Jeff T. Williams

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. I. Likelihood Formulation and Simulation Results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.

12 Variance component methods for detecting complex trait loci

Variance component-based linkage analysis has become a major statistical tool for the localization and evaluation of quantitative trait loci influencing complex phenotypes. The variance component approach has many benefits--it can, for example, be used to analyze large pedigrees, and it is able to accommodate multiple loci simultaneously in a true oligogenic model. Important biological phenomena such as genotype-environment interaction and epistasis are also examined easily in a variance component framework. In this chapter, we review the basic statistical features of variance component linkage analysis, with an emphasis on its power and robustness to distributional violations.

Joint Multipoint Linkage Analysis of Multivariate Qualitative and Quantitative Traits. II. Alcoholism and Event-Related Potentials

The availability of robust quantitative biological markers that are correlated with qualitative psychiatric phenotypes can potentially improve the power of linkage methods to detect quantitative-trait loci influencing psychiatric disorders. We apply a variance-component method for joint multipoint linkage analysis of multivariate discrete and continuous traits to the extended pedigree data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate analysis of qualitative alcoholism phenotypes and quantitative event-related potentials. Joint consideration of the DSM-IV diagnosis of alcoholism and the amplitude of the P300 component of the Cz event-related potential significantly increases the evidence for linkage of these traits to a chromosome 4 region near the class I alcohol dehydrogenase locus ADH3. A likelihood-ratio test for complete pleiotropy is significant, suggesting that the same quantitative-trait locus influences both risk of alcoholism and the amplitude of the P300 component.

Robust LOD scores for variance component-based linkage analysis

The variance component method is now widely used for linkage analysis of quantitative traits. Although this approach offers many advantages, the importance of the underlying assumption of multivariate normality of the trait distribution within pedigrees has not been studied extensively. Simulation studies have shown that traits with leptokurtic distributions yield linkage test statistics that exhibit excessive Type I error when analyzed naively. We derive analytical formulae relating the deviation from the expected asymptotic distribution of the lod score to the kurtosis and total heritability of the quantitative trait. A simple correction constant yields a robust lod score for any deviation from normality and for any pedigree structure, and effectively eliminates the problem of inflated Type I error due to misspecification of the underlying probability model in variance component‐based linkage analysis. Genet. Epidemiol. 19(Suppl 1):S8–S14, 2000.

Power of variance component linkage analysis to detect quantitative trait loci

Expressions are derived for the sample size required to achieve a given power in variance component linkage analysis of a quantitative trait in unascertained samples. For simplicity an additive model, comprising effects due to a single QTL, residual additive genetic factors, and individual-specific random environmental variation, is considered. Equations are given relating sample size to trait heritability for sibpairs, sib trios, nuclear families having two and three sibs, and arbitrary relative pairs. The effects of nonzero residual additive genetic variance and parental information are discussed, and a scale relationship for sample sizes with sibships and nuclear families is derived. For larger sampling structures such as extended pedigrees the inheritance space is randomly sampled and the relevant equations are solved numerically. Comparative power curves are presented for sibships of size 2-4 and for an extended pedigree of 48 individuals. Simulation results for sibpairs confirm the validity of the theoretical results.

High heritability of malaria parasite clearance rate indicates a genetic basis for artemisinin resistance in western Cambodia

In western Cambodia, malaria parasites clear slowly from the blood after treatment with artemisinin derivatives, but it is unclear whether this results from parasite, host, or other factors specific to this population. We measured heritability of clearance rate by evaluating patients infected with identical or nonidentical parasite genotypes, using methods analogous to human twin studies. A substantial proportion (56%-58%) of the variation in clearance rate is explained by parasite genetics. This has 2 important implications: (1) selection with artemisinin derivatives will tend to drive resistance spread and (2) because heritability is high, the genes underlying parasite clearance rate may be identified by genome-wide association.

Human Pedigree-Based Quantitative-Trait–Locus Mapping: Localization of Two Genes Influencing HDL-Cholesterol Metabolism

Common disorders with genetic susceptibilities involve the action of multiple genes interacting with each other and with environmental factors, making it difficult to localize the specific genetic loci responsible. An important route to the disentangling of this complex inheritance is through the study of normal physiological variation in quantitative risk factors that may underlie liability to disease. We present an analysis of HDL-cholesterol (HDL-C), which is inversely correlated with risk of heart disease. A variety of HDL subphenotypes were analyzed, including HDL particle-size classes and the concentrations and proportions of esterified and unesterified HDL-C. Results of a complete genomic screen in large, randomly ascertained pedigrees implicated two loci, one on chromosome 8 and the other on chromosome 15, that influence a component of HDL-C-namely, unesterified HDL2a-C. Multivariate analyses of multiple HDL phenotypes and simultaneous multilocus analysis of the quantitative-trait loci identified permit further characterization of the genetic effects on HDL-C. These analyses suggest that the action of the chromosome 8 locus is specific to unesterified cholesterol levels, whereas the chromosome 15 locus appears to influence both HDL-C concentration and distribution of cholesterol among HDL particle sizes.

Novel family-based approaches to genetic risk in thrombosis

Summary.  The genetic basis of thrombosis is complex, involving multiple genes and environmental factors. The field of common complex disease genetics has progressed enormously over the past 10 years with the development of powerful new molecular and analytical strategies that enable localization and identification of the causative genetic variants. During the course of these advances, a major paradigmatic change has been taking place that focuses on the genetic analysis of measurable quantitative traits that are correlated with disease risk vs. the previous emphasis on the analysis of the much less informative dichotomous disease trait. Because of their closer proximity to direct gene action, disease‐related quantitative phenotypes represent our best chance to identify the underlying quantitative trait loci (QTLs) that influence disease susceptibility. This approach works best when data can be collected on extended families. Unfortunately, family‐based designs are still relatively rare in thrombosis/hemostasis studies. In this review, we detail the reasons why the field would benefit from a more vigorous pursuit of modern family‐based genetic studies.

Quantitative trait nucleotide analysis using Bayesian model selection

Although much attention has been given to statistical genetic methods for the initial localization and fine mapping of quantitative trait loci (QTLs), little methodological work has been done to date on the problem of statistically identifying the most likely functional polymorphisms using sequence data. In this paper we provide a general statistical genetic framework, called Bayesian quantitative trait nucleotide (BQTN) analysis, for assessing the likely functional status of genetic variants. The approach requires the initial enumeration of all genetic variants in a set of resequenced individuals. These polymorphisms are then typed in a large number of individuals (potentially in families), and marker variation is related to quantitative phenotypic variation using Bayesian model selection and averaging. For each sequence variant a posterior probability of effect is obtained and can be used to prioritize additional molecular functional experiments. An example of this quantitative nucleotide analysis is provided using the GAW12 simulated data. The results show that the BQTN method may be useful for choosing the most likely functional variants within a gene (or set of genes). We also include instructions on how to use our computer program, SOLAR, for association analysis and BQTN analysis.

Searching for genes underlying normal variation in human adiposity

Abstract. A primary challenge in biomedical research today is the elucidation of the underlying genetic architecture of complex conditions such as obesity. In contrast to simple Mendelian disorders that result from a mutation in a single gene, complex phenotypes are the product of the action (as well as interaction) of multiple genes and environmental factors. The genetic configuration of these genes can range from effectively polygenic (i.e., many genes each with a relatively small contribution) to oligogenic (i.e., a few genes with relatively large measurable effects often expressed on a residual additive genetic background). While the task at hand is complicated, it is not intractable; however, it does require consideration of the nature of the disease and definition of its associated phenotypes in selecting the most appropriate study design. Here we will discuss the characteristics of obesity and its related phenotypes, which must be considered in designing analyses to identify the genes involved as well as reviewing what these approaches have provided in the search for genes influencing adiposity in humans