Haplotype reconstruction and estimation of haplotype frequencies from nuclear families with only one parent available

Recent literature has suggested that haplotype inference through close relatives, especially from nuclear families can be an alternative strategy in determining the linkage phase. In this paper, haplotype reconstruction and estimation of haplotype frequencies via expectation maximization (EM) algorithm including nuclear families with only one parent available is proposed. Parent and his (her) child are treated as parent-child pair with one shared haplotype. This reduces the number of potential haplotype pairs for both parent and child separately, resulting in a higher accuracy of the estimation. In a series of simulations, the comparisons of PHASE, GENEHUNTER, EM-based approach for complete nuclear families and our approach are carried out. In all situations, EM-based approach for trio data is comparable but slightly worse error rate than PHASE, our approach is slightly better and much faster than PHASE for incomplete trios, the performance of GENEHUNTER is very bad in simple nuclear family settings and dramatically decreased with the number of markers being increased. On the other hand, the comparison result of different sampling designs demonstrates that sampling trios is the most efficient design to estimate haplotype frequencies in populations under same genotyping cost.     

Likelihood-based association analysis for nuclear families and unrelated subjects with missing genotype data

Missing data occur in genetic association studies for several reasons including missing family members and uncertain haplotype phase. Maximum likelihood is a commonly used approach to accommodate missing data, but it can be difficult to apply to family-based association studies, because of possible loss of robustness to confounding by population stratification. Here a novel likelihood for nuclear families is proposed, in which distinct sets of association parameters are used to model the parental genotypes and the offspring genotypes. This approach is robust to population structure when the data are complete, and has only minor loss of robustness when there are missing data. It also allows a novel conditioning step that gives valid analysis for multiple offspring in the presence of linkage. Unrelated subjects are included by regarding them as the children of two missing parents. Simulations and theory indicate similar operating characteristics to TRANSMIT, but with no bias with missing data in the presence of linkage. In comparison with FBAT and PCPH, the proposed model is slightly less robust to population structure but has greater power to detect strong effects. In comparison to APL and MITDT, the model is more robust to stratification and can accommodate sibships of any size. The methods are implemented for binary and continuous traits in software, UNPHASED, available from the author.     

HAPLORE: a program for haplotype reconstruction in general pedigrees without recombination

MOTIVATION: Haplotype reconstruction is an essential step in genetic linkage and association studies. Although many methods have been developed to estimate haplotype frequencies and reconstruct haplotypes for a sample of unrelated individuals, haplotype reconstruction in large pedigrees with a large number of genetic markers remains a challenging problem. METHODS: We have developed an efficient computer program, HAPLORE (HAPLOtype REconstruction), to identify all haplotype sets that are compatible with the observed genotypes in a pedigree for tightly linked genetic markers. HAPLORE consists of three steps that can serve different needs in applications. In the first step, a set of logic rules is used to reduce the number of compatible haplotypes of each individual in the pedigree as much as possible. After this step, the haplotypes of all individuals in the pedigree can be completely or partially determined. These logic rules are applicable to completely linked markers and they can be used to impute missing data and check genotyping errors. In the second step, a haplotype-elimination algorithm similar to the genotype-elimination algorithms used in linkage analysis is applied to delete incompatible haplotypes derived from the first step. All superfluous haplotypes of the pedigree members will be excluded after this step. In the third step, the expectation-maximization (EM) algorithm combined with the partition and ligation technique is used to estimate haplotype frequencies based on the inferred haplotype configurations through the first two steps. Only compatible haplotype configurations with haplotypes having frequencies greater than a threshold are retained. RESULTS: We test the effectiveness and the efficiency of HAPLORE using both simulated and real datasets. Our results show that, the rule-based algorithm is very efficient for completely genotyped pedigree. In this case, almost all of the families have one unique haplotype configuration. In the presence of missing data, the number of compatible haplotypes can be substantially reduced by HAPLORE, and the program will provide all possible haplotype configurations of a pedigree under different circumstances, if such multiple configurations exist. These inferred haplotype configurations, as well as the haplotype frequencies estimated by the EM algorithm, can be used in genetic linkage and association studies. AVAILABILITY: The program can be downloaded from http://bioinformatics.med.yale.edu.     

Linkage disequilibrium mapping via cladistic analysis of phase-unknown genotypes and inferred haplotypes in the Genetic Analysis Workshop 14 simulated data

We recently described a method for linkage disequilibrium (LD) mapping, using cladistic analysis of phased single-nucleotide polymorphism (SNP) haplotypes in a logistic regression framework. However, haplotypes are often not available and cannot be deduced with certainty from the unphased genotypes. One possible two-stage approach is to infer the phase of multilocus genotype data and analyze the resulting haplotypes as if known. Here, haplotypes are inferred using the expectation-maximization (EM) algorithm and the best-guess phase assignment for each individual analyzed. However, inferring haplotypes from phase-unknown data is prone to error and this should be taken into account in the subsequent analysis. An alternative approach is to analyze the phase-unknown multilocus genotypes themselves. Here we present a generalization of the method for phase-known haplotype data to the case of unphased SNP genotypes. Our approach is designed for high-density SNP data, so we opted to analyze the simulated dataset. The marker spacing in the initial screen was too large for our method to be effective, so we used the answers provided to request further data in regions around the disease loci and in null regions. Power to detect the disease loci, accuracy in localizing the true site of the locus, and false-positive error rates are reported for the inferred-haplotype and unphased genotype methods. For this data, analyzing inferred haplotypes outperforms analysis of genotypes. As expected, our results suggest that when there is little or no LD between a disease locus and the flanking region, there will be no chance of detecting it unless the disease variant itself is genotyped.     

The reliability of haplotyping inference in nuclear families: misassignment rates for SNPs and microsatellites

Single nucleotide polymorphisms (SNPs) are widely used when investigators try to map complex disease genes. Although biallelic SNP markers are less informative than microsatellite markers, one can increase their information content by using haplotypes. However, assigning haplotypes (i.e., assigning phase) correctly can be problematic in the presence of SNP heterozygosity. For example, a doubly heterozygous individual, with genotype 12, 12, could have haplotypes 1-1/2-2 or 1-2/2-1 with equal probability; in the absence of additional information, there is no way to determine which haplotype is correct. Thus an algorithm that assigns haplotypes to such an individual will assign the wrong one 50% of the time. We have studied the frequency of haplotype misassignments, i.e., haplotypes that are misassigned solely because of inherent marker ambiguity (not because of errors in genotyping or calculation). We examined both SNPs and microsatellite markers. We used the computer programs GENEHUNTER and SIMWALK to assign the haplotypes. We simulated (a) families with 1-5 children, (b) haplotypes involving different numbers of marker loci (3, 5, 7 and 10 loci, all in linkage equilibrium), and (c) different allele frequencies. Misassignment rates are highest (a) in small families, (b) with many SNP loci, and (c) for loci with the greatest heterozygosity (i.e., where both alleles have frequency 0.5). For example, for triads (i.e., one-child families with both parents genotyped), misassignment rates for SNPs can reach almost 50%. Family sizes of 4-5 children are required in order to ensure a misassignment frequency of < or = 5% for ten-SNP haplotypes with allele frequencies of 0.25-0.5. For microsatellites, a family size of at least 2-3 children is necessary to keep haplotyping misassignments < or = 5%. Finally, we point out that it is misleading for a computer program to yield haplotype assignments without indicating that they may have been misassigned, and we discuss the implications of these misassignments for association and linkage analysis.     

Assigning Linkage Haplotypes from Parent and Progeny Genotypes

Given the genotypes of parents and progeny, their haplotypes over several or many linked loci can be easily assigned by listing the allele type at each locus along the haplotype known to be from each parent. Only a small number (5-10) of progeny per family is usually needed to assign the parental and progeny haplotypes. Any gaps left in the haplotypes may be filled in from the assigned haplotypes of relatives. The process is facilitated by having multiple alleles at the loci and by using more linked loci in the haplotype and with more progeny from the mating. Crossover haplotypes in the progeny can be identified by their being unique or uncommon, and the crossover point can often be detected if the locus linkage map order is known. The haplotyping method applies to outbreeding populations in plants, animals and man, as well as to traditional experimental crosses of inbred lines. The method also applies to half-sib families, whether the genotypes of the mates are known or unknown. The haplotyping procedure is already used in linkage analysis but does not seem to have been published. It should be useful in teaching and in genetic applications of haplotypes.     

Accounting for linkage in family-based tests of association with missing parental genotypes

In studies of complex diseases, a common paradigm is to conduct association analysis at markers in regions identified by linkage analysis, to attempt to narrow the region of interest. Family-based tests for association based on parental transmissions to affected offspring are often used in fine-mapping studies. However, for diseases with late onset, parental genotypes are often missing. Without parental genotypes, family-based tests either compare allele frequencies in affected individuals with those in their unaffected siblings or use siblings to infer missing parental genotypes. An example of the latter approach is the score test implemented in the computer program TRANSMIT. The inference of missing parental genotypes in TRANSMIT assumes that transmissions from parents to affected siblings are independent, which is appropriate when there is no linkage. However, using computer simulations, we show that, when the marker and disease locus are linked and the data set consists of families with multiple affected siblings, this assumption leads to a bias in the score statistic under the null hypothesis of no association between the marker and disease alleles. This bias leads to an inflated type I error rate for the score test in regions of linkage. We present a novel test for association in the presence of linkage (APL) that correctly infers missing parental genotypes in regions of linkage by estimating identity-by-descent parameters, to adjust for correlation between parental transmissions to affected siblings. In simulated data, we demonstrate the validity of the APL test under the null hypothesis of no association and show that the test can be more powerful than the pedigree disequilibrium test and family-based association test. As an example, we compare the performance of the tests in a candidate-gene study in families with Parkinson disease.     

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).     

HAPLOFREQ--estimating haplotype frequencies efficiently.

A commonly used tool in disease association studies is the search for discrepancies between the haplotype distribution in the case and control populations. In order to find this discrepancy, the haplotypes frequency in each of the populations is estimated from the genotypes. We present a new method HAPLOFREQ to estimate haplotype frequencies over a short genomic region given the genotypes or haplotypes with missing data or sequencing errors. Our approach incorporates a maximum likelihood model based on a simple random generative model which assumes that the genotypes are independently sampled from the population. We first show that if the phased haplotypes are given, possibly with missing data, we can estimate the frequency of the haplotypes in the population by finding the global optimum of the likelihood function in polynomial time. If the haplotypes are not phased, finding the maximum value of the likelihood function is NP-hard. In this case, we define an alternative likelihood function which can be thought of as a relaxed likelihood function. We show that the maximum relaxed likelihood can be found in polynomial time and that the optimal solution of the relaxed likelihood approaches asymptotically to the haplotype frequencies in the population. In contrast to previous approaches, our algorithms are guaranteed to converge in polynomial time to a global maximum of the different likelihood functions. We compared the performance of our algorithm to the widely used program PHASE, and we found that our estimates are at least 10% more accurate than PHASE and about ten times faster than PHASE. Our techniques involve new algorithms in convex optimization. These algorithms may be of independent interest. Particularly, they may be helpful in other maximum likelihood problems arising from survey sampling.     

Comparisons of methods for linkage analysis and haplotype reconstruction using extended pedigree data

We compare and contrast the performance of SIMPLE, a Monte Carlo based software, with that of several other methods for linkage and haplotype analyses, focusing on the simulated data from the New York City population. First, a whole-genome scan study based on the microsatellite markers was performed using GENEHUNTER. Because GENEHUNTER had to drop individuals for many of the pedigrees, we performed a follow-up study focusing on several regions of interest using SIMPLE, which can handle all pedigrees in their entirety. Second, 3 haplotyping programs, including that in SIMPLE, were used to reconstruct haplotypic configurations in pedigrees. SIMPLE emerges clearly as a preferred tool, as it can handle large pedigrees and produces haplotypic configurations without double recombinant haplotypes. For this study, we had knowledge of the simulating models at the time we performed the analysis.     

X-APL: an improved family-based test of association in the presence of linkage for the X chromosome

Family-based association methods have been developed primarily for autosomal markers. The X-linked sibling transmission/disequilibrium test (XS-TDT) and the reconstruction-combined TDT for X-chromosome markers (XRC-TDT) are the first association-based methods for testing markers on the X chromosome in family data sets. These are valid tests of association in family triads or discordant sib pairs but are not theoretically valid in multiplex families when linkage is present. Recently, XPDT and XMCPDT, modified versions of the pedigree disequilibrium test (PDT), were proposed. Like the PDT, XPDT compares genotype transmissions from parents to affected offspring or genotypes of discordant siblings; however, the XPDT can have low power if there are many missing parental genotypes. XMCPDT uses a Monte Carlo sampling approach to infer missing parental genotypes on the basis of true or estimated population allele frequencies. Although the XMCPDT was shown to be more powerful than the XPDT, variability in the statistic due to the use of an estimate of allele frequency is not properly accounted for. Here, we present a novel family-based test of association, X-APL, a modification of the test for association in the presence of linkage (APL) test. Like the APL, X-APL can use singleton or multiplex families and properly infers missing parental genotypes in linkage regions by considering identity-by-descent parameters for affected siblings. Sampling variability of parameter estimates is accounted for through a bootstrap procedure. X-APL can test individual marker loci or X-chromosome haplotypes. To allow for different penetrances in males and females, separate sex-specific tests are provided. Using simulated data, we demonstrated validity and showed that the X-APL is more powerful than alternative tests. To show its utility and to discuss interpretation in real-data analysis, we also applied the X-APL to candidate-gene data in a sample of families with Parkinson disease.     

Computing the minimum recombinant haplotype configuration from incomplete genotype data on a pedigree by integer linear programming.

We study the problem of reconstructing haplotype configurations from genotypes on pedigree data with missing alleles under the Mendelian law of inheritance and the minimum-recombination principle, which is important for the construction of haplotype maps and genetic linkage/association analyses. Our previous results show that the problem of finding a minimum-recombinant haplotype configuration (MRHC) is in general NP-hard. This paper presents an effective integer linear programming (ILP) formulation of the MRHC problem with missing data and a branch-and-bound strategy that utilizes a partial order relationship and some other special relationships among variables to decide the branching order. Nontrivial lower and upper bounds on the optimal number of recombinants are introduced at each branching node to effectively prune the search tree. When multiple solutions exist, a best haplotype configuration is selected based on a maximum likelihood approach. The paper also shows for the first time how to incorporate marker interval distance into a rule-based haplotyping algorithm. Our results on simulated data show that the algorithm could recover haplotypes with 50 loci from a pedigree of size 29 in seconds on a Pentium IV computer. Its accuracy is more than 99.8% for data with no missing alleles and 98.3% for data with 20% missing alleles in terms of correctly recovered phase information at each marker locus. A comparison with a statistical approach SimWalk2 on simulated data shows that the ILP algorithm runs much faster than SimWalk2 and reports better or comparable haplotypes on average than the first and second runs of SimWalk2. As an application of the algorithm to real data, we present some test results on reconstructing haplotypes from a genome-scale SNP dataset consisting of 12 pedigrees that have 0.8% to 14.5% missing alleles.     

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.     

The loss of statistical power to distinguish populations when certain samples are ambiguous

Case-control studies are used to map loci associated with a genetic disease. The usual case-control study tests for significant differences in frequencies of alleles at marker loci. In this paper, we consider the problem of comparing two or more marker loci simultaneously and testing for significant differences in haplotype rather than allele frequencies. We consider two situations. In the first, genotypes at marker loci are resolved into haplotypes by making use of biochemical methods or by genotyping family members. In the second, genotypes at marker loci are not resolved into haplotypes, but, by assuming random mating, haplotypes can be inferred using a likelihood method such as the expectation-maximization (EM) algorithm. We assume that a causative locus has two alleles with a multiplicative effect on the penetrance of a disease, with one allele increasing the penetrance by a factor pi. We find, for small values of pi-1 and large sample sizes, asymptotic results that predict the statistical power of a test for significant differences in haplotype frequencies between cases and a random sample of the population, both when haplotypes can be resolved and when haplotypes have to be inferred. The increase in power when haplotypes can be resolved can be expressed as a ratio R, which is the increase in sample size needed to achieve the same power when haplotypes are resolved over when they are not resolved. In general, R depends on the pattern of linkage disequilibrium between the causative allele and the marker haplotypes but is independent of the frequency of the causative allele and, to a first approximation, is independent of pi. For the special situation of two di-allelic marker loci, we obtain a simple expression for R and its upper bound.     

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.     

Efficient multipoint linkage analysis through reduction of inheritance space

Computational constraints currently limit exact multipoint linkage analysis to pedigrees of moderate size. We introduce new algorithms that allow analysis of larger pedigrees by reducing the time and memory requirements of the computation. We use the observed pedigree genotypes to reduce the number of inheritance patterns that need to be considered. The algorithms are implemented in a new version (version 2.1) of the software package GENEHUNTER. Performance gains depend on marker heterozygosity and on the number of pedigree members available for genotyping, but typically are 10-1,000-fold, compared with the performance of the previous release (version 2.0). As a result, families with up to 30 bits of inheritance information have been analyzed, and further increases in family size are feasible. In addition to computation of linkage statistics and haplotype determination, GENEHUNTER can also perform single-locus and multilocus transmission/disequilibrium tests. We describe and implement a set of permutation tests that allow determination of empirical significance levels in the presence of linkage disequilibrium among marker loci.     

Support for association of schizophrenia with genetic variation in the 6p22.3 gene,dysbindin, in sib-pair families with linkage and in an additional sample of triad families

Genetic variants in a gene on 6p22.3, dysbindin, have been shown recently to be associated with schizophrenia (Straub et al. 2002a). There is no doubt that replication in other independent samples would enhance the significance of this finding considerably. Since the gene is located in the center of the linkage peak on chromosome 6p that we reported earlier, we decided to test six of the most positive DNA polymorphisms in a sib-pair sample and in an independently ascertained sample of triads comprising 203 families, including the families for which we detected linkage on chromosome 6p. Evidence for association was observed in the two samples separately as well as in the combined sample (P=.00068 for SNP rs760761). Multilocus haplotype analysis increased the significance further to .00002 for a two-locus haplotype and to .00001 for a three-locus haplotype. Estimation of frequencies for six-locus haplotypes revealed one common haplotype with a frequency of 73.4% in transmitted, and only 57.6% in nontransmitted, parental haplotypes. All other six-locus haplotypes occurring at a frequency of >1% were less often transmitted than nontransmitted. Our results represent a first successful replication of linkage disequilibrium in psychiatric genetics detected in a region with previous evidence of linkage and will encourage the search for causes of schizophrenia by the genetic approach.     

The problem of sampling families rather than populations: relatedness among individuals in samples of juvenile brown trout Salmo trutta L.

In species exhibiting a nonrandom distribution of closely related individuals, sampling of a few families may lead to biased estimates of allele frequencies in populations. This problem was studied in two brown trout populations, based on analysis of mtDNA and microsatellites. In both samples mtDNA haplotype frequencies differed significantly between age classes, and in one sample 17 out of 18 individuals less than 1 year of age shared one particular mtDNA haplotype. Estimates of relatedness showed that these individuals most likely represented only three full-sib families. Older trout exhibiting the same haplotypes generally were not closely related.     

The impact of missing and erroneous genotypes on tagging SNP selection and power of subsequent association tests

OBJECTIVE: Single nucleotide polymorphisms (SNPs) serve as effective markers for localizing disease susceptibility genes, but current genotyping technologies are inadequate for genotyping all available SNP markers in a typical linkage/association study. Much attention has recently been paid to methods for selecting the minimal informative subset of SNPs in identifying haplotypes, but there has been little investigation of the effect of missing or erroneous genotypes on the performance of these SNP selection algorithms and subsequent association tests using the selected tagging SNPs. The purpose of this study is to explore the effect of missing genotype or genotyping error on tagging SNP selection and subsequent single marker and haplotype association tests using the selected tagging SNPs. METHODS: Through two sets of simulations, we evaluated the performance of three tagging SNP selection programs in the presence of missing or erroneous genotypes: Clayton's diversity based program htstep, Carlson's linkage disequilibrium (LD) based program ldSelect, and Stram's coefficient of determination based program tagsnp.exe. RESULTS: When randomly selected known loci were relabeled as 'missing', we found that the average number of tagging SNPs selected by all three algorithms changed very little and the power of subsequent single marker and haplotype association tests using the selected tagging SNPs remained close to the power of these tests in the absence of missing genotype. When random genotyping errors were introduced, we found that the average number of tagging SNPs selected by all three algorithms increased. In data sets simulated according to the haplotype frequecies in the CYP19 region, Stram's program had larger increase than Carlson's and Clayton's programs. In data sets simulated under the coalescent model, Carlson's program had the largest increase and Clayton's program had the smallest increase. In both sets of simulations, with the presence of genotyping errors, the power of the haplotype tests from all three programs decreased quickly, but there was not much reduction in power of the single marker tests. CONCLUSIONS: Missing genotypes do not seem to have much impact on tagging SNP selection and subsequent single marker and haplotype association tests. In contrast, genotyping errors could have severe impact on tagging SNP selection and haplotype tests, but not on single marker tests.     

Accuracy of haplotype frequency estimation for biallelic loci, via the expectation-maximization algorithm for unphased diploid genotype data

Haplotype analyses have become increasingly common in genetic studies of human disease because of their ability to identify unique chromosomal segments likely to harbor disease-predisposing genes. The study of haplotypes is also used to investigate many population processes, such as migration and immigration rates, linkage-disequilibrium strength, and the relatedness of populations. Unfortunately, many haplotype-analysis methods require phase information that can be difficult to obtain from samples of nonhaploid species. There are, however, strategies for estimating haplotype frequencies from unphased diploid genotype data collected on a sample of individuals that make use of the expectation-maximization (EM) algorithm to overcome the missing phase information. The accuracy of such strategies, compared with other phase-determination methods, must be assessed before their use can be advocated. In this study, we consider and explore sources of error between EM-derived haplotype frequency estimates and their population parameters, noting that much of this error is due to sampling error, which is inherent in all studies, even when phase can be determined. In light of this, we focus on the additional error between haplotype frequencies within a sample data set and EM-derived haplotype frequency estimates incurred by the estimation procedure. We assess the accuracy of haplotype frequency estimation as a function of a number of factors, including sample size, number of loci studied, allele frequencies, and locus-specific allelic departures from Hardy-Weinberg and linkage equilibrium. We point out the relative impacts of sampling error and estimation error, calling attention to the pronounced accuracy of EM estimates once sampling error has been accounted for. We also suggest that many factors that may influence accuracy can be assessed empirically within a data set-a fact that can be used to create "diagnostics" that a user can turn to for assessing potential inaccuracies in estimation.