparison of methods for selected sibling pairs

During the past few years, there has been a great deal of new work on methods for mapping quantitative-trait loci by use of sibling pairs and sibships. There are several new methods based on linear regression, as well as several more that are based on score statistics. In theory, most of the new methods should be relatively robust to violations of distributional assumptions and to selected sampling, but, in practice, there has been little evaluation of how the methods perform on selected samples. We survey most of the new regression-based statistics and score statistics and propose a few minor variations on the score statistics. We use simulation to evaluate the type I error and the power of all of the statistics, considering (a) population samples of sibling pairs and (b) sibling pairs ascertained on the basis of at least one sibling with a trait value in the top 10% of the distribution. Most of the statistics have correct type I error for selected samples. The statistics proposed by Xu et al. and by Sham and Purcell are generally the most powerful, along with one of our score statistic variants. Even among the methods that are most powerful for "nice" data, some are more robust than others to non-Gaussian trait models and/or misspecified trait parameters.