Multilocus association mapping using variable-length Markov chains

I propose a new method for association-based gene mapping that makes powerful use of multilocus data, is computationally efficient, and is straightforward to apply over large genomic regions. The approach is based on the fitting of variable-length Markov chain models, which automatically adapt to the degree of linkage disequilibrium (LD) between markers to create a parsimonious model for the LD structure. Edges of the fitted graph are tested for association with trait status. This approach can be thought of as haplotype testing with sophisticated windowing that accounts for extent of LD to reduce degrees of freedom and number of tests while maximizing information. I present analyses of two published data sets that show that this approach can have better power than single-marker tests or sliding-window haplotypic tests.     

Multipoint linkage analysis. A cautionary note.

Multipoint linkage analysis is commonly used to evaluate linkage of a disease to multiple markers in a small region. Multipoint analysis is particularly powerful when the IBD relations of family members at the trait locus are ambiguous. The increased power arises because, unlike single-marker analyses, multipoint analysis uses haplotype information from several markers to infer the IBD relations. We wish to temper this advantage with a cautionary note: multipoint analysis is sensitive to power loss due to misspecification of intermarker distances. Such misspecification is especially problematic when dealing with closely spaced markers. We present computer simulations comparing the power of single-point and multipoint analyses, both when IBD relations are ambiguous, and when the intermarker distances are misspecified. We conclude that when evaluating markers in a small region to confirm or refute previous findings, a situation in which p values of modest statistical significance are important, single marker analyses may provide more reliable measures of the strength of support for linkage than multipoint statistics.     

The APL test: extension to general nuclear families and haplotypes and examination of its robustness

OBJECTIVE: The Association in the Presence of Linkage test (APL) is a powerful statistical method that allows for missing parental genotypes in nuclear families. However, in its original form, the statistic does not easily extend to mixed nuclear family structures nor to multiple-marker haplotypes. Furthermore, the robustness of APL in practice has not been examined. Here we present a generalization of the APL model and examination of its robustness under a variety of non-standard scenarios. METHODS: The generalization is made possible by incorporating a bootstrap variance estimator instead of the original robust variance estimator. This allows for use of more than two affected siblings. Haplotype analysis was accomplished by combining estimation of haplotype phase into the EM algorithm. Computer simulation was used to examine robustness of the APL to departures from test assumptions. RESULTS: The extended APL tests both single-marker and multiple-marker haplotypes and shows more power than other association methods. Simulation results showed that the single-marker APL test is robust to the departure from HWE. For the haplotype test, violation of the HWE assumption can inflate type I error. We also evaluated general guidelines for the validity of APL with rare alleles and rare haplotypes. Software for the APL test is available from http://www.chg.duke.edu/research/apl.html.     

Further evidence for the increased power of LOD scores compared with nonparametric methods.

In genetic analysis of diseases in which the underlying model is unknown, "model free" methods-such as affected sib pair (ASP) tests-are often preferred over LOD-score methods, although LOD-score methods under the correct or even approximately correct model are more powerful than ASP tests. However, there might be circumstances in which nonparametric methods will outperform LOD-score methods. Recently, Dizier et al. reported that, in some complex two-locus (2L) models, LOD-score methods with segregation analysis-derived parameters had less power to detect linkage than ASP tests. We investigated whether these particular models, in fact, represent a situation that ASP tests are more powerful than LOD scores. We simulated data according to the parameters specified by Dizier et al. and analyzed the data by using a (a) single locus (SL) LOD-score analysis performed twice, under a simple dominant and a recessive mode of inheritance (MOI), (b) ASP methods, and (c) nonparametric linkage (NPL) analysis. We show that SL analysis performed twice and corrected for the type I-error increase due to multiple testing yields almost as much linkage information as does an analysis under the correct 2L model and is more powerful than either the ASP method or the NPL method. We demonstrate that, even for complex genetic models, the most important condition for linkage analysis is that the assumed MOI at the disease locus being tested is approximately correct, not that the inheritance of the disease per se is correctly specified. In the analysis by Dizier et al., segregation analysis led to estimates of dominance parameters that were grossly misspecified for the locus tested in those models in which ASP tests appeared to be more powerful than LOD-score analyses.     

Extending rare-variant testing strategies: analysis of noncoding sequence and imputed genotypes

Next Generation Sequencing Technology has revolutionized our ability to study the contribution of rare genetic variation to heritable traits. However, existing single-marker association tests are underpowered for detecting rare risk variants. A more powerful approach involves pooling methods that combine multiple rare variants from the same gene into a single test statistic. Proposed pooling methods can be limited because they generally assume high-quality genotypes derived from deep-coverage sequencing, which may not be available. In this paper, we consider an intuitive and computationally efficient pooling statistic, the cumulative minor-allele test (CMAT). We assess the performance of the CMAT and other pooling methods on datasets simulated with population genetic models to contain realistic levels of neutral variation. We consider study designs ranging from exon-only to whole-gene analyses that contain noncoding variants. For all study designs, the CMAT achieves power comparable to that of previously proposed methods. We then extend the CMAT to probabilistic genotypes and describe application to low-coverage sequencing and imputation data. We show that augmenting sequence data with imputed samples is a practical method for increasing the power of rare-variant studies. We also provide a method of controlling for confounding variables such as population stratification. Finally, we demonstrate that our method makes it possible to use external imputation templates to analyze rare variants imputed into existing GWAS datasets. As proof of principle, we performed a CMAT analysis of more than 8 million SNPs that we imputed into the GAIN psoriasis dataset by using haplotypes from the 1000 Genomes Project.     

Use of parents, sibs, and unrelated controls for detection of associations between genetic markers and disease.

Detecting the association between genetic markers and complex diseases can be a critical first step toward identification of the genetic basis of disease. Misleading associations can be avoided by choosing as controls the parents of diseased cases, but the availability of parents often limits this design to early-onset disease. Alternatively, sib controls offer a valid design. A general multivariate score statistic is presented, to detect the association between a multiallelic genetic marker locus and affection status; this general approach is applicable to designs that use parents as controls, sibs as controls, or even unrelated controls whose genotypes do not fit Hardy-Weinberg proportions or that pool any combination of these different designs. The benefit of this multivariate score statistic is that it will tend to be the most powerful method when multiple marker alleles are associated with affection status. To plan these types of studies, we present methods to compute sample size and power, allowing for varying sibship sizes, ascertainment criteria, and genetic models of risk. The results indicate that sib controls have less power than parental controls and that the power of sib controls can be increased by increasing either the number of affected sibs per sibship or the number of unaffected control sibs. The sample-size results indicate that the use of sib controls to test for associations, by use of either a single-marker locus or a genomewide screen, will be feasible for markers that have a dominant effect and for common alleles having a recessive effect. The results presented will be useful for investigators planning studies using sibs as controls.     

Genetic association mapping via evolution-based clustering of haplotypes

Multilocus analysis of single nucleotide polymorphism haplotypes is a promising approach to dissecting the genetic basis of complex diseases. We propose a coalescent-based model for association mapping that potentially increases the power to detect disease-susceptibility variants in genetic association studies. The approach uses Bayesian partition modelling to cluster haplotypes with similar disease risks by exploiting evolutionary information. We focus on candidate gene regions with densely spaced markers and model chromosomal segments in high linkage disequilibrium therein assuming a perfect phylogeny. To make this assumption more realistic, we split the chromosomal region of interest into sub-regions or windows of high linkage disequilibrium. The haplotype space is then partitioned into disjoint clusters, within which the phenotype–haplotype association is assumed to be the same. For example, in case-control studies, we expect chromosomal segments bearing the causal variant on a common ancestral background to be more frequent among cases than controls, giving rise to two separate haplotype clusters. The novelty of our approach arises from the fact that the distance used for clustering haplotypes has an evolutionary interpretation, as haplotypes are clustered according to the time to their most recent common ancestor. Our approach is fully Bayesian and we develop a Markov Chain Monte Carlo algorithm to sample efficiently over the space of possible partitions. We compare the proposed approach to both single-marker analyses and recently proposed multi-marker methods and show that the Bayesian partition modelling performs similarly in localizing the causal allele while yielding lower false-positive rates. Also, the method is computationally quicker than other multi-marker approaches. We present an application to real genotype data from the CYP2D6 gene region, which has a confirmed role in drug metabolism, where we succeed in mapping the location of the susceptibility variant within a small error.     

Effect of two- and three-locus linkage disequilibrium on the power to detect marker/phenotype associations

There has been much recent interest in describing the patterns of linkage disequilibrium (LD) along a chromosome. Most empirical studies that have examined this issue have concentrated on LD between collections of pairs of markers and have not considered the joint effect of a group of markers beyond these pairwise connections. Here, we examine many different patterns of LD defined by both pairwise and joint multilocus LD terms. The LD patterns we considered were chosen in part by examining those seen in real data. We examine how changes in these patterns affect the power to detect association when performing single-marker and haplotype-based case-control tests, including a novel haplotype test based on contrasting LD between affected and unaffected individuals. Through our studies we find that differences in power between single-marker tests and haplotype-based tests in general do not appear to be large. Where moderate to high levels of multilocus LD exist, haplotype tests tend to be more powerful. Single-marker tests tend to prevail when pairwise LD is high. For moderate pairwise values and weak multilocus LD, either testing strategy may come out ahead, although it is also quite likely that neither has much power.     

Methods to impute missing genotypes for population data

For large-scale genotyping studies, it is common for most subjects to have some missing genetic markers, even if the missing rate per marker is low. This compromises association analyses, with varying numbers of subjects contributing to analyses when performing single-marker or multi-marker analyses. In this paper, we consider eight methods to infer missing genotypes, including two haplotype reconstruction methods (local expectation maximization-EM, and fastPHASE), two k-nearest neighbor methods (original k-nearest neighbor, KNN, and a weighted k-nearest neighbor, wtKNN), three linear regression methods (backward variable selection, LM.back, least angle regression, LM.lars, and singular value decomposition, LM.svd), and a regression tree, Rtree. We evaluate the accuracy of them using single nucleotide polymorphism (SNP) data from the HapMap project, under a variety of conditions and parameters. We find that fastPHASE has the lowest error rates across different analysis panels and marker densities. LM.lars gives slightly less accurate estimate of missing genotypes than fastPHASE, but has better performance than the other methods.     

Testing association of statistically inferred haplotypes with discrete and continuous traits in samples of unrelated individuals

There have been increasing efforts to relate drug efficacy and disease predisposition with genetic polymorphisms. We present statistical tests for association of haplotype frequencies with discrete and continuous traits in samples of unrelated individuals. Haplotype frequencies are estimated through the expectation-maximization algorithm, and each individual in the sample is expanded into all possible haplotype configurations with corresponding probabilities, conditional on their genotype. A regression-based approach is then used to relate inferred haplotype probabilities to the response. The relationship of this technique to commonly used approaches developed for case-control data is discussed. We confirm the proper size of the test under H(0) and find an increase in power under the alternative by comparing test results using inferred haplotypes with single-marker tests using simulated data. More importantly, analysis of real data comprised of a dense map of single nucleotide polymorphisms spaced along a 12-cM chromosomal region allows us to confirm the utility of the haplotype approach as well as the validity and usefulness of the proposed statistical technique. The method appears to be successful in relating data from multiple, correlated markers to response.     

A theoretical treatment of interval mapping of a disease gene using transmission disequilibrium tests

The genetic basis of the transmission disequilibrium test (TDT) for two-marker loci is explored from first principles. In this case, parents doubly heterozygous for a given haplotype at the pair of marker loci that are each in linkage disequilibrium with the disease gene with the further possibility of a second-order linkage disequilibrium are considered. The number of times such parents transmit the given haplotype to their affected offspring is counted and compared with the frequencies of haplotypes that are not transmitted. This is done separately for the coupling and repulsion phases of doubly heterozygous genotypes. Expectations of the counts for each of the sixteen cells possible with four-marker gametic types (transmitted vs not transmitted) are derived. Based on a test of symmetry in a square 4 x 4 contingency table, chi-square tests are proposed for the null hypothesis of no linkage between the markers and the disease gene. The power of the tests is discussed in terms of the corresponding non-centrality parameters for the alternative hypothesis that both the markers are linked with the disease locus. The results indicate that the power increases with the decrease in recombination probability and that it is higher for a lower frequency of the disease gene. Taking a pair of markers in an interval for exploring the linkage with the disease gene seems to be more informative than the single-marker case since the values of the non-centrality parameters tend to be consistently higher than their counterparts in the single-marker case. Limitations of the proposed test are also discussed.     

Associations between sperm competition and natural variation in male reproductive genes on the third chromosome of Drosophila melanogaster

We applied association analysis to elucidate the genetic basis for variation in phenotypes affecting postcopulatory sexual selection in a natural population of Drosophila melanogaster. We scored 96 third chromosome substitution lines for nine phenotypes affecting sperm competitive ability and genotyped them at 72 polymorphisms in 13 male reproductive genes. Significant heterogeneity among lines (P < 0.01) was detected for all phenotypes except male-induced refractoriness (P = 0.053). We identified 24 associations (8 single-marker associations, 12 three-marker haplotype associations, and 4 cases of epistasis revealed by single-marker interactions). Fewer than 9 of these associations are likely to be false positives. Several associations were consistent with previous findings [Acp70A with the male's influence on the female's refractoriness to remating (refractory), Esterase-6 with a male's remating probability (remating) and a measure of female offspring production (fecundity)], but many are novel associations with uncharacterized seminal fluid proteins. Four genes showed evidence for pleiotropic effects [CG6168 with a measure of sperm competition (P2') and refractory, CG14560 with a defensive measure of sperm competition (P1') and a measure of female fecundity, Acp62F with P2' and a measure of female fecundity, and Esterase-6 with remating and a measure of female fecundity]. Our findings provide evidence that pleiotropy and epistasis are important factors in the genetic architecture of male reproductive success and show that haplotype analyses can identify associations missed in the single-marker approach.     

The role of parametric linkage methods in complex trait analyses using microsatellites

Many investigators of complexly inherited familial traits bypass classical segregation analysis to perform model-free genome-wide linkage scans. Because model-based or parametric linkage analysis may be the most powerful means to localize genes when a model can be approximated, model-free statistics may result in a loss of power to detect linkage. We performed limited segregation analyses on the electrophysiological measurements that have been collected for the Collaborative Study on the Genetics of Alcoholism. The resulting models are used in whole-genome scans. Four genomic regions provided a model-based LOD > 2 and only 3 of these were detected (p < 0.05) by a model-free approach. We conclude that parametric methods, using even over-simplified models of complex phenotypes, may complement nonparametric methods and decrease false positives.     

A theoretical treatment of interval mapping of a disease gene using transmission disequilibrium tests

The genetic basis of the transmission disequilibrium test (TDT) for two-marker loci is explored from first principles. In this case, parents doubly heterozygous for a given haplotype at the pair of marker loci that are each in linkage disequilibrium with the disease gene with the further possibility of a second-order linkage disequilibrium are considered. The number of times such parents transmit the given haplotype to their affected offspring is counted and compared with the frequencies of haplotypes that are not transmitted. This is done separately for the coupling and repulsion phases of doubly heterozygous genotypes. Expectations of the counts for each of the sixteen cells possible with four-marker gametic types (transmitted vs not transmitted) are derived. Based on a test of symmetry in a square 4 × 4 contingency table, chi-square tests are proposed for the null hypothesis of no linkage between the markers and the disease gene. The power of the tests is discussed in terms of the corresponding non-centrality parameters for the alternative hypothesis that both the markers are linked with the disease locus. The results indicate that the power increases with the decrease in recombination probability and that it is higher for a lower frequency of the disease gene. Taking a pair of markers in an interval for exploring the linkage with the disease gene seems to be more informative than the single-marker case since the values of the non-centrality parameters tend to be consistently higher than their counterparts in the single-marker case. Limitations of the proposed test are also discussed.     

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.     

Haplotype-sharing analysis using Mantel statistics for combined genetic effects

We applied a new approach based on Mantel statistics to analyze the Genetic Analysis Workshop 14 simulated data with prior knowledge of the answers. The method was developed in order to improve the power of a haplotype sharing analysis for gene mapping in complex disease. The new statistic correlates genetic similarity and phenotypic similarity across pairs of haplotypes from case-control studies. The genetic similarity is measured as the shared length between haplotype pairs around a genetic marker. The phenotypic similarity is measured as the mean corrected cross-product based on the respective phenotypes. Cases with phenotype P1 and unrelated controls were drawn from the population of Danacaa. Power to detect main effects was compared to the X2-test for association based on 3-marker haplotypes and a global permutation test for haplotype association to test for main effects. Power to detect gene x gene interaction was compared to unconditional logistic regression. The results suggest that the Mantel statistics might be more powerful than alternative tests.     

On different approximations to multilocus identity-by-descent calculations and the resulting power of variance component-based linkage analysis

An empirical comparison between three different methods for estimation of pair-wise identity-by-descent (IBD) sharing at marker loci was conducted in order to quantify the resulting differences in power and localization precision in variance components-based linkage analysis. On the examined simulated, error-free data set, it was found that an increase in accuracy of allele sharing calculation resulted in an increase in power to detect linkage. Linkage analysis based on approximate multi-marker IBD matrices computed by a Markov chain Monte Carlo approach was much more powerful than linkage analysis based on exact single-marker IBD probabilities. A "multiple two-point" approximation to true "multipoint" IBD computation was found to be roughly intermediate in power. Both multi-marker approaches were similar to each other in accuracy of localization of the quantitative trait locus and far superior to the single-marker approach. The overall conclusions of this study with respect to power are expected to also hold for different data structures and situations, even though the degree of superiority of one approach over another depends on the specific circumstances. It should be kept in mind, however, that an increase in computational accuracy is expected to go hand in hand with a decrease in robustness to various sources of errors.     

Resampling-based multiple testing methods with covariate adjustment: application to investigation of antiretroviral drug susceptibility

Summary .   Identifying genetic mutations that cause clinical resistance to antiretroviral drugs requires adjustment for potential confounders, such as the number of active drugs in a HIV-infected patient's regimen other than the one of interest. Motivated by this problem, we investigated resampling-based methods to test equal mean response across multiple groups defined by HIV genotype, after adjustment for covariates. We consider construction of test statistics and their null distributions under two types of model: parametric and semiparametric. The covariate function is explicitly specified in the parametric but not in the semiparametric approach. The parametric approach is more precise when models are correctly specified, but suffer from bias when they are not; the semiparametric approach is more robust to model misspecification, but may be less efficient. To help preserve type I error while also improving power in both approaches, we propose resampling approaches based on matching of observations with similar covariate values. Matching reduces the impact of model misspecification as well as imprecision in estimation. These methods are evaluated via simulation studies and applied to a data set that combines results from a variety of clinical studies of salvage regimens. Our focus is on relating HIV genotype to viral susceptibility to abacavir after adjustment for the number of active antiretroviral drugs (excluding abacavir) in the patient's regimen.     

Genetic spatial autocorrelation can readily detect sex-biased dispersal

Sex-biased dispersal is expected to generate differences in the fine-scale genetic structure of males and females. Therefore, spatial analyses of multilocus genotypes may offer a powerful approach for detecting sex-biased dispersal in natural populations. However, the effects of sex-biased dispersal on fine-scale genetic structure have not been explored. We used simulations and multilocus spatial autocorrelation analysis to investigate how sex-biased dispersal influences fine-scale genetic structure. We evaluated three statistical tests for detecting sex-biased dispersal: bootstrap confidence intervals about autocorrelation r values and recently developed heterogeneity tests at the distance class and whole correlogram levels. Even modest sex bias in dispersal resulted in significantly different fine-scale spatial autocorrelation patterns between the sexes. This was particularly evident when dispersal was strongly restricted in the less-dispersing sex (mean distance <200 m), when differences between the sexes were readily detected over short distances. All tests had high power to detect sex-biased dispersal with large sample sizes (n ≥ 250). However, there was variation in type I error rates among the tests, for which we offer specific recommendations. We found congruence between simulation predictions and empirical data from the agile antechinus, a species that exhibits male-biased dispersal, confirming the power of individual-based genetic analysis to provide insights into asymmetries in male and female dispersal. Our key recommendations for using multilocus spatial autocorrelation analyses to test for sex-biased dispersal are: (i) maximize sample size, not locus number; (ii) concentrate sampling within the scale of positive structure; (iii) evaluate several distance class sizes; (iv) use appropriate methods when combining data from multiple populations; (v) compare the appropriate groups of individuals.     

Linkage analysis in the presence of errors IV: joint pseudomarker analysis of linkage and/or linkage disequilibrium on a mixture of pedigrees and singletons when the mode of inheritance cannot be accurately specified

There is a lot of confusion in the literature about the "differences" between "model-based" and "model-free" methods and about which approach is better suited for detection of the genes predisposing to complex multifactorial phenotypes. By starting from first principles, we demonstrate that the differences between the two approaches have more to do with study design than statistical analysis. When simple data structures are repeatedly ascertained, no assumptions about the genotype-phenotype relationship need to be made for the analysis to be powerful, since simple data structures admit only a small number of df. When more complicated and/or heterogeneous data structures are ascertained, however, the number of df in the underlying probability model is too large to have a powerful, truly "model-free" test. So-called "model-free" methods typically simplify the underlying probability model by implicitly assuming that, in some sense, all meioses connecting two affected individuals are informative for linkage with identical probability and that the affected individuals in a pedigree share as many disease-predisposing alleles as possible. By contrast, "model-based" methods add structure to the underlying parameter space by making assumptions about the genotype-phenotype relationship, making it possible to probabilistically assign disease-locus genotypes to all individuals in the data set on the basis of the observed phenotypes. In this study, we demonstrate the equivalence of these two approaches in a variety of situations and exploit this equivalence to develop more powerful and efficient likelihood-based analogues of "model-free" tests of linkage and/or linkage disequilibrium. Through the use of a "pseudomarker" locus to structure the space of observations, sib-pairs, triads, and singletons can be analyzed jointly, which will lead to tests that are more well-behaved, efficient, and powerful than traditional "model-free" tests such as the affected sib-pair, transmission/disequilibrium, haplotype relative risk, and case-control tests. Also described is an extension of this approach to large pedigrees, which, in practice, is equivalent to affected relative-pair analysis. The proposed methods are equally applicable to two-point and multipoint analysis (using complex-valued recombination fractions).