Mapping Complex Disease Genes Research Articles

Assessing the Impact of Population Stratification on Association Studies of Rare Variation

Aims: The study of rare variants, which can potentially explain a great proportion of heritability, has emerged as an important topic in human gene mapping of complex diseases. Although several statistical methods have been developed to increase the power to detect disease-related rare variants, none of these methods address an important issue that often arises in genetic studies: false positives due to population stratification. Using simulations, we investigated the impact of population stratification on false-positive rates of rare-variant association tests. Methods: We simulated a series of case-control studies assuming various sample sizes and levels of population structure. Using such data, we examined the impact of population stratification on rare-variant collapsing and burden tests of rare variation. We further evaluated the ability of 2 existing methods (principal component analysis and genomic control) to correct for stratification in such rare-variant studies. Results: We found that population stratification can have a significant influence on studies of rare variants especially when the sample size is large and the population is severely stratified. Our results showed that principal component analysis performed quite well in most situations, while genomic control often yielded conservative results. Conclusions: Our results imply that researchers need to carefully match cases and controls on ancestry in order to avoid false positives caused by population structure in studies of rare variants, particularly if genome-wide data are not available.

A Class Representative Model for Pure Parsimony Haplotyping under Uncertain Data

The Pure Parsimony Haplotyping (PPH) problem is a NP-hard combinatorial optimization problem that consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. PPH has attracted more and more attention in recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from mapping complex disease genes to inferring population histories, passing through designing drugs, functional genomics and pharmacogenetics. In this article we investigate, for the first time, a recent version of PPH called the Pure Parsimony Haplotype problem under Uncertain Data (PPH-UD). This version mainly arises when the input genotypes are not accurate, i.e., when some single nucleotide polymorphisms are missing or affected by errors. We propose an exact approach to solution of PPH-UD based on an extended version of Catanzaro et al. [1] class representative model for PPH, currently the state-of-the-art integer programming model for PPH. The model is efficient, accurate, compact, polynomial-sized, easy to implement, solvable with any solver for mixed integer programming, and usable in all those cases for which the parsimony criterion is well suited for haplotype estimation.

A practical parameterised algorithm for the individual haplotyping problem MLF

Haplotypes are more useful in complex disease gene mapping than single-nucleotide polymorphisms (SNPs). However, haplotypes are difficult to obtain directly using biological experiments, which has prompted research into efficient computational methods for determining haplotypes. The individual haplotyping problem called Minimum Letter Flip (MLF) is a computational problem that, given a set of aligned DNA sequence fragment data of an individual, induces the corresponding haplotypes by flipping minimum SNPs. There has been no practical exact algorithm for solving the problem. Due to technical limits in DNA sequencing experiments, the maximum length of a fragment sequenced directly is about 1kb. In consequence, with a genome-average SNP density of 1.84 SNPs per 1 kb of DNA sequence, the maximum number k1 of SNP sites that a fragment covers is usually small. Moreover, in order to save time and money, the maximum number k2 of fragments that cover an SNP site is usually no more than 19. Building on these fragment data properties, the current paper introduces a new parameterised algorithm with running time O(nk22k2 + mlogm + mk1), where m is the number of fragments and n is the number of SNP sites. In practical biological applications, the algorithm solves the MLF problem efficiently even if m and n are large.

CollHaps: A Heuristic Approach to Haplotype Inference by Parsimony

Haplotype data play a relevant role in several genetic studies, e.g., mapping of complex disease genes, drug design, and evolutionary studies on populations. However, the experimental determination of haplotypes is expensive and time-consuming. This motivates the increasing interest in techniques for inferring haplotype data from genotypes, which can instead be obtained quickly and economically. Several such techniques are based on the maximum parsimony principle, which has been justified by both experimental results and theoretical arguments. However, the problem of haplotype inference by parsimony was shown to be NP-hard, thus limiting the applicability of exact parsimony-based techniques to relatively small data sets. In this paper, we introduce collapse rule, a generalization of the well-known Clark's rule, and describe a new heuristic algorithm for haplotype inference (implemented in a program called CollHaps), based on parsimony and the iterative application of collapse rules. The performance of CollHaps is tested on several data sets. The experiments show that CollHaps enables the user to process large data sets obtaining very "parsimonious" solutions in short processing times. They also show a correlation, especially for large data sets, between parsimony and correct reconstruction, supporting the validity of the parsimony principle to produce accurate solutions.

A Class Representative Model for Pure Parsimony Haplotyping

Haplotyping estimation from aligned single nucleotide polymorphism fragments has attracted increasing attention in recent years because of its importance in the analysis of fine-scale genetic data. Its application fields range from mapping of complex disease genes to inferring population histories, passing through designing drugs, functional genomics, and pharmacogenetics. The literature proposes several criteria for haplotyping populations, each of them characterized by biological motivations. One of the most important haplotyping criteria is parsimony, which consists of finding the minimum number of haplotypes necessary to explain a given set of genotypes. Parsimonious haplotype estimation is an 𝒩𝒫-hard problem for which the literature has proposed several integer programming (IP) models. Here, we describe a new polynomial-sized IP model based on the concept of class representatives, already used for the coloring problem. We propose valid inequalities to strengthen our model and show, through computational experiments, that our model outperforms the best IP models currently known in literature.

The pure parsimony haplotyping problem: overview and computational advances

AbstractHaplotyping estimation from aligned single‐nucleotide polymorphism fragments has attracted more and more attention in recent years due to its importance in analysis of many fine‐scale genetic data. Its application fields range from mapping of complex disease genes to inferring population histories, passing through designing drugs, functional genomics, and pharmacogenetics. The literature proposes a number of estimation criteria to select a set of haplotypes among possible alternatives. Usually, such criteria can be expressed under the form of objective functions, and the sets of haplotypes that optimize them are referred to as optimal. One of the most important estimation criteria is the pure parsimony, which states that the optimal set of haplotypes for a given set of genotypes is that having minimal cardinality. Finding the minimal number of haplotypes necessary to explain a given set of genotypes involves solving an optimization problem, called the pure parsimony haplotyping (PPH) estimation problem, which is notoriously ‐hard. This article provides an overview of PPH, and discusses the different approaches to solution that occur in the literature.

Ordered‐subset analysis (OSA) for family‐based association mapping of complex traits

Association analysis provides a powerful tool for complex disease gene mapping. However, in the presence of genetic heterogeneity, the power for association analysis can be low since only a fraction of the collected families may carry a specific disease susceptibility allele. Ordered-subset analysis (OSA) is a linkage test that can be powerful in the presence of genetic heterogeneity. OSA uses trait-related covariates to identify a subset of families that provide the most evidence for linkage. A similar strategy applied to genetic association analysis would likely result in increased power to detect association. Association in the presence of linkage (APL) is a family-based association test (FBAT) for nuclear families with multiple affected siblings that properly infers missing parental genotypes when linkage is present. We propose here APL-OSA, which applies the OSA method to the APL statistic to identify a subset of families that provide the most evidence for association. A permutation procedure is used to approximate the distribution of the APL-OSA statistic under the null hypothesis that there is no relationship between the family-specific covariate and the family-specific evidence for allelic association. We performed a comprehensive simulation study to verify that APL-OSA has the correct type I error rate under the null hypothesis. This simulation study also showed that APL-OSA can increase power relative to other commonly used association tests (APL, FBAT and FBAT with covariate adjustment) in the presence of genetic heterogeneity. Finally, we applied APL-OSA to a family study of age-related macular degeneration, where cigarette smoking was used as a covariate.

Most pooling variation in array-based DNA pooling is attributable to array error rather than pool construction error

Genome-wide association (GWA) approaches are important in complex disease gene mapping studies but are often prohibitively expensive. Array-based DNA pooling has been shown to offer substantial cost savings compared with individual genotyping. This reduced cost potentially brings well-powered GWA studies well within the reach of most laboratories. The main factor, which affects the efficiency of pooling compared with individual genotyping is the magnitude of the pooling error variance. By examining variation between and within pools it is shown that most of the error associated with pooling is attributable to array variation not pooling construction variation (assuming the pools are not small and the pools are accurately constructed). With Affymetrix HindIII 50K arrays used here the array-specific variance is seven times the pooling construction variance. This has important implications for optimal study design for array-based pooling. Given carefully constructed pools, resources should be allocated to increasing the number of arrays per sample rather than to constructing multiple pools.

Gene mapping of complex diseases - A comparison of methods from statistics informnation theory, and signal processing

The goal of gene mapping is to identify the genetic loci that are responsible for the apparent genotypes such as complex diseases. In this work, a review and comparison of three different gene mapping methods is presented along with the assumptions and imposed constraints. The first method relies on standard statistical techniques and follows a probabilistic approach to deal with the problem. The second method is based on a well-known concept from information theory. The idea is to model the available data as random variables and measure the dependence between them using mutual information. The last method explores blind source separation techniques by finding a suitable model that involves mixing various sources so that independent component analysis can be applied

In silico method for inferring genotypes in pedigrees

Our genotype inference method combines sparse marker data from a linkage scan and high-resolution SNP genotypes for several individuals to infer genotypes for related individuals. We illustrate the method's utility by inferring over 53 million SNP genotypes for 78 children in the Centre d'Etude du Polymorphisme Humain families. The method can be used to obtain high-density genotypes in different family structures, including nuclear families commonly used in complex disease gene mapping studies.

A Combinatorial Searching Method for Detecting a Set of Interacting Loci Associated with Complex Traits

Complex diseases are presumed to be the results of the interaction of several genes and environmental factors, with each gene only having a small effect on the disease. Mapping complex disease genes therefore becomes one of the greatest challenges facing geneticists. Most current approaches of association studies essentially evaluate one marker or one gene (haplotype approach) at a time. These approaches ignore the possibility that effects of multilocus functional genetic units may play a larger role than a single-locus effect in determining trait variability. In this article, we propose a Combinatorial Searching Method (CSM) to detect a set of interacting loci (may be unlinked) that predicts the complex trait. In the application of the CSM, a simple filter is used to filter all the possible locus-sets and retain the candidate locus-sets, then a new objective function based on the cross-validation and partitions of the multi-locus genotypes is proposed to evaluate the retained locus-sets. The locus-set with the largest value of the objective function is the final locus-set and a permutation procedure is performed to evaluate the overall p-value of the test for association between the final locus-set and the trait. The performance of the method is evaluated by simulation studies as well as by being applied to a real data set. The simulation studies show that the CSM has reasonable power to detect high-order interactions. When the CSM is applied to a real data set to detect the locus-set (among the 13 loci in the ACE gene) that predicts systolic blood pressure (SBP) or diastolic blood pressure (DBP), we found that a four-locus gene-gene interaction model best predicts SBP with an overall p-value = 0.033, and similarly a two-locus gene-gene interaction model best predicts DBP with an overall p-value = 0.045.

A Fine-Scale Linkage-Disequilibrium Measure Based on Length of Haplotype Sharing

High-throughput genotyping technologies for SNPs have enabled the recent completion of the International HapMap Project (phase I), which has stimulated much interest in studying genomewide linkage-disequilibrium (LD) patterns. Conventional LD measures, such as D' and r(2), are two-point measurements, and their relationship with physical distance is highly noisy. We propose a new LD measure, Delta , defined in terms of the correlation coefficient for shared haplotype lengths around two loci, thereby borrowing information from multiple loci. A U-statistic-based estimator of Delta , which takes into consideration the dependence structure of the observed data, is developed and compared with an estimator based on the usual empirical correlation coefficient. Furthermore, we propose methods for inferring LD-decay rates and recombination hotspots on the basis of Delta . The results from coalescent-simulation studies and analysis of HapMap SNP data demonstrate that the proposed estimators of Delta are superior to the two most popular conventional LD measures, in terms of their close relationship with physical distance and recombination rate, their small variability, and their strong robustness to marker-allele frequencies. These merits may offer new opportunities for mapping complex disease genes and for investigating recombination mechanisms on the basis of better-quantified LD.

Use of phenotypic covariates in association analysis by sequential addition of cases

Optimal use of phenotype information is important in complex disease gene mapping. We describe a method, sequential addition, for the analysis of case-control data by taking into account of a quantitative trait that is measured in cases but not in controls. The method also provides an estimate of the best phenotype definition for future studies. We demonstrate proof of principle, using an example of incorporation of age-at-onset data into a study of a small sample for association between APOE and late-onset Alzheimer's disease. The sequential addition method finds evidence of association when conventional case-control methods fail. We also illustrate the use of the method for taking account of a dimensional measure of psychosis in a study of the schizophrenia susceptibility gene, dysbindin, in bipolar disorder.

A Bayesian genome screening of maximum number of drinks as an alcoholism phenotype with the new Haseman-Elston method

Common human disorders, such as alcoholism, may be the result of interactions of many genes as well as environmental risk factors. Therefore, it is important to incorporate gene × gene and gene × environment interactions in complex disease gene mapping. In this study, we applied a robust Bayesian genome screening method that can incorporate interaction effects to map genes underlying alcoholism through its application to the data of the Collaborative Studies on Genetics of Alcoholism provided by Genetic Analysis Workshop 14. Our Bayesian genome screening method uses the regression-based stochastic variable selection, coupled with the new Haseman-Elston method to identify markers linked to phenotypes of interest. Compared to traditional linkage methods based on single-gene disease models, our method allows for multilocus disease models for simultaneous screening including both main and interaction (epistatic) effects. It is conceptually simple and computationally efficient through the use of Gibbs sampler. We conducted genome-wide analysis and comparison between scans based on microsatellites and single-nucleotide polymorphisms. A total of 328 microsatellites and 11,560 single-nucleotide polymorphisms (by Affymetrix) on 22 autosomal chromosomes and sex chromosome were used.

A survey of haplotype variants at several disease candidate genes: the importance of rare variants for complex diseases

Background: The haplotype based association method offers a powerful approach to complex disease gene mapping. In this method, a few common haplotypes that account for the vast majority of chromosomes...

Identifying SNPs predictive of phenotype using random forests

There has been a great interest and a few successes in the identification of complex disease susceptibility genes in recent years. Association studies, where a large number of single-nucleotide polymorphisms (SNPs) are typed in a sample of cases and controls to determine which genes are associated with a specific disease, provide a powerful approach for complex disease gene mapping. Genes of interest in those studies may contain large numbers of SNPs that classical statistical methods cannot handle simultaneously without requiring prohibitively large sample sizes. By contrast, high-dimensional nonparametric methods thrive on large numbers of predictors. This work explores the application of one such method, random forests, to the problem of identifying SNPs predictive of the phenotype in the case-control study design. A random forest is a collection of classification trees grown on bootstrap samples of observations, using a random subset of predictors to define the best split at each node. The observations left out of the bootstrap samples are used to estimate prediction error. The importance of a predictor is quantified by the increase in misclassification occurring when the values of the predictor are randomly permuted. We extend the concept of importance to pairs of predictors, to capture joint effects, and we explore the behavior of importance measures over a range of two-locus disease models in the presence of a varying number of SNPs unassociated with the phenotype. We illustrate the application of random forests with a data set of asthma cases and unaffected controls genotyped at 42 SNPs in ADAM33, a previously identified asthma susceptibility gene. SNPs and SNP pairs highly associated with asthma tend to have the highest importance index value, but predictive importance and association do not always coincide.

Estimating haplotype frequencies and standard errors for multiple single nucleotide polymorphisms.

Estimating haplotype frequencies becomes increasingly important in the mapping of complex disease genes, as millions of single nucleotide polymorphisms (SNPs) are being identified and genotyped. When genotypes at multiple SNP loci are gathered from unrelated individuals, haplotype frequencies can be accurately estimated using expectation-maximization (EM) algorithms (Excoffier and Slatkin, 1995; Hawley and Kidd, 1995; Long et al., 1995), with standard errors estimated using bootstraps. However, because the number of possible haplotypes increases exponentially with the number of SNPs, handling data with a large number of SNPs poses a computational challenge for the EM methods and for other haplotype inference methods. To solve this problem, Niu and colleagues, in their Bayesian haplotype inference paper (Niu et al., 2002), introduced a computational algorithm called progressive ligation (PL). But their Bayesian method has a limitation on the number of subjects (no more than 100 subjects in the current implementation of the method). In this paper, we propose a new method in which we use the same likelihood formulation as in Excoffier and Slatkin's EM algorithm and apply the estimating equation idea and the PL computational algorithm with some modifications. Our proposed method can handle data sets with large number of SNPs as well as large numbers of subjects. Simultaneously, our method estimates standard errors efficiently, using the sandwich-estimate from the estimating equation, rather than the bootstrap method. Additionally, our method admits missing data and produces valid estimates of parameters and their standard errors under the assumption that the missing genotypes are missing at random in the sense defined by Rubin (1976).

Association of PADI4 and rheumatoid arthritis: a successful multidisciplinary approach

The identification of functionally relevant polymorphisms of peptidylarginine deiminase 4, an enzyme that catalyzes the post-translational citrullination of proteins, as a rheumatoid arthritis gene is one of the most convincing success stories of complex disease gene mapping to date. In addition to an extensive single nucleotide polymorphism-based association study in a Japanese cohort, a range of techniques have been used to validate this finding.

Genotyping error detection through tightly linked markers.

The identification of genotyping errors is an important issue in mapping complex disease genes. Although it is common practice to genotype multiple markers in a candidate region in genetic studies, the potential benefit of jointly analyzing multiple markers to detect genotyping errors has not been investigated. In this article, we discuss genotyping error detections for a set of tightly linked markers in nuclear families, and the objective is to identify families likely to have genotyping errors at one or more markers. We make use of the fact that recombination is a very unlikely event among these markers. We first show that, with family trios, no extra information can be gained by jointly analyzing markers if no phase information is available, and error detection rates are usually low if Mendelian consistency is used as the only standard for checking errors. However, for nuclear families with more than one child, error detection rates can be greatly increased with the consideration of more markers. Error detection rates also increase with the number of children in each family. Because families displaying Mendelian consistency may still have genotyping errors, we calculate the probability that a family displaying Mendelian consistency has correct genotypes. These probabilities can help identify families that, although showing Mendelian consistency, may have genotyping errors. In addition, we examine the benefit of available haplotype frequencies in the general population on genotyping error detections. We show that both error detection rates and the probability that an observed family displaying Mendelian consistency has correct genotypes can be greatly increased when such additional information is available.

HLA in coeliac disease: unravelling the complex genetics of a complex disorder.

Coeliac disease (gluten sensitive enteropathy) is a common, polygenic and multifactorial disorder that serves as a pioneering model for the study of inflammatory disease. A major environmental factor is known (ingested gluten from wheat), and there is unprecedented genetic and functional evidence pinpointing HLA-DQA1*05-DQB1*02 ( DQ2) and DQA1*03-DQB1*0302 ( DQ8) in disease predisposition. We discuss the current state of play in coeliac disease genetics, focussing particularly on the HLA complex. Emerging evidence suggests that additional HLA risk loci exert weak effects, independent of DQA1*05-DQB1*02, on the B8-DR3-DQ2 haplotype. There is also good evidence from linkage studies of disease gene(s) on chromosome 5q. We discuss the role and implications of linkage disequilibrium and haplotype blocks in complex disease gene mapping. We briefly address findings from studies of animal models for chronic inflammatory disease, and consider roles for both common genes associated with multiple inflammatory diseases, and genes unique to coeliac disease. The coeliac genetics research community has established a sound foundation for the identification of additional disease genes in the not-too-distant future. Functional studies will play a critical role, and coeliac disease has a promising future in this respect. Coeliac disease continues to function as a model disorder, facilitating the development and implementation of complex disease gene mapping strategies.