Consanguinity and the transmission/disequilibrium test for allelic association.

Consanguineous marriages, usually between first cousins or between uncle and niece, are common in certain societies. The transmission/disequilibrium test (TDT) compares the transmission from parents to an affected child of alleles at a marker locus, and differential transmission indicates linkage and allelic association between the marker locus and a disease locus. We investigate the consequences for the TDT, as a test for allelic association, of consanguineous marriages. For each parental marker mating type, we calculate the frequency of each disease mating type, and the associated probability that an offspring is affected. We use Bayes' Theorem to estimate the probability that an affected child inherits the given allele from a heterozygous parent, then combine our results across marker mating types. The effect of consanguineous marriage is usually small. For candidate genes, the effects were greater for uncle-niece marriages, for rare disease alleles, and for high genotype relative risk. For markers, the effects were generally negligible. The Type I error probability of the TDT is essentially unchanged by intermarriage, except for a purely recessive disease allele. The power of the TDT is increased for a recessive allele and decreased for a dominant allele. However, consideration of levels of consanguinity that arise in practice indicates that standard power calculations for the TDT will usually need only minor modification.     

On selecting markers for association studies: patterns of linkage disequilibrium between two and three diallelic loci

Association studies depend on linkage disequilibrium (LD) between a causative mutation and linked marker loci. Selecting markers that give the best chance of showing useful levels of LD with the causative mutation will increase the chances of successfully detecting an association. This report examines the variation in the extent of LD between a disease locus and one or two diallelic marker loci (termed single nucleotide polymorphisms or SNPs). We use a simulation method based on the neutral coalescent in a population of variable size to find the distribution of LD as a function of allele frequencies, the recombination rate, and the population history. Given that LD exists, the allele frequencies determine if a site will be useful for detecting an association with the disease mutation. We show that there is extensive variation in LD even for closely linked loci, implying that several markers may be needed to detect a disease locus. The distribution of LD between common variants is strongly influenced by ancestral population size. We show that in general, best results will be obtained if the frequencies of marker alleles are at least as large as the frequency of the causative mutation. Haplotypes of two or more SNPs generally have a higher probability than individual SNPs of showing useful LD with a disease mutation, although exceptions are described.     

Global transmission/disequilibrium tests based on haplotype sharing in multiple candidate genes

It is well recognized that multiple genes are likely contributing to the susceptibility of most common complex diseases. Studying one gene at a time might reduce our chance to identify disease susceptibility genes with relatively small effect sizes. Therefore, it is crucial to develop statistical methods that can assess the effect of multiple genes collectively. Motivated by the increasingly available high-density markers across the whole human genome, we propose a class of TDT-type methods that can jointly analyze haplotypes from multiple candidate genes (linked or unlinked). Our approach first uses a linear signed rank statistic to compare at an individual gene level the structural similarity among transmitted haplotypes against that among non-transmitted haplotypes. The results of the ranked comparisons from all considered genes are subsequently combined into global statistics, which can simultaneously test the association of the set of genes with the disease. Using simulation studies, we find that the proposed tests yield correct type I error rates in stratified populations. Compared with the gene-by-gene test, the new global tests appear to be more powerful in situations where all candidate genes are associated with the disease.     

Genome scanning for complex disease genes using the transmission/disequilibrium test and haplotype-based haplotype relative risk

Two tests for allelic association were applied to a simulated complex disease for the Genetic Analysis Workshop 9. The transmission/disequilibrium test [Spielman et al., 1993] and the haplotype-based haplotype relative risk approach [Terwilliger and Ott, 1992] were used to detect disease-associated alleles in a set of 360 computer-simulated markers located on six chromosomes and genotyped in 200 nuclear families. This analysis emulates a genome-based search for linked markers. Computer simulations were also performed to clarify statistical properties of the TDT. ©1995 Wiley-Liss, Inc.     

A general and accurate approach for computing the statistical power of the transmission disequilibrium test for complex disease genes.

Transmission disequilibrium test (TDT) is a nuclear family-based analysis that can test linkage in the presence of association. It has gained extensive attention in theoretical investigation and in practical application; in both cases, the accuracy and generality of the power computation of the TDT are crucial. Despite extensive investigations, previous approaches for computing the statistical power of the TDT are neither accurate nor general. In this paper, we develop a general and highly accurate approach to analytically compute the power of the TDT. We compare the results from our approach with those from several other recent papers, all against the results obtained from computer simulations. We show that the results computed from our approach are more accurate than or at least the same as those from other approaches. More importantly, our approach can handle various situations, which include (1) families that consist of one or more children and that have any configuration of affected and nonaffected sibs; (2) families ascertained through the affection status of parent(s); (3) any mixed sample with different types of families in (1) and (2); (4) the marker locus is not a disease susceptibility locus; and (5) existence of allelic heterogeneity. We implement this approach in a user-friendly computer program: TDT Power Calculator. Its applications are demonstrated. The approach and the program developed here should be significant for theoreticians to accurately investigate the statistical power of the TDT in various situations, and for empirical geneticists to plan efficient studies using the TDT.     

Localization of breast cancer susceptibility loci by genome-wide SNP linkage disequilibrium mapping

We studied the feasibility of a novel approach to localize breast cancer susceptibility genes, using a low-density genome-wide panel of single-nucleotide polymorphisms and taking advantage of large regions of linkage disequilibrium (LD) flanking Jewish disease genes in high-risk cases. With Affymetrix GeneChip arrays, we genotyped 8,576 polymorphisms in three sets of Ashkenazi Jewish breast cancer cases: a "validation" set of 27 breast cancer cases, all of whom carried the BRCA2*6174delT founder mutation; a "field" set of 19 breast cancer cases from male breast cancer kindreds, which simulated conditions for finding new genes; and a "test" set of 57 probands from breast cancer kindreds (4 or more cases/kindred), in which mutations in BRCA1 and BRCA2 had been excluded. To identify associations, we compared the frequency of genotypes and haplotypes in cases vs. controls by the Fisher's exact test and a maximum likelihood ratio test. In the "validation" set, we demonstrated the presence of a region of linkage disequilibrium on BRCA2*6174delT chromosomes that spanned over 5 million bases. In the "field" set, we showed that this large region of linkage disequilibrium flanking BRCA2 was detectable despite the presence of heterogeneity in the sample set. Finally, in the "test" set, at least three regions of interest emerged that could contain novel breast cancer genes, one of which had been identified previously by linkage analysis. While these results demonstrate the feasibility of genome-wide association strategies, further application of this approach will critically depend on optimizing the density and distribution of SNPs and the size and type of study design.     

The transmission disequilibrium test and imprinting effects test based on case-parent pairs

The transmission disequilibrium test (TDT) based on case-parents trios is a powerful tool in linkage analysis and association studies. When only one parent is available, the 1-TDT is applicable in the absence of imprinting. In the presence of imprinting, a statistic is proposed, based on case-mother pairs and case-father pairs to test for linkage when association is present as well as to test for association when linkage is present. The recombination fractions are allowed to be sex-specific in this test statistic. Meanwhile, a statistic based on case-parent pairs is proposed to test for imprinting. Both test statistics can be extended to include families with more than one affected offspring. A number of simulation studies are conducted to investigate the validity of the proposed tests. The effects of different ratios of the numbers of case-mother pairs and case-father pairs on the powers of the proposed tests are studied through simulation. The results show that the optimal ratio is 1:1. How to combine case-parents, case-mother pairs, and case-father pairs jointly in testing for linkage, association, and imprinting is addressed.     

Genomic scanning and the transmission/disequilibrium test: Analysis of error rates

A multi-allelic extension of the transmission/disequilibrium test (TDT) was applied to quantitative data from GAW10 Problem 2A by using thresholds to define affection status. Every one of 367 marker loci was screened. It was found that TDT results at neighboring loci are uncorrelated in these data (where the markers are in linkage equilibrium). It was also found that the chi-square statistics for both tests are larger than they should be so that the probability of false linkage detections is increased. Alternative approaches to the chi-square should be considered for assessing statistical significance. Results at marker D5G15 were strong, probably because of linkage without association. © 1997 Wiley-Liss, Inc.     

CAPL: a novel association test using case-control and family data and accounting for population stratification

The recent successes of GWAS based on large sample sizes motivate combining independent datasets to obtain larger sample sizes and thereby increase statistical power. Analysis methods that can accommodate different study designs, such as family-based and case-control designs, are of general interest. However, population stratification can cause spurious association for population-based association analyses. For family-based association analysis that infers missing parental genotypes based on the allele frequencies estimated in the entire sample, the parental mating-type probabilities may not be correctly estimated in the presence of population stratification. Therefore, any approach to combining family and case-control data should also properly account for population stratification. Although several methods have been proposed to accommodate family-based and case-control data, all have restrictions. Most of them require sampling a homogeneous population, which may not be a reasonable assumption for data from a large consortium. One of the methods, FamCC, can account for population stratification and uses nuclear families with arbitrary number of siblings but requires parental genotype data, which are often unavailable for late-onset diseases. We extended the family-based test, Association in the Presence of Linkage (APL), to combine family and case-control data (CAPL). CAPL can accommodate case-control data and families with multiple affected siblings and missing parents in the presence of population stratification. We used simulations to demonstrate that CAPL is a valid test either in a homogeneous population or in the presence of population stratification. We also showed that CAPL can have more power than other methods that combine family and case-control data.     

Effect of polygenes on Xiong's transmission disequilibrium test of a QTL in nuclear families with multiple children.

The transmission disequilibrium test (TDT), originally developed for mapping disease genes, has recently been extended to identify quantitative trait loci (QTL). For quantitative traits important for human health, generally multiple QTLs are involved. In the investigation of the statistical properties of the TDT, background polygenes (QTLs other than the QTL under test) generally have not been explicitly considered. The effects of background polygenes on the statistical properties of the TDT are thus largely unknown. Investigation of these effects will provide more realistic analyses of the statistical properties of the TDT under biologically plausible situations, and thus provide more accurate guidelines on the application of the TDT in practice. A general TDT (TDT(G)) has been developed to test linkage of a QTL in nuclear families that may be composed of more than one heterozygous parent and multiple children. Using the TDT(G) as an example, we develop an analytical method to investigate the effects of background polygenes on the power of the TDT. The accuracy of our analytical method is validated by computation simulations. We found that the power of the TDT(G) is increased with background polygenes when more than one child is employed in nuclear families, and the effect is stronger with more children per family recruited for study. The power of the TDT(G) increases dramatically when the number of children recruited from each nuclear family increases from one to two or from two to three. The type one error rate is not affected by the presence of background polygenes. The results of this study should be of theoretical significance in generalizing the investigation of the TDT to biologically plausible situations with background polygenes. They should also be of practical values in providing guidance on the recruitment of nuclear families with multiple children with the TDT(G).     

Haplotype sharing transmission/disequilibrium tests that allow for genotyping errors

The present study introduces new Haplotype Sharing Transmission/Disequilibrium Tests (HS-TDTs) that allow for random genotyping errors. We evaluate the type I error rate and power of the new proposed tests under a variety of scenarios and perform a power comparison among the proposed tests, the HS-TDT and the single-marker TDT. The results indicate that the HS-TDT shows a significant increase in type I error when applied to data in which either Mendelian inconsistent trios are removed or Mendelian inconsistent markers are treated as missing genotypes, and the magnitude of the type I error increases both with an increase in sample size and with an increase in genotyping error rate. The results also show that a simple strategy, that is, merging each rare haplotype to a most similar common haplotype, can control the type I error inflation for a wide range of genotyping error rates, and after merging rare haplotypes, the power of the test is very similar to that without merging the rare haplotypes. Therefore, we conclude that a simple strategy may make the HS-TDT robust to genotyping errors. Our simulation results also show that this strategy may also be applicable to other haplotype-based TDTs.     

Contrasting linkage disequilibrium as a multilocus family‐based association test

Linkage disequilibrium (LD) of genetic loci is routinely estimated and graphically illustrated in genetic association studies. It has been suggested that the information in LD is also useful for association mapping and genetic association can be detected by comparing LD patterns between cases and controls. Here, we extend this idea to analyze case‐parents data by comparing LD patterns between transmitted and nontransmitted genotypes. We provide the condition when contrasting LD is valid for testing gene‐gene interactions. A permutation procedure is given to assess statistical significance. One advantage of our proposed methods is that haplotype information is not required. Thus, the implementation of our methods is straightforward and the resulted tests are free from potential bias caused by assumptions made to estimate haplotypes in silico. Since our test statistics use pairwise LD measurements, they are less affected by missing data than many other multilocus methods. With simulated data, we demonstrate that examining LD patterns of case‐parents data is a useful multilocus association mapping strategy and it complements existing association mapping methods. The application of our methods to a Crohn's disease data set shows that our methods can detect multilocus association that might be missed by other association methods. Our permutation procedure can also be modified to allow multiple offspring from a family to be analyzed. Genet. Epidemiol. 2011. © 2011 Wiley‐Liss, Inc. 35: 487‐498, 2011     

VALID: visualization of association study results and linkage disequilibrium

Promising findings from genetic association studies are commonly presented with two distinct figures: one gives the association study results and the other indicates linkage disequilibrium (LD) between genetic markers in the region(s) of interest. Fully interpreting the results of such studies requires synthesizing the information in these figures, which is generally done in a subjective and unsystematic manner. Here we present a method to formally combine association results and LD and display them in the same figure; we have developed a freely available web‐based application that can be used to generate figures to display the combined data. To demonstrate this approach we apply it to fine mapping data from the prostate cancer 8q24 loci. Combining these two sources of information in a single figure allows one to more clearly assess patterns of association, facilitating the interpretation of genome‐wide and fine mapping data and improving our ability to localize causal variants. Genet. Epidemiol. 33:599–603, 2009. © 2009 Wiley‐Liss, Inc.     

A general method for linkage disequilibrium correction for multipoint linkage and association

Lately, many different methods of linkage, association or joint analysis for family data have been invented and refined. Common to most of those is that they require a map of markers that are in linkage equilibrium. However, at the present day, high-density single nucleotide polymorphisms (SNPs) maps are both more inexpensive to create and they have lower genotyping error. When marker data is incomplete, the crucial and computationally most demanding moment in the analysis is to calculate the inheritance distribution at a certain position on the chromosome. Recently, different ways of adjusting traditional methods of linkage analysis to denser maps of SNPs in linkage disequilibrium (LD) have been proposed. We describe a hidden Markov model which generalizes the Lander-Green algorithm. It combines Markov chain for inheritance vectors with a Markov chain modelling founder haplotypes and in this way takes account for LD between SNPs. It can be applied to association, linkage or combined association and linkage analysis, general phenotypes and arbitrary score functions. We also define a joint likelihood for linkage and association that extends an idea of Kong and Cox (1997 Am. J. Hum. Genet. 61: 1179-1188) for pure linkage analysis.     

The ordered transmission disequilibrium test: detection of modifier genes

We consider the problem of detection of modifier genes that lead to variations in a disease‐related continuous variable (DRCV), such as the age of onset or a measure of disease severity, in a strategy of candidate genes. We propose a novel method, the ordered transmission disequilibrium test (OTDT), to test for a relation between the clinical heterogeneity expressed by a DRCV and marker genotypes of a candidate gene. The OTDT applies to trio families with one patients and his parents, all three genotyped at a bi‐allelic marker M. The OTDT aims to find a critical value of the DRCV which separates the sample of families in two subsamples in which the transmission rates are significantly different. We investigate the power of the method by simulations under various genetic models and covariate distributions and compare it with a linear regression analysis. Genet. Epidemiol. 2008. ©2008 Wiley‐Liss, Inc.     

Haplotype sharing analysis with SNPs in candidate genes: the Genetic Analysis Workshop 12 example

Haplotype sharing analysis was used to investigate the association of affection status with single nucleotide polymorphism (SNP) haplotypes within candidate gene 1 in one sample each from the isolated and the general population of Genetic Analysis Workshop (GAW) 12 simulated data. Gene 1 has direct influence on affection and harbors more than 70 SNPs. Haplotype sharing analysis depends heavily on previous haplotype estimation. Using GENEHUNTER haplotypes, strong evidence was found for most SNPs in the isolated population sample, thus providing evidence for an involvement of this gene, but the maximum -log(10)(p) values for the haplotype sharing statistics (HSS) test statistic did not correspond to the location of the true variant in either population. In comparison, transmission disequilibrium test (TDT) analysis showed the strongest results at the disease-causing variant in both populations, and these were outstanding in the general population. In this example, TDT analysis appears to perform better than HSS in identifying the disease-causing variant, using SNPs within a candidate gene in an outbred population. Simulations showed that the performance of HSS is hampered by closely spaced SNPs in strong linkage disequilibrium with the functional variant and by ambiguous haplotypes.     

Linkage disequilibrium mapping with genotype data.

Linkage disequilibrium mapping has proven a powerful tool for locating disease genes. Although all existing linkage disequilibrium mapping methods implicitly assume that individual haplotypes can be inferred, only genotypes are directly observable in practice, and haplotypes cannot always be uniquely resolved based on genotype data. In this article, we propose a likelihood-based linkage disequilibrium mapping approach to analyzing multilocus genotype data arising from case-control studies. Results from extensive simulation studies suggest that this approach may be a useful tool to fine map disease genes using case-control data.     

Extent and distribution of linkage disequilibrium in the Old Order Amish

Knowledge of the extent and distribution of linkage disequilibrium (LD) is critical to the design and interpretation of gene mapping studies. Because the demographic history of each population varies and is often not accurately known, it is necessary to empirically evaluate LD on a population‐specific basis. Here we present the first genome‐wide survey of LD in the Old Order Amish (OOA) of Lancaster County Pennsylvania, a closed population derived from a modest number of founders. Specifically, we present a comparison of LD between OOA individuals and US Utah participants in the International HapMap project (abbreviated CEU) using a high‐density single nucleotide polymorphism (SNP) map. Overall, the allele (and haplotype) frequency distributions and LD profiles were remarkably similar between these two populations. For example, the median absolute allele frequency difference for autosomal SNPs was 0.05, with an inter‐quartile range of 0.02–0.09, and for autosomal SNPs 10–20 kb apart with common alleles (minor allele frequency≥0.05), the LD measure r² was at least 0.8 for 15 and 14% of SNP pairs in the OOA and CEU, respectively. Moreover, tag SNPs selected from the HapMap CEU sample captured a substantial portion of the common variation in the OOA (～88%) at r²≥0.8. These results suggest that the OOA and CEU may share similar LD profiles for other common but untyped SNPs. Thus, in the context of the common variant‐common disease hypothesis, genetic variants discovered in gene mapping studies in the OOA may generalize to other populations. Genet. Epidemiol. 34: 146–150, 2010. © 2009 Wiley‐Liss, Inc.     

Use of unphased multilocus genotype data in indirect association studies

It is usually assumed that detection of a disease susceptability gene via marker polymorphisms in linkage disequilibrium with it is facilitated by consideration of marker haplotypes. However, capture of the marker haplotype information requires resolution of gametic phase, and this must usually be inferred statistically. Recently, we questioned the value of the marker haplotype information, and suggested that certain analyses of multivariate marker data, not based on haplotypes explicitly and not requiring resolution of gametic phase, are often more powerful than analyses based on haplotypes. Here, we review this work and assess more carefully the situations in which our conclusions might apply. We also relate these analyses to alternative approaches to haplotype analysis, namely those based on haplotype similarity and those inspired by cladistics.     

Multipoint linkage disequilibrium mapping using case-control designs

Case-control study has been and continues to be one of the most popular designs in epidemiology. More recently, this design has been adopted to test for candidate genes when searching for disease genetic etiology. In this report, we present a multipoint linkage disequilibrium (LD) mapping approach with the focus on estimating the location of the target trait locus. It builds upon a representation, which shows that the difference between a case and a control in probabilities of carrying the target allele of a marker is proportional to that of the trait locus and that the proportionality factor is simply a measure of LD between the trait locus and the marker. Our method has the desired properties that (1) there is no need to specify phases of genotypic data with multiple markers, (2) it provides an estimate of location of the disease locus along with sampling uncertainty to help investigators to narrow chromosomal regions, and (3) a single test statistic is provided to test for LD in the framed region rather than testing the hypothesis one marker at a time. Our simulation work suggests that the proposed method performs well in terms of bias and coverage probability. Extension of the proposed method to account for confounding and genetic heterogeneity is discussed. We apply the proposed method to a published case-control data set for cystic fibrosis.