Genome-wide linkage analysis in a general population sample using sigma 2A random effects (SSARs) fitted by Gibbs sampling

We used variance components analysis to investigate the underlying determinants of the quantitative phenotypes (Q1-Q5) and their interrelationships in replicate 42 of the Genetic Analysis Workshop 12 simulated general population. Variance components models were fitted using Gibbs sampling in WinBUGS v1.3. Sigma-squared-A-random-effects (SSARs) were estimated for each phenotype, and were used as derived phenotypes in subsequent linkage analyses. Whole-genome, multipoint linkage analyses were based upon a new Haseman-Elston identity-by descent sib-pair method that takes a weighted combination of the trait-sum and trait-difference. The five quantitative traits simulated were closely correlated with each other and with affection status. The whole-genome screen of quantitative traits associated with the simulated complex disease suggested that one or more major loci regulating Q1 localizes to chromosome 2p and that one or more major loci regulating Q5 may localize to chromosome 1p.     

临床试验中分类数据的处理方法比较

目的通过模拟比较,探讨分析多中心临床试验中高维列联表资料的有效方法。方法采用Monte Carlo模拟比较CMH检验与logistic回归处理多分类单向有序、无序资料以及CMH检验与一般线性模型GLM(General Linear Model)处理双向有序资料的区别。结果多分类单向有序和无序资料采用CMH检验和logistic回归分析结果相同,检验效能基本一致。双向有序资料采用GLM与CMH检验分析结果相同,检验效能基本一致。结论在多中心临床试验中,高维列联表资料的统计分析可以用logistic回归或GLM代替CMH卡方检验。     

A genomic imprinting test for ordinal traits in pedigree data

Genomic imprinting can lead maternally and paternally derived alleles with identical nucleotide sequences to function differently and has been found to affect the complex inheritance of a variety of human disorders. Statistical methods that differentiate the parent-of-origin effects on human diseases are available for binary traits and continuous traits. However, numerous common diseases are measured on discrete ordinal scales. Imprinting may also contribute to the complex genetic basis of these traits. In a previous study, we proposed a latent variable model and developed computationally efficient score statistic to test linkage of ordinal traits for any size pedigree while adjusting for non-genetic covariates. In this study, we extend the latent variable model to incorporate parent-of-origin information and further develop a score statistic for testing the imprinting effect in linkage analysis. We evaluated the properties of our test statistic using simulations. We then applied our method to the Collaborative Study on the Genetics of Alcoholism and found a novel locus on chromosome 18 that shows a strong signal for imprinting. In addition, we identified two loci on chromosomes 3 and 4 significantly (p<0.0001) linked with alcoholism.     

Multipoint development of the weighted pairwise correlation (WPC) linkage method for pedigrees of arbitrary size and application to the analysis of breast cancer and alcoholism familial data.

The weighted pairwise correlation (WPC) method is a simple and powerful model-free method of linkage analysis that has the advantages of being applicable to binary, ordered categorical, quantitative, or censored traits, and to consider all pairs of relatives in large pedigrees. The originally implemented approach was limited to the use of the identical by state (IBS) information, and we recently extended the WPC method to incorporate the identical by descent (IBD) information for two-point linkage analysis. Here, we develop a multipoint WPC method suitable for pedigrees of arbitrary size and large number of markers. The multipoint IBD estimation procedure for relative pairs is based on the efficient regression approach developed for pedigrees implemented in SOLAR. A robust and fast Monte-Carlo procedure is used to determine reliable P values. Application of the method to the 214 pedigrees from the Breast Cancer Linkage Consortium provided for the Genetic Analysis Workshop (GAW) 9 shows that multipoint WPC statistic values were not far from two-point maximum lod-score values obtained by the classical parametric linkage method and were higher than multipoint variance component analysis lod-scores obtained with SOLAR. The multipoint WPC method is also used to analyze the familial Collaborative Study of the Genetics of Alcoholism data on alcoholism released for GAW11. It allows a better specification of the linkage results previously obtained within the chromosome 4 region.     

Use of exact and adjusted liability scores to detect genes affecting common traits

We used the Haseman-Elston sib-pair test to screen for linkage of markers to genes for disease susceptibility in the simulated data as given in Problem 2 of GAW9. We applied the analysis to the underlying quantitative liability trait (Q1), other covariates of Q1 (Q2-Q4), and the dichotomous affection status trait. In addition, we analyzed the residual Q1 after adjusting for the covariates. Using the sib-pair linkage test, we identified a large region of chromosome 5 affecting the residual value of Q1, a region of chromosome 2 affecting Q3, and a region of chromosome 1 possibly affecting Q2. The analysis of the dichotomous traits did not reveal any regions to be significant. This is likely to be due to lack of information since the families were not selected through affected probands. © 1995 Wiley-Liss, Inc.     

A score for Bayesian genome screening

Bayesian Monte Carlo Markov chain (MCMC) techniques have shown promise in dissecting complex genetic traits. The methods introduced by Heath ([1997], Am. J. Hum. Genet. 61:748-760), and implemented in the program Loki, have been able to localize genes for complex traits in both real and simulated data sets. Loki estimates the posterior probability of quantitative trait loci (QTL) at locations on a chromosome in an iterative MCMC process. Unfortunately, interpretation of the results and assessment of their significance have been difficult. Here, we introduce a score, the log of the posterior placement probability ratio (LOP), for assessing oligogenic QTL detection and localization. The LOP is the log of the posterior probability of linkage to the real chromosome divided by the posterior probability of linkage to an unlinked pseudochromosome, with marker informativeness similar to the marker data on the real chromosome. Since the LOP cannot be calculated exactly, we estimate it in simultaneous MCMC on both real and pseudochromosomes. We investigate empirically the distributional properties of the LOP in the presence and absence of trait genes. The LOP is not subject to trait model misspecification in the way a lod score may be, and we show that the LOP can detect linkage for loci of small effect when the lod score cannot. We show how, in the absence of linkage, an empirical distribution of the LOP may be estimated by simulation and used to provide an assessment of linkage detection significance.     

Genetic analysis of phenotypes derived from longitudinal data: Presentation Group 1 of Genetic Analysis Workshop 13

The participants of Presentation Group 1 used the GAW13 data to derive new phenotypes, which were then analyzed for linkage and, in one case, for association to the genetic markers. Since the trait measurements ranged over longer time periods, the participants looked at the time dependence of particular traits in addition to the trait itself. The phenotypes analyzed with the Framingham data can be roughly divided into 1) body weight-related traits, which also include a type 2 diabetes progression trait, and 2) traits related to systolic blood pressure. Both trait classes are associated with metabolic syndrome. For traits related to body weight, linkage was consistently identified by at least two participating groups to genetic regions on chromosomes 4, 8, 11, and 18. For systolic blood pressure, or its derivatives, at least two groups obtained linkage for regions on chromosomes 4, 6, 8, 11, 14, 16, and 19. Five of the 13 participating groups focused on the simulated data. Due to the rather sparse grid of microsatellite markers, an association analysis for several traits was not successful. Linkage analysis of hypertension and body mass index using LODs and heterogeneity LODs (HLODs) had low power. For the glucose phenotype, a combination of random coefficient regression models and variance component linkage analysis turned out to be strikingly powerful in the identification of a trait locus simulated on chromosome 5. Haseman-Elston regression methods, applied to the same phenotype, had low power, but the above-mentioned chromosome 5 locus was not included in this analysis.     

Practical Application of Residuals from Survival Models in Quantitative Trait Linkage Analysis

A number of familial diseases have an age‐of‐onset component, which can be considered as a censored quantitative trait. However, few software resources are available for the use of time‐to‐event endpoints in linkage analysis. The purpose of this analysis was to examine the use of martingale residuals from Cox survival models as quantitative traits for familial diseases with variable age at onset. We used these residuals as quantitative traits in variance components linkage scans for the 50 replicates of the general population simulated data for chromosomes 6 and 7. The region on chromosome 6 containing markers D06G034 and D06G035 demonstrated evidence for linkage, consistent with the underlying genetic model. This analysis demonstrates the applicability of using martingale residuals as a quantitative trait in linkage analyses of diseases that depend on age of onset. © 2001 Wiley‐Liss, Inc.     

Screening for linkage using a multipoint identity-by-descent method

The multipoint identity-by-descent method (MIM) was used to analyze simulated data for quantitative traits from GAW9. A two-stage method of implementation was used. First, polymorphic markers spaced 6-12 cM apart were used to identify chromosomes of interest for each trait Q1-Q4; and second, for each of these chromosomes, markers spaced 2 cM apart were used to confirm the linkage detected and refine the region for the susceptibility loci. MIM performed well at both levels of mapping, correctly detecting major genes for trait Q3 on chromosome 2, trait Q2 on chromosome 1, and trait Q4 on chromosome 5. © 1995 Wiley-Liss, Inc.     

Analysis of mixed categorical data in 2 x K contingency tables

2 x K contingency tables having both ordinal and nominal categories are often encountered in various types of studies. Such data are referred to as 'mixed' categorical data in this article. To apply a method for ordered categorical data one has to discard the nominal categories, and to apply a method for nominal categories one has to discard the ordering information inherent in the ordered categories. Therefore, investigators often either discard observations in nominal categories or discard the ordering of the categories before analysing such data. Some information will be lost in both approaches. A method for analysing data in 2 x K 'mixed' tables is proposed in this paper which can be considered as an extension of well known methods for nominal and ordered categories. The proposed method utilizes observations in the nominal categories as well as the ordering information. If all the categories were ordered then the proposed method reduces to the trend test, and if all the categories were nominal then the proposed method reduced to Pearson's chi-square test.     

Association and linkage with quantitative traits

This paper examines two approaches for the analysis of quantitative traits: (1) association studies and (2) linkage studies. The trait studied was Q1 from simulated Problem 2 data set in Genetic Analysis Workshop 9. Our purpose was to evaluate associations present in the data, to identify nongenetic and genetic predictors of the trait, and to explore the simulated genome for linkage. Through the association study, we found evidence for the primary major gene associated with this trait. The linkage study found evidence of residual genetic effect acting through other traits. Adjustments of Q1 for Q2 and Q3 led to a failure to find significant effects of MG2 and MG3. This supports the suggestion that adjustment for genetically influenced traits for effects of other genetic traits can reduce the power to detect major gene effects. In summary, we detected the major gene directly associated with the trait of interest through association studies. Linkage analysis detected evidence for two other genes associated to a lesser degree with the trait. © 1995 Wiley-Liss, Inc.     

Variance‐components methods for linkage and association analysis of ordinal traits in general pedigrees

Many complex human diseases such as alcoholism and cancer are rated on ordinal scales. Well‐developed statistical methods for the genetic mapping of quantitative traits may not be appropriate for ordinal traits. We propose a class of variance‐component models for the joint linkage and association analysis of ordinal traits. The proposed models accommodate arbitrary pedigrees and allow covariates and gene‐environment interactions. We develop efficient likelihood‐based inference procedures under the proposed models. The maximum likelihood estimators are approximately unbiased, normally distributed, and statistically efficient. Extensive simulation studies demonstrate that the proposed methods perform well in practical situations. An application to data from the Collaborative Study on the Genetics of Alcoholism is provided. Genet. Epidemiol. 34: 232–237, 2010. © 2009 Wiley‐Liss, Inc.     

Test of Association for Quantitative Traits in General Pedigrees: The Quantitative Pedigree Disequilibrium Test

Many statistical methods have been proposed in recent years to test for genetic linkage and association between genetic markers and traits of interest through unrelated nuclear families. However, most of these methods are not valid tests of association in the presence of linkage when some of the nuclear families are related. As a result, related nuclear families in large pedigrees cannot be included in a single analysis to test for linkage disequilibrium. Recently, Martin et al. [Am J Hum Genet 67:146–54, 2000] proposed the pedigree disequilibrium test (PDT) to test for linkage and association in general pedigrees for qualitative traits. In this article, we develop a similar quantitative pedigree disequilibrium test (QPDT) to test for linkage and association in general pedigrees for quantitative traits. We apply both the PDT and the QPDT to analyze the sequence data from the seven candidate genes in the simulated data sets in the Genetic Analysis Workshop 12. © 2001 Wiley‐Liss, Inc.     

Genetic model-free linkage analysis using the maximum-likelihood-binomial method for categorical traits

Within the simulated data of the 11th Genetic Analysis Workshop, we searched for the genes controlling the disease. We analyzed 200 families from Studies 2 and 3 presenting both mild and severe forms of disease. Linkage analysis was performed using the recently developed genetic model-free maximum-likelihood-binomial (MLB) method which overcomes the problem of multiple sibs by considering the sibship as a whole. The MLB allowed us to consider the disease as either a binary (affected/unaffected) or an ordered categorical (differentiating the two forms of disease and including effects of environmental factors) phenotype. In both studies, two regions provided evidence for linkage at a significance level below 10(-4). One is located on chromosome 3 (from D3G041 to D3G047), and the other on chromosome 5 (from D5G034 to D5G041). In Study 2, the most significant results were obtained by combining both forms of disease, suggesting that they are under the same genetic control, while in Study 3, the stronger results were obtained when considering severe subjects alone, suggesting that only the severe form is under the control of both locus B and C. The subsequent knowledge of the true model allowed a posterior interpretation of our results, in particular the difference in optimal coding schemes observed between Studies 2 and 3, and the failure to locate locus A.     

Gaussian-based routines to impute categorical variables in health surveys

The multivariate normal (MVN) distribution is arguably the most popular parametric model used in imputation and is available in most software packages (e.g., SAS PROC MI, R package norm). When it is applied to categorical variables as an approximation, practitioners often either apply simple rounding techniques for ordinal variables or create a distinct 'missing' category and/or disregard the nominal variable from the imputation phase. All of these practices can potentially lead to biased and/or uninterpretable inferences. In this work, we develop a new rounding methodology calibrated to preserve observed distributions to multiply impute missing categorical covariates. The major attractiveness of this method is its flexibility to use any 'working' imputation software, particularly those based on MVN, allowing practitioners to obtain usable imputations with small biases. A simulation study demonstrates the clear advantage of the proposed method in rounding ordinal variables and, in some scenarios, its plausibility in imputing nominal variables. We illustrate our methods on a widely used National Survey of Children with Special Health Care Needs where incomplete values on race posed a valid threat on inferences pertaining to disparities.     

Cumulative logit models for ordinal data: a case study involving allergic rhinitis severity scores

Ordered categorical data arise in numerous settings, a common example being pain scores in analgesic trials. The modelling of such data is intrinsically more difficult than the modelling of continuous data due to the constraints on the underlying probabilities and the reduced amount of information that discrete outcomes contain. In this paper we discuss the class of cumulative logit models, which provide a natural framework for ordinal data analysis. We show how viewing the categorical outcome as the discretization of an underlying continuous response allows a natural interpretation of model parameters. We also show how covariates are incorporated into the model and how various types of correlation among repeated measures on the same individual may be accounted for. The models are illustrated using longitudinal allergy data consisting of sneezing scores measured on a four-point scale. Our approach throughout is Bayesian and we present a range of simple diagnostics to aid model building.     

A semiquantitative whole genome screen analysis of alcohol dependence

Two whole genome screens were applied to sibling pairs from the Collaborative Study on the Genetics of Alcoholism (COGA) family data to compare a semiquantitative method with a standard qualitative approach. The semiquantitative method used a score derived from 11 symptoms, and the qualitative approach used the COGA criteria for alcohol dependence. There was no concordance in the regions identified by the two models. Three regions of nominal significance were identified using the symptom score. In these three regions, correlated traits were also analyzed to determine whether linkage could be attributed to their intermediate effect. The evidence for linkage to one locus on chromosome 6 could be explained by linkage to the personality trait harm avoidance.     

Ordered multinomial regression for genetic association analysis of ordinal phenotypes at Biobank scale

Logistic regression is the primary analysis tool for binary traits in genome-wide association studies (GWAS). Multinomial regression extends logistic regression to multiple categories. However, many phenotypes more naturally take ordered, discrete values. Examples include (a) subtypes defined from multiple sources of clinical information and (b) derived phenotypes generated by specific phenotyping algorithms for electronic health records (EHR). GWAS of ordinal traits have been problematic. Dichotomizing can lead to a range of arbitrary cutoff values, generating inconsistent, hard to interpret results. Using multinomial regression ignores trait value hierarchy and potentially loses power. Treating ordinal data as quantitative can lead to misleading inference. To address these issues, we analyze ordinal traits with an ordered, multinomial model. This approach increases power and leads to more interpretable results. We derive efficient algorithms for computing test statistics, making ordinal trait GWAS computationally practical for Biobank scale data. Our method is available as a Julia package OrdinalGWAS.jl. Application to a COPDGene study confirms previously found signals based on binary case–control status, but with more significance. Additionally, we demonstrate the capability of our package to run on UK Biobank data by analyzing hypertension as an ordinal trait.     

The Power of Transmission Disequilibrium Tests for Quantitative Traits

We develop a score statistic to test for linkage in the presence of linkage disequilibrium for quantitative traits. We then extend this method to analyze multiple tightly linked markers. One potential limitation with the use of many genetic markers is the large number of degrees of freedom involved that may reduce the overall power to detect linkage. To overcome this limitation, we propose to group haplotypes on the basis of haplotype similarity before performing transmission disequilibrium tests. Finally, we apply these methods to the Genetic Analysis Workshop 12 simulated data and compare their power. © 2001 Wiley‐Liss, Inc.