The effect of selective sampling on mapping quantitative trait loci

Sib pairs were selectively sampled for extreme concordance or discordance for the quantitative trait Q1, a simulated phenotype (GAW10). Two selective sampling criteria were used (SC1 and SC2), and results for these were compared to linkage analyses using all pairs (ALL). In total 773 sib pairs were available, which reduced to an average of 59.7 pairs under SC1, and 134.1 pairs under SC2. Whole genome screens were performed on 10 different data replicates for each selection criterion (ALL, SC1, and SC2). Fine screens were then performed over regions which indicated at least suggestive linkage, and these regions were also fine screened in an independent data replicate in an attempt to repeat any areas found. The results for the coarse genome screens were similar under each of the criteria, although in general lower maxima and slightly more erratic lods were found under the stricter selection methods. The correct region on chromosome 5 (responsible for approximately 22% of the variance of Q1) was detected (p < 0.0001) in 6/10 of the data replicates using ALL, and 4/10 using SC1 and SC2. The second quantitative trait locus (QTL) on chromosome 8 (only 0.5% of the variance of Q1) was detected in only a single data replicate using SC1. False positive rates were similar for each criterion, whereas power decreased using selective sampling compared to ALL, although this was probably due to an insufficient initial sample size. © 1997 Wiley-Liss, Inc.     

A brute force dichotomization approach to quantitative trait linkage analysis

The effect of dichotomizing a continuous phenotype in linkage analysis of a simulated oligogenic trait is explored. We conclude that dichotomization does not in itself preclude the detection of loci which account for as little as 16% of the genetic variance of the disease. The effects of inclusion of known covariates and quantitative trait linkage analysis are also discussed. © 1995 Wiley-Liss, Inc.     

Linkage analysis of Alzheimer's disease with methods using relative pairs

Four relative-pair methods for detecting genetic linkage were applied to familial Alzheimer's disease data. Results obtained using an extended Haseman-Elston test and a weighted rank pairwise correlation test, which both use information from all relative pairs, were consistent with previously published likelihood results and appear to be more powerful than affected sib pair methods. © 1993 Wiley-Liss, Inc.     

Multipoint linkage mapping using sibpairs: non-parametric estimation of trait effects with quantitative covariates

Multipoint linkage analysis using sibpair designs remains a common approach to help investigators to narrow chromosomal regions for traits (either qualitative or quantitative) of interest. Despite its popularity, the success of this approach depends heavily on how issues such as genetic heterogeneity, gene-gene, and gene-environment interactions are properly handled. If addressed properly, the likelihood of detecting genetic linkage and of efficiently estimating the location of the trait locus would be enhanced, sometimes drastically. Previously, we have proposed an approach to deal with these issues by modeling the genetic effect of the target trait locus as a function of covariates pertained to the sibpairs. Here the genetic effect is simply the probability that a sibpair shares the same allele at the trait locus from their parents. Such modeling helps to divide the sibpairs into more homogeneous subgroups, which in turn helps to enhance the chance to detect linkage. One limitation of this approach is the need to categorize the covariates so that a small and fixed number of genetic effect parameters are introduced. In this report, we take advantage of the fact that nowadays multiple markers are readily available for genotyping simultaneously. This suggests that one could estimate the dependence of the generic effect on the covariates nonparametrically. We present an iterative procedure to estimate (1) the genetic effect nonparametrically and (2) the location of the trait locus through estimating functions developed by Liang et al. ([2001a] Hum Hered 51:67-76). We apply this new method to the linkage study of schizophrenia to illustrate how the onset ages of each sibpair may help to address the issue of genetic heterogeneity. This analysis sheds new light on the dependence of the trait effect on onset ages from affected sibpairs, an observation not revealed previously. In addition, we have carried out some simulation work, which suggests that this method provides accurate inference for estimating the location of quantitative trait loci.     

Multilocus linkage disequilibrium mapping of epistatic quantitative trait loci that regulate HIV dynamics: a simulation approach

The time-dependent change of HIV particle load, i.e. HIV dynamics, is likely to be controlled by a multitude of quantitative trait loci (QTL) that interact with each other as well as with various developmental and environmental factors in a coordinated manner. In this article, we have derived a new statistical model for mapping the epistatic QTL responsible for HIV dynamics in a natural human population. This model, constructed on the integrated theme of functional mapping and linkage disequilibrium (LD) mapping, can make use of information from multiple markers genotyped from the human genome. It allows for the test and estimation of genetic actions and interactions involved in the control of HIV progression and provides a general platform to identify the detailed genetic architecture of resistance or susceptibility of humans to HIV on a dynamic scale. We have generalized this model to accommodate various complicated clincal designs for AIDS studies. Simulation studies with different scenarios are performed to examine the statistical behaviour of the model. The genetic and statistical extensions of this mapping model to HIV/AIDS genomic research are discussed.     

How can maximum likelihood methods reveal candidate gene effects on a quantitative trait?

Different maximum likelihood approaches were used to explore the role of candidate genes in the variability of quantitative trait Q1 while accounting for the effects of age, Q2, and Q3. Segregation analysis, under the class D regressive model, provides evidence for a Mendelian gene effect on the adjusted trait Q1. Results of gene mapping through lod-score analyses remain puzzling. Pairwise lod scores indicate a possible linkage with the candidate gene C5 which is excluded when using tightly linked informative marker loci. Finally, our combined segregation and linkage analysis clearly shows that a C5 linked gene is involved in Q1 variability. However, given the lod-score results within the C5 region, we postulate a more complex mechanism for Q1 than a single di-allelic C5 linked gene. The knowledge of the true model (C5 is MG1 and has three alleles) permits a partial explanation of our results. This study demonstrates the advantages of using complementary approaches to reveal the role of candidate genes in complex traits, and the value of simultaneous estimation of linkage and segregation parameters. © 1995 Wiley-Liss, Inc.     

Accumulating quantitative trait linkage evidence across multiple datasets using the posterior probability of linkage

Genome scans for complex disorders are frequently inconclusive, prompting researchers to increase sample size in an effort to obtain stronger evidence. However, increasing sample size in the presence of locus heterogeneity may actually, on average, decrease the linkage signal at a true susceptibility gene. The posterior probability of linkage, or PPL, was specifically designed to address this issue in the context of categorical trait analysis, by appropriately accumulating evidence either for or against linkage as new data are added. We now formulate a quantitative trait (QT) analog, the QT-PPL, which directly measures the evidence that a QT is linked to a genetic marker or location. The new QT-PPL is based on a classical single-locus QT likelihood with the trait parameters (allele frequency, genotypic means and variances) integrated out. We show using simulations that the QT-PPL is robust to two key modeling violations (multiple trait loci and non-normality in the form of excess kurtosis), as well as being inherently ascertainment corrected, and illustrate the advantages of the QT-PPL for accumulating linkage evidence across multiple sets of data compared to other QT linkage methods.     

Multilocus quantitative trait analysis using the multipoint identity-by-descent method

The multipoint identity-by-descent method (MIM) was extended to test for evidence of quantitative trait loci in two independent genetic regions. This method is a fast and feasible implementation of a multiple-marker, two-region linkage analysis for quantitative traits. It tests for significant evidence of quantitative trait loci (QTL) in neither, one or both genetic regions tested, and could be extended to an arbitrary number of independent genetic regions. A two-stage analysis was used for the nuclear family data from GAW10. Initially, an analysis of the genomic search was carried out using single-region MIM, with sets of six adjacent markers. Chromosomal regions that showed some evidence of linkage were identified and used in a two-region MIM analysis. © 1997 Wiley-Liss, Inc.     

Multivariate and multilocus variance components method,based on structural relationships to assess quantitative trait linkage via SEGPATH

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.     

Empirical evaluation of genome scans for linkage of a quantitative trait associated with a complex disorder

Nonparametric sib-pair analysis (Haseman-Elston) was used to search for evidence of linkage between a putative locus for a complex quantitative trait Q1 and genome-wide markers (367 markers from 10 chromosomes) for the first 100 replicates of nuclear family data. The characteristics of the statistically positive linkage results [the magnitude of p-values (p), the number of supporting flanking markers, and the percentage of positive replicates] were compared for true linkage (major and minor genes) and false positive evidence for linkage. Discriminant analysis was used to evaluate which characteristics of these statistically positive linkage results are good indicators to discriminate true linkage from false positive evidence for linkage. Sensitivity and false positive rates of several proposed criteria for linkage, as well as the criteria based on our results were evaluated. The relationship between the map location of the marker with the lowest p-value and the map location of the true underlying gene was also evaluated, which provided useful information for fine mapping and replication studies. © 1997 Wiley-Liss, Inc.     

Bivariate combined linkage and association mapping of quantitative trait loci

In this paper, bivariate/multivariate variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL), based on combinations of pedigree and population data. Suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In the region, multiple markers such as single nucleotide polymorphisms are typed. Two regression models, "genotype effect model" and "additive effect model", are proposed to model the association between the markers and the trait locus. The linkage information, i.e., recombination fractions between the QTL and the markers, is modeled in the variance and covariance matrix. By analytical formulae, we show that the "genotype effect model" can be used to model the additive and dominant effects simultaneously; the "additive effect model" only takes care of additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. By analytical power analysis, we show that bivariate models can be more powerful than univariate models. For moderate-sized samples, the proposed models lead to correct type I error rates; and so the models are reasonably robust. As a practical example, the method is applied to analyze the genetic inheritance of rheumatoid arthritis for the data of The North American Rheumatoid Arthritis Consortium, Problem 2, Genetic Analysis Workshop 15, which confirms the advantage of the proposed bivariate models.     

A statistical model for high-resolution mapping of quantitative trait loci determining HIV dynamics

Are there specific genes that control the pathogenesis of HIV infection? This question, which is of fundamental importance in designing personalized strategies of gene therapy to control HIV infection, can be examined by genetic mapping approaches. In this article, we present a new statistical model for unravelling the genetic mechanisms for the dynamic change of HIV that causes AIDS by marker‐based linkage disequilibrium (LD) analyses. This new model is the extension of our functional mapping theory to integrate viral load trajectories within a genetic mapping framework. Earlier studies of HIV dynamics have led to various mathematical functions for modelling the kinetic curves of plasma virions and CD4 lymphocytes in HIV patients. Through incorporating these functions into the LD‐based mapping procedure, we can identify and map individual quantitative trait loci (or QTL) responsible for viral pathogenesis. We derive a closed‐form solution for estimating QTL allele frequency and marker‐QTL linkage disequilibrium in the context of EM algorithm and implement the simplex algorithm to estimate the mathematical parameters describing the curve shapes of HIV pathogenesis. We performed different simulation scenarios based on currently used clinical designs in AIDS/HIV research to illustrate the utility and power of our model for genetic mapping of HIV dynamics. The implications of our model for genetic and genomic research into AIDS pathogenesis are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Nonparametric Linkage Regression II: Identification of Influential Pedigrees in Tests for Linkage

We applied case‐deletion‐based diagnostics to the combined Caucasian genome scan data for asthma and IgE from the Collaborative Study on the Genetics of Asthma (CSGA) and German family studies in order to identify influential pedigrees in tests for linkage. These methods identified 12 pedigrees whose data appear not to fit the asthma linkage model and for whom alternative genetic and nongenetic explanations can be explored. The methods also identified four pedigrees for chromosome 1 and two pedigrees for chromosome 2 that provide strong evidence for linkage at their respective loci. Similarly, these methods helped identify four pedigrees that strongly influenced the linkage tests for IgE. From these data, we can construct an enriched subset of pedigrees to be used in further analysis for mapping region‐specific putative trait predisposing loci. © 2001 Wiley‐Liss, Inc.     

Detecting case-control expression quantitative trait loci using locally most powerful or maximin robust rank tests

In testing genome-wide gene expression quantitative trait loci, efficiency robust statistical methods and their computational convenience are most relevant. For this purpose, we propose to use a modified locally most powerful rank test for the analysis of case-control expression data. This modified rank test statistic is computationally simple, robust for non-normally distributed expression data, and asymptotically locally most powerful. It depends on the specification of a location distribution form for data but is not sensitive to misspecifications. When such a location distribution form cannot be specified, we apply Gastwirth's maximin efficiency robust rank test to gene expression data to maximize the worst Pitman asymptotic relative efficiency among a family of location distributions. We conduct simulation studies to assess their performance and use an application to real data for illustration.     

Bivariate quantitative trait linkage analysis: Pleiotropy versus co-incident linkages

Power to detect linkage and localization of a major gene were compared in univariate and bivariate variance components linkage analysis of three related quantitative traits in general pedigrees. Although both methods demonstrated adequate power to detect loci of moderate effect, bivariate analysis improved both power and localization for correlated quantitative traits mapping to the same chromosomal region, regardless of whether co-localization was the result of pleiotropy. Additionally, a test of pleiotropy versus co-incident linkage was shown to have adequate power and a low error rate. © 1997 Wiley-Liss, Inc.     

Testing causal hypotheses in multivariate linkage analysis of quantitative traits: General formulation and application to sibpair data

We provide a general framework for the development of model-free methods for the linkage analysis of multivariate phenotypic data. It is possible within this framework to test both for linkage of a set of phenotypes to one or more markers and for the presence of structural relations among the phenotypes themselves. This report presents the general model, paying special attention to the assumptions that enter its formulation, and outlines the estimation procedures that may be used. Genet. Epidemiol. 15:263–278, 1998. © 1998 Wiley-Liss, Inc.     

Methods to estimate genetic components of variance for quantitative traits in family studies

The aim of this paper was to compare several methods of estimating the genetic components of a quantitative trait in familial data. The Expectation and Maximization (E‐M) algorithm, the Newton‐Raphson method, and the scoring method were compared for estimating polygenic and environmental effects on nuclear families. We also compared scoring and quasilikelihood (QL) methods when a linked genetic marker was available to estimate effects from a major gene. Generally, all procedures performed similarly in estimating polygenic and environmental variance components. The E‐M algorithm yielded more precise estimators when heritability was low. The scoring method was much faster than the other methods and yielded slightly more precise estimates of mean effects but slightly less precise estimates of the variance components. Estimates of major gene effects were not affected by the number of alleles at the trait locus. For these relatively large sample sizes, QL and scoring had similar precision, but QL took 32 times longer than scoring. Finally, we compared the results of applying these methods to data from the Bogalusa Heart Study. Results showed larger imprecision when the QL method was applied, consistent with earlier studies that showed decreased precision of quasilikelihood compared with maximum likelihood in moderately small sample sizes. Genet. Epidemiol. 17:64–76, 1999. © 1999 Wiley‐Liss, Inc.     

Comparing apples and oranges: equating the power of case‐control and quantitative trait association studies

Genome‐wide association studies have achieved unprecedented success in the identification of novel genes and pathways implicated in complex traits. Typically, studies for disease use a case‐control (CC) design and studies for quantitative traits (QT) are population based. The question that we address is what is the equivalence between CC and QT association studies in terms of detection power and sample size? We compare the binary and continuous traits by assuming a threshold model for disease and assuming that the effect size on disease liability has similar feature as on QT. We derive the approximate ratio of the non‐centrality parameter (NCP) between CC and QT association studies, which is determined by sample size, disease prevalence (K) and the proportion of cases (v) in the CC study. For disease with prevalence <0.1, CC association study with equal numbers of cases and controls (v=0.5) needs smaller sample size than QT association study to achieve equivalent power, e.g. a CC association study of schizophrenia (K=0.01) needs only ～55% sample size required for association study of height. So a planned meta‐analysis for height on ～120,000 individuals has power equivalent to a CC study on 33,100 schizophrenia cases and 33,100 controls, a size not yet achievable for this disease. With equal sample size, when v=K, the power of CC association study is much less than that of QT association study because of the information lost by transforming a quantitative continuous trait to a binary trait. Genet. Epidemiol. 34: 254–257, 2010. © 2009 Wiley‐Liss, Inc.     

Mapping quantitative traits in unselected families: algorithms and examples

Linkage analysis has been widely used to identify from family data genetic variants influencing quantitative traits. Common approaches have both strengths and limitations. Likelihood ratio tests typically computed in variance component analysis can accommodate large families but are highly sensitive to departure from normality assumptions. Regression‐based approaches are more robust but their use has primarily been restricted to nuclear families. In this paper, we develop methods for mapping quantitative traits in moderately large pedigrees. Our methods are based on the score statistic, which in contrast to the likelihood ratio statistic can use nonparametric estimators of variability to achieve robustness of the false‐positive rate against departures from the hypothesized phenotypic model. Because the score statistic is easier to calculate than the likelihood ratio statistic, our basic mapping methods utilize relatively simple computer code that performs statistical analysis on output from any program that computes estimates of identity by descent. This simplicity also permits development and evaluation of methods to deal with multivariate and ordinal phenotypes, and with gene‐gene and gene‐environment interaction. We demonstrate our methods on simulated data and on fasting insulin, a quantitative trait measured in the Framingham Heart Study. Genet. Epidemiol. 33:617–627, 2009. © 2009 Wiley‐Liss, Inc.     

Linkage Analysis of Quantitative Traits in Randomly Ascertained Pedigrees: Comparison of Penetrance‐Based and Variance Component Analysis

Penetrance‐based linkage analysis and variance component linkage analysis are two methods that are widely used to localize genes influencing quantitative traits. Using computer programs PAP and SOLAR as representative software implementations, we have conducted an empirical comparison of both methods' power to map quantitative trait loci in extended, randomly ascertained pedigrees, using simulated data. Two‐point linkage analyses were conducted on several quantitative traits of different genetic and environmental etiology using both programs, and the lod scores were compared. The two methods appear to have similar power when the underlying quantitative trait locus is diallelic, with one or the other method being slightly more powerful depending on the characteristics of the quantitative trait and the quantitative trait locus. In the case of a multiallelic quantitative trait locus, however, the variance component approach has much greater power. These findings suggest that one should give careful thought to the likely allelic architecture of the quantitative trait to be analyzed when choosing between these two analytical approaches. It may be the case in general that linkage methods which explicitly or implicitly rely on the assumption of a diallelic trait locus fare poorly when this assumption is incorrect. © 2001 Wiley‐Liss, Inc.