Non-iterative, regression-based estimation of haplotype associations with censored survival outcomes

The general availability of reliable and affordable genotyping technology has enabled genetic association studies to move beyond small case-control studies to large prospective studies. For prospective studies, genetic information can be integrated into the analysis via haplotypes, with focus on their association with a censored survival outcome. We develop non-iterative, regression-based methods to estimate associations between common haplotypes and a censored survival outcome in large cohort studies. Our non-iterative methods--weighted estimation and weighted haplotype combination--are both based on the Cox regression model, but differ in how the imputed haplotypes are integrated into the model. Our approaches enable haplotype imputation to be performed once as a simple data-processing step, and thus avoid implementation based on sophisticated algorithms that iterate between haplotype imputation and risk estimation. We show that non-iterative weighted estimation and weighted haplotype combination provide valid tests for genetic associations and reliable estimates of moderate associations between common haplotypes and a censored survival outcome, and are straightforward to implement in standard statistical software. We apply the methods to an analysis of HSPB7-CLCNKA haplotypes and risk of adverse outcomes in a prospective cohort study of outpatients with chronic heart failure.     

The accuracy of statistical methods for estimation of haplotype frequencies: an example from the CD4 locus

Haplotype analysis has become increasingly important for the study of human disease as well as for reconstruction of human population histories. Computer programs have been developed to estimate haplotype frequencies statistically from marker phenotypes in unrelated individuals. However, there currently are few empirical reports on the accuracy of statistical estimates that must infer linkage phase. We have analyzed haplotypes at the CD4 locus on chromosome 12 that consist of a short tandem-repeat polymorphism and an Alu insertion/deletion polymorphism located 9.8 kb apart, in 398 individuals from 10 geographically diverse sub-Saharan African populations. Haplotype frequency estimates obtained using gene counting based on molecularly haplotyped (phase-known) data were compared with haplotype frequency estimates obtained using the expectation-maximization algorithm. We show that the estimated frequencies of common haplotypes do not differ significantly with the use of phase-known versus phase-unknown data. However, rare haplotypes are occasionally miscalled when their presence/absence must be inferred. Thus, for those research questions for which the common haplotypes are most important, frequency estimates based on the phase-unknown marker-typing results from unrelated individuals will be sufficient. However, in cases where knowledge of rare haplotypes is critical, molecular haplotyping will be necessary to determine linkage phase unambiguously.     

Little loss of information due to unknown phase for fine-scale linkage-disequilibrium mapping with single-nucleotide-polymorphism genotype data

We present the results of a simulation study that indicate that true haplotypes at multiple, tightly linked loci often provide little extra information for linkage-disequilibrium fine mapping, compared with the information provided by corresponding genotypes, provided that an appropriate statistical analysis method is used. In contrast, a two-stage approach to analyzing genotype data, in which haplotypes are inferred and then analyzed as if they were true haplotypes, can lead to a substantial loss of information. The study uses our COLDMAP software for fine mapping, which implements a Markov chain-Monte Carlo algorithm that is based on the shattered coalescent model of genetic heterogeneity at a disease locus. We applied COLDMAP to 100 replicate data sets simulated under each of 18 disease models. Each data set consists of haplotype pairs (diplotypes) for 20 SNPs typed at equal 50-kb intervals in a 950-kb candidate region that includes a single disease locus located at random. The data sets were analyzed in three formats: (1). as true haplotypes; (2). as haplotypes inferred from genotypes using an expectation-maximization algorithm; and (3). as unphased genotypes. On average, true haplotypes gave a 6% gain in efficiency compared with the unphased genotypes, whereas inferring haplotypes from genotypes led to a 20% loss of efficiency, where efficiency is defined in terms of root mean integrated square error of the location of the disease locus. Furthermore, treating inferred haplotypes as if they were true haplotypes leads to considerable overconfidence in estimates, with nominal 50% credibility intervals achieving, on average, only 19% coverage. We conclude that (1). given appropriate statistical analyses, the costs of directly measuring haplotypes will rarely be justified by a gain in the efficiency of fine mapping and that (2). a two-stage approach of inferring haplotypes followed by a haplotype-based analysis can be very inefficient for fine mapping, compared with an analysis based directly on the genotypes.     

Estimating haplotype effects on dichotomous outcome for unphased genotype data using a weighted penalized log-likelihood approach

OBJECTIVE: To develop a method to estimate haplotype effects on dichotomous outcomes when phase is unknown, that can also estimate reliable effects of rare haplotypes. METHODS: In short, the method uses a logistic regression approach, with weights attached to all possible haplotype combinations of an individual. An EM-algorithm was used: in the E-step the weights are estimated, and the M-step consists of maximizing the joint log-likelihood. When rare haplotypes were present, a penalty function was introduced. We compared four different penalties. To investigate statistical properties of our method, we performed a simulation study for different scenarios. The evaluation criteria are the mean bias of the parameter estimates, the root of the mean squared error, the coverage probability, power, Type I error rate and the false discovery rate. RESULTS: For the unpenalized approach, mean bias was small, coverage probabilities were approximately 95%, power ranged from 15.2 to 44.7% depending on haplotype frequency, and Type I error rate was around 5%. All penalty functions reduced the standard errors of the rare haplotypes, but introduced bias. This trade-off decreased power. CONCLUSION: The unpenalized weighted log-likelihood approach performs well. A penalty function can help to estimate an effect for rare haplotypes.     

A deductive method of haplotype analysis in pedigrees.

Derivation of haplotypes from pedigree data by means of likelihood techniques requires large computational resources and is thus highly limited in terms of the complexity of problems that can be analyzed. The present paper presents 20 rules of logic that are both necessary and sufficient for deriving haplotypes by means of nonstatistical techniques. As a result, automated haplotype analysis that uses these rules is fast and efficient, requiring computer memory that increases only linearly (rather than exponentially) with family size and the number of factors under analysis. Some error analysis is also possible. The rules are completely general with regard to any system of completely linked, discrete genetic markers that are autosomally inherited. There are no limitations on pedigree structure or the amount of missing data, although the existence of incomplete data usually reduces the fraction of haplotypes that can be completely determined.     

Accuracy of genomic selection using different methods to define haplotypes

Genomic selection uses total breeding values for juvenile animals, predicted from a large number of estimated marker haplotype effects across the whole genome. In this study the accuracy of predicting breeding values is compared for four different models including a large number of markers, at different marker densities for traits with heritabilities of 50 and 10%. The models estimated the effect of (1) each single-marker allele [single-nucleotide polymorphism (SNP)1], (2) haplotypes constructed from two adjacent marker alleles (SNP2), and (3) haplotypes constructed from 2 or 10 markers, including the covariance between haplotypes by combining linkage disequilibrium and linkage analysis (HAP_IBD2 and HAP_IBD10). Between 119 and 2343 polymorphic SNPs were simulated on a 3-M genome. For the trait with a heritability of 10%, the differences between models were small and none of them yielded the highest accuracies across all marker densities. For the trait with a heritability of 50%, the HAP_IBD10 model yielded the highest accuracies of estimated total breeding values for juvenile and phenotyped animals at all marker densities. It was concluded that genomic selection is considerably more accurate than traditional selection, especially for a low-heritability trait.     

Identification of equine major histocompatibility complex haplotypes using polymorphic microsatellites

A system for identifying equine major histocompatibility complex (MHC) haplotypes was developed based on five polymorphic microsatellites located within the MHC region on ECA 20. Molecular signatures for 50 microsatellite haplotypes were recognized from typing 353 horses. Of these, 23 microsatellite haplotypes were associated with 12 established equine leucocyte antigen (ELA) haplotypes in Thoroughbreds and Standardbreds. Five ELA serotypes were associated with multiple microsatellite subhaplotypes, expanding the estimates of diversity in the equine MHC. The strong correlations between serological and microsatellite typing demonstrated a linkage to known MHC class I protein polymorphisms and validated this assay as a useful supplement to ELA serotyping, and in some applications, a feasible alternative method for MHC genotyping in horse families and in population studies.     

The impact of using related individuals for haplotype reconstruction in population studies

Recent studies have highlighted the dangers of using haplotypes reconstructed directly from population data for a fine-scale mapping analysis. Family data may help resolve ambiguity, yet can be costly to obtain. This study is concerned with the following question: How much family data (if any) should be used to facilitate haplotype reconstruction in a population study? We conduct a simulation study to evaluate how changes in family information can affect the accuracy of haplotype frequency estimates and phase reconstruction. To reconstruct haplotypes, we introduce an EM-based algorithm that can efficiently accommodate unrelated individuals, parent-child trios, and arbitrarily large half-sib pedigrees. Simulations are conducted for a diverse set of haplotype frequency distributions, all of which have been previously published in empirical studies. A wide variety of important results regarding the effectiveness of using pedigree data in a population study are presented in a coherent, unified framework. Insight into the different properties of the haplotype frequency distribution that can influence experimental design is provided. We show that a preliminary estimate of the haplotype frequency distribution can be valuable in large population studies with fixed resources.     

Low genetic diversity and significant structuring of the common hamster populations <Emphasis Type="Italic">Cricetus cricetus</Emphasis> in Poland revealed by the mtDNA control region sequence variation

The genetic diversity of 12 populations in the present range of the common hamster Cricetus cricetus (Linnaeus, 1758) in Poland was established. The 366 bp of the mtDNA control region was sequenced for 195 individuals. As few as seven haplotypes were found and their distribution was geographically structured. The large geographic areas were fixed or almost fixed for a single haplotype and three groups of populations, that do not share any haplotypes, have been defined. Proportions of genetic diversity attributable to variation between groups of populations, between populations within groups and within populations were 93.64, 1.92 and 4.45% (SAMOVA: p < 0.001 for all estimates), respectively. Such pattern of variation is most probably the result of historical, postglacial bottlenecks and present genetic drift after the population decline in the last few decades.     

Inference of haplotype effects in case-control studies using unphased genotype and environmental data

A retrospective likelihood-based approach was proposed to test and estimate the effect of haplotype on disease risk using unphased genotype data with adjustment for environmental covariates. The proposed method was also extended to handle the data in which the haplotype and environmental covariates are not independent. Likelihood ratio tests were constructed to test the effects of haplotype and gene-environment interaction. The model parameters such as haplotype effect size was estimated using an Expectation Conditional-Maximization (ECM) algorithm developed by Meng and Rubin (1993). Model-based variance estimates were derived using the observed information matrix. Simulation studies were conducted for three different genetic effect models, including dominant effect, recessive effect, and additive effect. The results showed that the proposed method generated unbiased parameter estimates, proper type I error, and true beta coverage probabilities. The model performed well with small or large sample sizes, as well as short or long haplotypes.     

Maximum likelihood estimation of linkage disequilibrium in half-sib families

Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ=0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium.     

Rivers influence the population genetic structure of bonobos (Pan paniscus)

Bonobos are large, highly mobile primates living in the relatively undisturbed, contiguous forest south of the Congo River. Accordingly, gene flow among populations is assumed to be extensive, but may be impeded by large, impassable rivers. We examined mitochondrial DNA control region sequence variation in individuals from five distinct localities separated by rivers in order to estimate relative levels of genetic diversity and assess the extent and pattern of population genetic structure in the bonobo. Diversity estimates for the bonobo exceed those for humans, but are less than those found for the chimpanzee. All regions sampled are significantly differentiated from one another, according to genetic distances estimated as pairwise FSTs, with the greatest differentiation existing between region East and each of the two Northern populations (N and NE) and the least differentiation between regions Central and South. The distribution of nucleotide diversity shows a clear signal of population structure, with some 30% of the variance occurring among geographical regions. However, a geographical patterning of the population structure is not obvious. Namely, mitochondrial haplotypes were shared among all regions excepting the most eastern locality and the phylogenetic analysis revealed a tree in which haplotypes were intermixed with little regard to geographical origin, with the notable exception of the close relationships among the haplotypes found in the east. Nonetheless, genetic distances correlated with geographical distances when the intervening distances were measured around rivers presenting effective current-day barriers, but not when straight-line distances were used, suggesting that rivers are indeed a hindrance to gene flow in this species.     

Screening for recently selected alleles by analysis of human haplotype similarity

There is growing interest in the use of haplotype-based methods for detecting recent selection. Here, we describe a method that uses a sliding window to estimate similarity among the haplotypes associated with any given single-nucleotide polymorphism (SNP) allele. We used simulations of natural selection to provide estimates of the empirical power of the method to detect recently selected alleles and found it to be comparable in power to the popular long-range haplotype test and more powerful than methods based on nucleotide diversity. We then applied the method to a recently selected allele--the sickle mutation at the HBB locus--and found it to have a signal of selection that was significantly stronger than that of simulated models both with and without strong selection. Using this method, we also evaluated >4,000 SNPs on chromosome 20, indicating the applicability of the method to regional data sets.     

Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.     

Haplotype reconstruction error as a classical misclassification problem: introducing sensitivity and specificity as error measures

Background

Statistically reconstructing haplotypes from single nucleotide polymorphism (SNP) genotypes, can lead to falsely classified haplotypes. This can be an issue when interpreting haplotype association results or when selecting subjects with certain haplotypes for subsequent functional studies. It was our aim to quantify haplotype reconstruction error and to provide tools for it.

Methods and Results

By numerous simulation scenarios, we systematically investigated several error measures, including discrepancy, error rate, and R², and introduced the sensitivity and specificity to this context. We exemplified several measures in the KORA study, a large population-based study from Southern Germany. We find that the specificity is slightly reduced only for common haplotypes, while the sensitivity was decreased for some, but not all rare haplotypes. The overall error rate was generally increasing with increasing number of loci, increasing minor allele frequency of SNPs, decreasing correlation between the alleles and increasing ambiguity.

Conclusions

We conclude that, with the analytical approach presented here, haplotype-specific error measures can be computed to gain insight into the haplotype uncertainty. This method provides the information, if a specific risk haplotype can be expected to be reconstructed with rather no or high misclassification and thus on the magnitude of expected bias in association estimates. We also illustrate that sensitivity and specificity separate two dimensions of the haplotype reconstruction error, which completely describe the misclassification matrix and thus provide the prerequisite for methods accounting for misclassification.     

Disclosing the genetic structure of Brazil through analysis of male lineages with highly discriminating haplotypes

In a large variety of genetic studies, probabilistic inferences are made based on information available in population databases. The accuracy of the estimates based on population samples are highly dependent on the number of chromosomes being analyzed as well as the correct representation of the reference population. For frequency calculations the size of a database is especially critical for haploid markers, and for countries with complex admixture histories it is important to assess possible substructure effects that can influence the coverage of the database. Aiming to establish a representative Brazilian population database for haplotypes based on 23 Y chromosome STRs, more than 2,500 Y chromosomes belonging to Brazilian, European and African populations were analyzed. No matter the differences in the colonization history of the five geopolitical regions that currently exist in Brazil, for the Y chromosome haplotypes of the 23 studied Y-STRs, a lack of genetic heterogeneity was found, together with a predominance of European male lineages in all regions of the country. Therefore, if we do not consider the diverse Native American or Afro-descendent isolates, which are spread through the country, a single Y chromosome haplotype frequency database will adequately represent the urban populations in Brazil. In comparison to the most commonly studied group of 17 Y-STRs, the 23 markers included in this work allowed a high discrimination capacity between haplotypes from non-related individuals within a population and also increased the capacity to discriminate between paternal relatives. Nevertheless, the expected haplotype mutation rate is still not enough to distinguish the Y chromosome profiles of paternally related individuals. Indeed, even for rapidly mutating Y-STRs, a very large number of markers will be necessary to differentiate male lineages from paternal relatives.     

An entropy-based genome-wide transmission/disequilibrium test

Availability of a large collection of single nucleotide polymorphisms (SNPs) and efficient genotyping methods enable the extension of linkage and association studies for complex diseases from small genomic regions to the whole genome. Establishing global significance for linkage or association requires small P-values of the test. The original TDT statistic compares the difference in linear functions of the number of transmitted and nontransmitted alleles or haplotypes. In this report, we introduce a novel TDT statistic, which uses Shannon entropy as a nonlinear transformation of the frequencies of the transmitted or nontransmitted alleles (or haplotypes), to amplify the difference in the number of transmitted and nontransmitted alleles or haplotypes in order to increase statistical power with large number of marker loci. The null distribution of the entropy-based TDT statistic and the type I error rates in both homogeneous and admixture populations are validated using a series of simulation studies. By analytical methods, we show that the power of the entropy-based TDT statistic is higher than the original TDT, and this difference increases with the number of marker loci. Finally, the new entropy-based TDT statistic is applied to two real data sets to test the association of the RET gene with Hirschsprung disease and the Fcγ receptor genes with systemic lupus erythematosus. Results show that the entropy-based TDT statistic can reach p-values that are small enough to establish genome-wide linkage or association analyses.     

Multipoint identity-by-descent prediction using dense markers to map quantitative trait loci and estimate effective population size

A novel multipoint method, based on an approximate coalescence approach, to analyze multiple linked markers is presented. Unlike other approximate coalescence methods, it considers all markers simultaneously but only two haplotypes at a time. We demonstrate the use of this method for linkage disequilibrium (LD) mapping of QTL and estimation of effective population size. The method estimates identity-by-descent (IBD) probabilities between pairs of marker haplotypes. Both LD and combined linkage and LD mapping rely on such IBD probabilities. The method is approximate in that it considers only the information on a pair of haplotypes, whereas a full modeling of the coalescence process would simultaneously consider all haplotypes. However, full coalescence modeling is computationally feasible only for few linked markers. Using simulations of the coalescence process, the method is shown to give almost unbiased estimates of the effective population size. Compared to direct marker and haplotype association analyses, IBD-based QTL mapping showed clearly a higher power to detect a QTL and a more realistic confidence interval for its position. The modeling of LD could be extended to estimate other LD-related parameters such as recombination rates.     

High diversity of alpha-globin haplotypes in a Senegalese population, including many previously unreported variants.

RFLP haplotypes at the alpha-globin gene complex have been examined in 190 individuals from the Niokolo Mandenka population of Senegal: haplotypes were assigned unambiguously for 210 chromosomes. The Mandenka share with other African populations a sample size-independent haplotype diversity that is much greater than that in any non-African population: the number of haplotypes observed in the Mandenka is typically twice that seen in the non-African populations sampled to date. Of these haplotypes, 17.3% had not been observed in any previous surveys, and a further 19.1% have previously been reported only in African populations. The haplotype distribution shows clear differences between African and non-African peoples, but this is on the basis of population-specific haplotypes combined with haplotypes common to all. The relationship of the newly reported haplotypes to those previously recorded suggests that several mutation processes, particularly recombination as homologous exchange or gene conversion, have been involved in their production. A computer program based on the expectation-maximization (EM) algorithm was used to obtain maximum-likelihood estimates of haplotype frequencies for the entire data set: good concordance between the unambiguous and EM-derived sets was seen for the overall haplotype frequencies. Some of the low-frequency haplotypes reported by the estimation algorithm differ greatly, in structure, from those haplotypes known to be present in human populations, and they may not represent haplotypes actually present in the sample.