Unobserved Genotypes Research Articles

Likelihood Approach for Detecting Imprinting and In Utero Maternal Effects Using General Pedigrees from Prospective Family‐Based Association Studies

Genetic imprinting and in utero maternal effects are causes of parent-of-origin effect but they are confounded with each other. Tests attempting to detect only one of these effects would have a severely inflated type I error rate if the assumption of the absence of the other effect is violated. Some existing methods avoid the potential confounding by modeling imprinting and in utero maternal effect simultaneously. However, these methods are not amendable to extended families, which are commonly recruited in family-based studies. In this article, we propose a likelihood approach for detecting imprinting and maternal effects (LIME) using general pedigrees from prospective family-based association studies. LIME formulates the probability of familial genotypes without the Hardy-Weinberg equilibrium assumption by introducing a novel concept called conditional mating type between marry-in founders and their nonfounder spouses. Further, a logit link is used to model the penetrance. To deal with the issue of incomplete pedigree genotypic data, LIME imputes the unobserved genotypes implicitly by considering all compatible ones conditional on the observed genotypes. We carried out a simulation study to evaluate the relative power and type I error of LIME and two existing methods. The results show that the use of extended pedigree data, even with incomplete information, can achieve much greater power than using nuclear families for detecting imprinting and in utero maternal effects without leading to inflated type I error rates.

Imputation of low-frequency variants using the HapMap3 benefits from large, diverse reference sets

Imputation allows the inference of unobserved genotypes in low-density data sets, and is often used to test for disease association at variants that are poorly captured by standard genotyping chips (such as low-frequency variants). Although much effort has gone into developing the best imputation algorithms, less is known about the effects of reference set choice on imputation accuracy. We assess the improvements afforded by increases in reference size and diversity, specifically comparing the HapMap2 data set, which has been used to date for imputation, and the new HapMap3 data set, which contains more samples from a more diverse range of populations. We find that, for imputation into Western European samples, the HapMap3 reference provides more accurate imputation with better-calibrated quality scores than HapMap2, and that increasing the number of HapMap3 populations included in the reference set grant further improvements. Improvements are most pronounced for low-frequency variants (frequency <5%), with the largest and most diverse reference sets bringing the accuracy of imputation of low-frequency variants close to that of common ones. For low-frequency variants, reference set diversity can improve the accuracy of imputation, independent of reference sample size. HapMap3 reference sets provide significant increases in imputation accuracy relative to HapMap2, and are of particular use if highly accurate imputation of low-frequency variants is required. Our results suggest that, although the sample sizes from the 1000 Genomes Pilot Project will not allow reliable imputation of low-frequency variants, the larger sample sizes of the main project will allow.

MaCH: using sequence and genotype data to estimate haplotypes and unobserved genotypes.

Genome-wide association studies (GWAS) can identify common alleles that contribute to complex disease susceptibility. Despite the large number of SNPs assessed in each study, the effects of most common SNPs must be evaluated indirectly using either genotyped markers or haplotypes thereof as proxies. We have previously implemented a computationally efficient Markov Chain framework for genotype imputation and haplotyping in the freely available MaCH software package. The approach describes sampled chromosomes as mosaics of each other and uses available genotype and shotgun sequence data to estimate unobserved genotypes and haplotypes, together with useful measures of the quality of these estimates. Our approach is already widely used to facilitate comparison of results across studies as well as meta-analyses of GWAS. Here, we use simulations and experimental genotypes to evaluate its accuracy and utility, considering choices of genotyping panels, reference panel configurations, and designs where genotyping is replaced with shotgun sequencing. Importantly, we show that genotype imputation not only facilitates cross study analyses but also increases power of genetic association studies. We show that genotype imputation of common variants using HapMap haplotypes as a reference is very accurate using either genome-wide SNP data or smaller amounts of data typical in fine-mapping studies. Furthermore, we show the approach is applicable in a variety of populations. Finally, we illustrate how association analyses of unobserved variants will benefit from ongoing advances such as larger HapMap reference panels and whole genome shotgun sequencing technologies.

Methods for testing association between uncertain genotypes and quantitative traits

Interpretability and power of genome-wide association studies can be increased by imputing unobserved genotypes, using a reference panel of individuals genotyped at higher marker density. For many markers, genotypes cannot be imputed with complete certainty, and the uncertainty needs to be taken into account when testing for association with a given phenotype. In this paper, we compare currently available methods for testing association between uncertain genotypes and quantitative traits. We show that some previously described methods offer poor control of the false-positive rate (FPR), and that satisfactory performance of these methods is obtained only by using ad hoc filtering rules or by using a harsh transformation of the trait under study. We propose new methods that are based on exact maximum likelihood estimation and use a mixture model to accommodate nonnormal trait distributions when necessary. The new methods adequately control the FPR and also have equal or better power compared to all previously described methods. We provide a fast software implementation of all the methods studied here; our new method requires computation time of less than one computer-day for a typical genome-wide scan, with 2.5 M single nucleotide polymorphisms and 5000 individuals.

MaCH: Using sequence and genotype data to estimate haplotypes and unobserved genotypes

MaCH: Using sequence and genotype data to estimate haplotypes and unobserved genotypes

MaCH: using sequence and genotype data to estimate haplotypes and unobserved genotypes

MaCH: using sequence and genotype data to estimate haplotypes and unobserved genotypes

Application of imputation methods to the analysis of rheumatoid arthritis data in genome-wide association studies

Most genetic association studies only genotype a small proportion of cataloged single-nucleotide polymorphisms (SNPs) in regions of interest. With the catalogs of high-density SNP data available (e.g., HapMap) to researchers today, it has become possible to impute genotypes at untyped SNPs. This in turn allows us to test those untyped SNPs, the motivation being to increase power in association studies. Several imputation methods and corresponding software packages have been developed for this purpose. The objective of our study is to apply three widely used imputation methods and corresponding software packages to a data from a genome-wide association study of rheumatoid arthritis from the North American Rheumatoid Arthritis Consortium in Genetic Analysis Workshop 16, to compare the performances of the three methods, to evaluate their strengths and weaknesses, and to identify additional susceptibility loci underlying rheumatoid arthritis. The software packages used in this paper included a program for Bayesian imputation-based association mapping (BIMBAM), a program for imputing unobserved genotypes in case-control association studies (IMPUTE), and a program for testing untyped alleles (TUNA). We found some untyped SNP that showed significant association with rheumatoid arthritis. Among them, a few of these were not located near any typed SNP that was found to be significant and thus may be worth further investigation.

A Multivariate Regression Model for Continuous Genetic Traits

Summary In many commonly used models for multivariate traits, the likelihood is specified as a mixture of nested sums of products over the unobserved genotypes of all the family members, in which the familial covariance matrices vary in size and structure for different families, and their sizes can be immense for large family units. These issues pose computational difficulties in many applications. Bonney’s compound regressive model for univariate traits simplifies the familial covariance structure and reduces the mixture of nested sums only to the parent–offspring level, thus enhancing computation significantly. This model has been extended to the multivariate case in the absence of unobserved genotypes. Here, we further extend this model to incorporate major genes, covariates and multiple loci. As is typical in practice, this causes new computational difficulties. We study the computational issues and explore the behaviour of this extended model.

An EM algorithm for mapping binary disease loci: application to fibrosarcoma in a four-way cross mouse family.

Many diseases show dichotomous phenotypic variation but do not follow a simple Mendelian pattern of inheritance. Variances of these binary diseases are presumably controlled by multiple loci and environmental variants. A least-squares method has been developed for mapping such complex disease loci by treating the binary phenotypes (0 and 1) as if they were continuous. However, the least-squares method is not recommended because of its ad hoc nature. Maximum Likelihood (ML) and Bayesian methods have also been developed for binary disease mapping by incorporating the discrete nature of the phenotypic distribution. In the ML analysis, the likelihood function is usually maximized using some complicated maximization algorithms (e.g. the Newton-Raphson or the simplex algorithm). Under the threshold model of binary disease, we develop an Expectation Maximization (EM) algorithm to solve for the maximum likelihood estimates (MLEs). The new EM algorithm is developed by treating both the unobserved genotype and the disease liability as missing values. As a result, the EM iteration equations have the same form as the normal equation system in linear regression. The EM algorithm is further modified to take into account sexual dimorphism in the linkage maps. Applying the EM-implemented ML method to a four-way-cross mouse family, we detected two regions on the fourth chromosome that have evidence of QTLs controlling the segregation of fibrosarcoma, a form of connective tissue cancer. The two QTLs explain 50-60% of the variance in the disease liability. We also applied a Bayesian method previously developed (modified to take into account sex-specific maps) to this data set and detected one additional QTL on chromosome 13 that explains another 26% of the variance of the disease liability. All the QTLs detected primarily show dominance effects.

Technical Note: Determining Peeling Order Using Sparse Matrix Algorithms

To study the effect of individual genes by segregation or linkage analyses, the likelihood of the model needs to be evaluated. The likelihood can be computed efficiently using the Elston-Stewart algorithm. This algorithm involves summing over the unobserved genotypes in the pedigree, which is called peeling. An important aspect of this algorithm is to determine the order of peeling to maximize efficiency. This paper shows how determining peeling order is related to a problem in solving systems of symmetric sparse linear equations. It also shows how algorithms developed to efficiently solve those systems, can be used to determine the optimal order of peeling in the Elston-Stewart algorithm.

Modeling Disease Incidence Rates in Families

We apply an extended Cox model to study latent genes and measured environmental exposures simultaneously as risk factors for disease. Using this method, we assume Mendelian transmission of the genes and either dominant or recessive gene action. We compared the results from this model with those obtained under a model that includes the environmental variables and a family risk score. We demonstrate the method in samples of 1,433 Caucasian families (N = 6,791) and 206 African-American families (N = 771) from the National Heart, Lung, and Blood Institute Family Heart Study. In Caucasians, we found evidence suggesting that having ever smoked increased the risk of coronary heart disease only in individuals who carry a genetic susceptibility. We also noted that in both Caucasian and African-American families, the relative risk of coronary heart disease for ever-treated vs never-treated for high serum total cholesterol increased after including an unobserved susceptibility genotype in the model. This finding implied that there may be genes influencing coronary heart disease independent of those that influence total cholesterol. Such findings were not evident when genetic risk was summarized by the family history score. We also discuss the extension of the model to address the etiology of complex diseases.

Iteratively reweighted least squares mapping of quantitative trait loci.

Mapping quantitative trait loci (QTL) is a typical problem of regression with uncertain independent variables because the genotype of a putative QTL is not observed. Rather, the genotype is inferred from marker information. The method of maximum likelihood (ML) methods is considered to be the optimal solution for this problem because the distribution of the unobserved QTL genotype is fully taken into account. The simple linear regression method (REG) is a first-order approximation to ML and usually performs very well. In this study, an iteratively reweighted least squares method (IRWLS) is proposed. The new method is a second-order approximation to ML because both the expectation and the variance of the unobserved QTL genotype are taken into consideration. The IRWLS is developed in the context of a single large outbred family. The properties of IRWLS are demonstrated and compared with REG and ML via replicated Monte Carlo simulations. The conclusions are: (1) when marker information content is high, the three methods perform equally well, but ML and IRWLS outperform REG when marker information content is low and the variance explained by the QTL is high; (2) when the residual distribution is not normal, ML can fail or have low power to detect small QTLs, but REG and IRWLS are robust to non-normality; and (3) when the residual distribution is normal, the performance of IRWLS is almost identical to ML, but the computational speed of IRWLS is many times faster than that of ML.

Segregation Analysis of Case-Control Data Using Generalized Estimating Equations

Generalized estimating equations (GEEs) (Liang and Zeger, 1986, Biometrika 73, 13-22) are used to fit genetic models to binary disease data for families of subjects in case-control studies. The GEEs include model specification of both the disease probabilities and the two-way (and possibly three-way) correlation coefficients of the family disease data. These quantities are modelled as nonlinear functions of unobserved genotypes, observed environmental covariates, and the unknown parameters; the functions reflect the method used to ascertain the family data. Goodness of fit is tested by allowing more flexible forms for the correlation coefficients, regressing them against covariates specific to the relevant pair (or triple) of family members. The approach is applied to family data obtained from simulated and real case-control studies. This semiparametric approach is less dependent on unverifiable assumptions and more computationally tractable than other methods for segregation analysis.