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Collapsing multiple variants into one variable and testing their collective effect is a useful strategy for rare variant association analysis. Direct collapsing, however, is not valid or may significantly lose power when a group of variants to be collapsed have heterogeneous effects on target traits (i.e. some positive and some negative). This could be especially true for quantitative traits (such as blood pressure and body mass index), regardless of whether subjects are sampled randomly from a population or selectively from two extreme tails of the trait distribution. To deal with this problem, we propose a novel, data-driven method, the P-value Weighted Sum Test (PWST), which allows each variant to be individually weighted according to the evidence of association from the data itself. Specifically, both significance and direction of individual variant effects are used to calculate a single weighted sum score based on rescaled left-tail P-values from single-variant analysis, after which a permutation test of association is performed between the score and the trait. Our simulation under different sampling strategies shows that PWST significantly increases statistical power when there are heterogeneous variant effects. The appeal of the PWST approach is illustrated in an application to sequence data by detecting the collective effect of variants in the peroxisome proliferator-activated receptor alpha (PPARα) gene on triglycerides (TG) response to fenofibrate treatment from 300 subjects in the Genetics of Lipid Lowering and Diet Network study., (© 2011 Wiley Periodicals, Inc.)

Coronary artery calcification (CAC) is an important measure of subclinical coronary atherosclerosis and an independent predictor of coronary heart disease. To identify the genetic loci contributing to CAC, we conducted a genome-wide scan with 374 microsatellite markers by applying admixture mapping to 618 African American participants in the US National Heart, Lung, and Blood Institute Family Heart Study, in which 868 European American participants from family heart study and 157 Africans genotyped by the Marshfield Medical Genetics Center were used as the two reference founding populations for the African Americans, and a computer program based on a Markov Chain Monte Carlo algorithm, STRUCTURE 2.1, was used to estimate European and African ancestries among African Americans. A permutation test for random repeated sampling regression of CAC score on marker specific African ancestry found 22 markers statistically significant at the 0.05 level and four markers, D10S189 at 10p14, D20S159 at 20q13, D12S1294 at 12q14, and D6S1053 at 6q12, significant at the 0.01 level. D10S189 and D6S1053 were further confirmed at the 0.05 significance level by regression of CAC on allelic copy number, in which individual ancestry was used as a genetic background covariate to control possible stratification in African Americans. On the basis of the results from this and other independent studies, the location of D6S1053 at 80cM on chromosome 6 (6q12) seems to harbor a highly promising quantitative trait loci for atherosclerosis.

A general-purpose modeling framework for performing path and segregation analysis jointly, called SEGPATH (Province and Rao [1995] Stat. Med. 7:185-198), has been extended to cover "model-free" robust, variance-components linkage analysis, based on identity-by-descent (IBD) sharing. These extended models can be used to analyze linkage to a single marker or to perform multipoint linkage analysis, with a single phenotype or multivariate vector of phenotypes, in pedigrees. Within a single, consistent approach, SEGPATH models can perform segregation analysis, path analysis, linkage analysis, or combinations thereof. SEGPATH models can incorporate environmental or other measured covariate fixed effects (including measured genotypes), genotype-specific covariate effects, population heterogeneity models, repeated-measures models, longitudinal models, autoregressive models, developmental models, gene-by-environment interaction models, etc., with or without linkage components. The data analyzed can have any missing value structure (assumed missing at random), with entire individuals missing, or missing on one or more measurements. Corrections for ascertainment can be made on a vector of phenotypes and/or other measures. Because of the flexibility of the class of models, the SEGPATH approach can also be used in nongenetic applications where there is a hierarchical structure, such as longitudinal, repeated-measures, time series, or nested models. A variety of specific models are provided, as well as some comparisons with other linkage analysis models. Particular applications demonstrate the importance of correctly accounting for the extraneous sources of familial resemblance, as can be done easily with these SEGPATH models, so as to give added power to detect linkage as well as to protect against spuriously inferring linkage., (Copyright 2003 Wiley-Liss, Inc.)

The simulated data problem was designed via an interactive process by the Simulation Problem Organizing Committee and the selected data simulators. Based on discussions at the previous Genetic Analysis Workshop, many of the features of previous simulation problems, such as a complex disease, genome scan, and replication, were retained and in addition, a population genetics model was used to generate the simulated genes. We describe the process that was used to structure the problem and summarize the discussions about many of the scientific issues that were considered.

We discuss the Genetic Analysis Workshop 11 analyses of data from the Collaborative Study on the Genetics of Alcoholism from a methodological perspective, concentrating on approaches and issues relevant to linkage and association studies of complex human phenotypes. Genome screening by parametric linkage, nonparametric linkage, association, and combined linkage/association methods are discussed. Issues particular to complex disease include etiologic heterogeneity, multivariate phenotype modeling, and parent-of-origin effects. Other methodological topics discussed are new and enhanced methods, ascertainment, weighting of nonindependent sib pairs, and data cleaning and validation.

In cases where sibship data are collected for a quantitative trait locus (QTL) linkage study without access to parental genotypes, the proportion of genes shared identical by descent must be estimated using the marker allele frequencies. No systematic study has been conducted to date to evaluate the effect of misspecification of these frequencies on a test of quantitative trait linkage. Analysis of both simulated and actual data on quantitative traits was carried out under various sets of allele frequency estimates. While correctly specifying the allele frequency distribution led to a slightly more powerful test and higher lod scores, the differences were small and would not likely alter the conclusion of a study. These results suggest that, at least for QTL analysis, there is a great deal of tolerance for misspecifying marker allele frequencies with little, if any, appreciable effect on the linkage test. However, the observed variations may be sufficiently large to alter the priority on might give to a positive finding for follow up.

We investigated the power of the affected sibpair method for detecting a disease locus when the disease is inherited through two bi-allelic loci. The power was computed for all possible values of the gene frequencies and penetrances that lead to a given population prevalence and a given sibling relative risk. A method to generate rapidly all possible models that give a specific population prevalence and relative risk is provided. We applied it to the case of a two-locus disease with a prevalence of 10% and a low sibling relative risk of 1.5. For this particular example, regardless of the true underlying model, a sample size (N = 450 for alpha = 0.05, N = 1,500 for alpha = 0.0001) may be determined such that one would expect enough power (0.80) to detect at least one of the two disease genes. In addition to the general case, we examined a special class of models in which the marginal penetrances at each locus are either recessive or dominant. In this instance, the gene frequencies were excellent predictors of the power afforded by a particular sample size. These methods have been implemented in a C program called SIBPOWER which is freely available from the first author. With this program, investigators can perform their own power calculations for any two-locus model of their choice thus avoiding the need to use single-locus approximations that may grossly underestimate the necessary sample size.

An assumption-free algorithm has been applied to compute the probabilities of all possible identity-by-descent (IBD) configurations when the parents have not been genotyped. These probabilities can be used to determine the amount of information that a particular sibship will bring to a nonparametric linkage analysis. It is shown that the number of possible configurations can be extremely large even when the markers are closely spaced and are rather polymorphic. Further, it is not always possible to reduce this number to a manageable one simply by consideration of the relative probabilities of the configurations.

We compare the results of genomic scans conducted with the Haseman-Elston sib-pair method using either (1) the average marker information from several adjacent loci or (2) each marker individually. Under smoothing, the squared sib-pair trait difference is regressed on the average number of alleles shared identical by descent averaged at several adjacent loci. This results in a significant decrease in the number of false-positives when compared to the individual marker approach. Linkage of Q4 to MG4 was found only with smoothing but not the individual marker approach. Overall, smoothing resulted in the loss of two true linkages.

Fulker and Cardon's interval mapping extension of Haseman and Elston's sib-pair linkage method was used to map loci affecting the quantitative phenotypes presented as part of Problem 2, both adjusted and not adjusted for covariates: Q1 was adjusted for age and the environmental factor (EF); Q2 and Q3 for EF; and Q4 for age, sex, and EF. Adjusted Q2 and Q4 were also log-transformed. The effect of candidate locus C5 (D5G28) on Q1 was detected by a test of association--apparently, allele 1 of C5 is protective (leading to lower values of Q1), allele 2 has no effect, and allele 3 contributes to elevated levels of Q1. C5 accounted for 5.2% of the variation in Q1; it was included as an additional concomitant in the adjustment procedure. Analysis of the correlational structure among the variables revealed that Q4 was not associated with either affected status or Q1 after controlling for the effects of age, and we concluded that Q4 probably does not itself play a role in the etiology of the disease. Mapping studies using a significance level of 0.05 lead to the detection of all the genes, but also resulted in a high frequency of false positive results. On the other hand, using a 0.0005 significance level resulted in the detection of D2G10-11 for both Q1 and Q3, and D1G2 was detected for Q2. One false positive was detected using this significance level and the effects of D1G2 on Q1 and D5G22-23 on Q4 were missed. There was no systematic effect of adjustment for covariates on the detection of loci, although in general, analysis of adjusted phenotypes yielded substantially higher rates of false positives. Finally, this mapping approach correctly located D1G2 and D2G10-11 for Q1 using the nonadjusted phenotype, and D1G10-11 for Q3 using the adjusted phenotype. The maximum difference between the estimated map location from the true location was 1.5 cM. It would be important to estimate the error interval around these inferred locations in order to assess the utility of this method for fine mapping over small (e.g,. 2 cM) intervals.

A single 51-member kindred, ascertained on the basis of a normotriglyceridemic proband with depressed high-density lipoprotein cholesterol (HDL-C) and myocardial infarctions at ages 40 and 42, was studied with respect to quantitative variation in HDL-C and apolipoprotein (apo) AI and AII levels. The results of bivariate segregation analysis suggest that the etiology of depressed HDL-C involves one or possibly two major loci: one has a pleiotropic effect on apo AI and apo AII levels and, possibly another one that affects apo AI levels. Both the major loci were characterized as having a dominant allele leading to depression of the respective trait(s). In addition, analysis of the cosegregation of HDL-C and apo AI levels gave evidence of residual nonfamilial factors common to both traits, leading to a positive covariance between them. This could reflect the role of apo AI in the transformation of nascent HDL-C particles into mature ones via its cofactor activity to lecithin cholesterol acyltransferase. The proposed two-locus model represents one possible etiology for the heterogeneous disorder of hypoalphalipoproteinemia. This analysis of a single pedigree does not completely define the genetic mechanism, but it does illustrate a useful new analytic approach.