Susceptibility of biallelic haplotype and genotype frequencies to genotyping error

With the availability of fast genotyping methods and genomic databases, the search for statistical association of single nucleotide polymorphisms with a complex trait has become an important methodology in medical genetics. However, even fairly rare errors occurring during the genotyping process can lead to spurious association results and decrease in statistical power. We develop a systematic approach to study how genotyping errors change the genotype distribution in a sample. The general M-marker case is reduced to that of a single-marker locus by recognizing the underlying tensor-product structure of the error matrix. Both method and general conclusions apply to the general error model; we give detailed results for allele-based errors of size depending both on the marker locus and the allele present. Multiple errors are treated in terms of the associated diffusion process on the space of genotype distributions. We find that certain genotype and haplotype distributions remain unchanged under genotyping errors, and that genotyping errors generally render the distribution more similar to the stable one. In case-control association studies, this will lead to loss of statistical power for nondifferential genotyping errors and increase in type I error for differential genotyping errors. Moreover, we show that allele-based genotyping errors do not disturb Hardy-Weinberg equilibrium in the genotype distribution. In this setting we also identify maximally affected distributions. As they correspond to situations with rare alleles and marker loci in high linkage disequilibrium, careful checking for genotyping errors is advisable when significant association based on such alleles/haplotypes is observed in association studies.     

Cheap, accurate and rapid allele frequency estimation of single nucleotide polymorphisms by primer extension and DHPLC in DNA pools

At present, the cost of genotyping single nucleotide polymorphisms (SNPs) in large numbers of subjects poses a formidable problem for molecular genetic approaches to complex diseases. We have tested the possibility of using primer extension and denaturing high performance liquid chromatography to estimate allele frequencies of SNPs in pooled DNA samples. Our data show that this method should allow the accurate estimation of absolute allele frequencies in pooled samples of DNA and also of the difference in allele frequency between different pooled DNA samples. This technique therefore offers an efficient and cheap method for genotyping SNPs in large case-control and family-based association samples.     

A central resource for accurate allele frequency estimation from pooled DNA genotyped on DNA microarrays

Analysing pooled DNA on microarrays is an efficient way to genotype hundreds of individuals for thousands of markers for genome-wide association. Although direct comparison of case and control fluorescence scores is possible, correction for differential hybridization of alleles is important, particularly for rare single nucleotide polymorphisms. Such correction relies on heterozygous fluorescence scores and requires the genotyping of hundreds of individuals to obtain sufficient estimates of the correction factor, completely negating any benefit gained by pooling samples. We explore the effect of differential hybridization on test statistics and provide a solution to this problem in the form of a central resource for the accumulation of heterozygous fluorescence scores, allowing accurate allele frequency estimation at no extra cost.     

Matching strategies for genetic association studies in structured populations

Association studies in populations that are genetically heterogeneous can yield large numbers of spurious associations if population subgroups are unequally represented among cases and controls. This problem is particularly acute for studies involving pooled genotyping of very large numbers of single-nucleotide-polymorphism (SNP) markers, because most methods for analysis of association in structured populations require individual genotyping data. In this study, we present several strategies for matching case and control pools to have similar genetic compositions, based on ancestry information inferred from genotype data for approximately 300 SNPs tiled on an oligonucleotide-based genotyping array. We also discuss methods for measuring the impact of population stratification on an association study. Results for an admixed population and a phenotype strongly confounded with ancestry show that these simple matching strategies can effectively mitigate the impact of population stratification.     

A note on using permutation-based false discovery rate estimates to compare different analysis methods for microarray data

MOTIVATION: False discovery rate (FDR) is defined as the expected percentage of false positives among all the claimed positives. In practice, with the true FDR unknown, an estimated FDR can serve as a criterion to evaluate the performance of various statistical methods under the condition that the estimated FDR approximates the true FDR well, or at least, it does not improperly favor or disfavor any particular method. Permutation methods have become popular to estimate FDR in genomic studies. The purpose of this paper is 2-fold. First, we investigate theoretically and empirically whether the standard permutation-based FDR estimator is biased, and if so, whether the bias inappropriately favors or disfavors any method. Second, we propose a simple modification of the standard permutation to yield a better FDR estimator, which can in turn serve as a more fair criterion to evaluate various statistical methods. RESULTS: Both simulated and real data examples are used for illustration and comparison. Three commonly used test statistics, the sample mean, SAM statistic and Student's t-statistic, are considered. The results show that the standard permutation method overestimates FDR. The overestimation is the most severe for the sample mean statistic while the least for the t-statistic with the SAM-statistic lying between the two extremes, suggesting that one has to be cautious when using the standard permutation-based FDR estimates to evaluate various statistical methods. In addition, our proposed FDR estimation method is simple and outperforms the standard method.     

A mixture model for estimating the local false discovery rate in DNA microarray analysis

MOTIVATION: Statistical methods based on controlling the false discovery rate (FDR) or positive false discovery rate (pFDR) are now well established in identifying differentially expressed genes in DNA microarray. Several authors have recently raised the important issue that FDR or pFDR may give misleading inference when specific genes are of interest because they average the genes under consideration with genes that show stronger evidence for differential expression. The paper proposes a flexible and robust mixture model for estimating the local FDR which quantifies how plausible each specific gene expresses differentially. RESULTS: We develop a special mixture model tailored to multiple testing by requiring the P-value distribution for the differentially expressed genes to be stochastically smaller than the P-value distribution for the non-differentially expressed genes. A smoothing mechanism is built in. The proposed model gives robust estimation of local FDR for any reasonable underlying P-value distributions. It also provides a single framework for estimating the proportion of differentially expressed genes, pFDR, negative predictive values, sensitivity and specificity. A cervical cancer study shows that the local FDR gives more specific and relevant quantification of the evidence for differential expression that can be substantially different from pFDR. AVAILABILITY: An R function implementing the proposed model is available at http://www.geocities.com/jg_liao/software     

Penalized Multimarker vs. Single-Marker Regression Methods for Genome-Wide Association Studies of Quantitative Traits

The data from genome-wide association studies (GWAS) in humans are still predominantly analyzed using single-marker association methods. As an alternative to single-marker analysis (SMA), all or subsets of markers can be tested simultaneously. This approach requires a form of penalized regression (PR) as the number of SNPs is much larger than the sample size. Here we review PR methods in the context of GWAS, extend them to perform penalty parameter and SNP selection by false discovery rate (FDR) control, and assess their performance in comparison with SMA. PR methods were compared with SMA, using realistically simulated GWAS data with a continuous phenotype and real data. Based on these comparisons our analytic FDR criterion may currently be the best approach to SNP selection using PR for GWAS. We found that PR with FDR control provides substantially more power than SMA with genome-wide type-I error control but somewhat less power than SMA with Benjamini–Hochberg FDR control (SMA-BH). PR with FDR-based penalty parameter selection controlled the FDR somewhat conservatively while SMA-BH may not achieve FDR control in all situations. Differences among PR methods seem quite small when the focus is on SNP selection with FDR control. Incorporating linkage disequilibrium into the penalization by adapting penalties developed for covariates measured on graphs can improve power but also generate more false positives or wider regions for follow-up. We recommend the elastic net with a mixing weight for the Lasso penalty near 0.5 as the best method.     

Predicting functionally important SNP classes based on negative selection

Background  

With the advent of cost-effective genotyping technologies, genome-wide association studies allow researchers to examine hundreds of thousands of single nucleotide polymorphisms (SNPs) for association with human disease. Recently, many researchers applying this strategy have detected strong associations to disease with SNP markers that are either not in linkage disequilibrium with any nonsynonymous SNP or large distances from any annotated gene. In such cases, no well-established standard practice for effective SNP selection for follow-up studies exists. We aim to identify and prioritize groups of SNPs that are more likely to affect phenotypes in order to facilitate efficient SNP selection for follow-up studies.     

Simple and efficient analysis of disease association with missing genotype data

Missing genotype data arise in association studies when the single-nucleotide polymorphisms (SNPs) on the genotyping platform are not assayed successfully, when the SNPs of interest are not on the platform, or when total sequence variation is determined only on a small fraction of individuals. We present a simple and flexible likelihood framework to study SNP-disease associations with such missing genotype data. Our likelihood makes full use of all available data in case-control studies and reference panels (e.g., the HapMap), and it properly accounts for the biased nature of the case-control sampling as well as the uncertainty in inferring unknown variants. The corresponding maximum-likelihood estimators for genetic effects and gene-environment interactions are unbiased and statistically efficient. We developed fast and stable numerical algorithms to calculate the maximum-likelihood estimators and their variances, and we implemented these algorithms in a freely available computer program. Simulation studies demonstrated that the new approach is more powerful than existing methods while providing accurate control of the type I error. An application to a case-control study on rheumatoid arthritis revealed several loci that deserve further investigations.     

Family-based association tests using genotype data with uncertainty

Family-based association studies have been widely used to identify association between diseases and genetic markers. It is known that genotyping uncertainty is inherent in both directly genotyped or sequenced DNA variations and imputed data in silico. The uncertainty can lead to genotyping errors and missingness and can negatively impact the power and Type I error rates of family-based association studies even if the uncertainty is independent of disease status. Compared with studies using unrelated subjects, there are very few methods that address the issue of genotyping uncertainty for family-based designs. The limited attempts have mostly been made to correct the bias caused by genotyping errors. Without properly addressing the issue, the conventional testing strategy, i.e. family-based association tests using called genotypes, can yield invalid statistical inferences. Here, we propose a new test to address the challenges in analyzing case-parents data by using calls with high accuracy and modeling genotype-specific call rates. Our simulations show that compared with the conventional strategy and an alternative test, our new test has an improved performance in the presence of substantial uncertainty and has a similar performance when the uncertainty level is low. We also demonstrate the advantages of our new method by applying it to imputed markers from a genome-wide case-parents association study.     

Prioritize and select SNPs for association studies with multi-stage designs.

Large-scale whole genome association studies are increasingly common, due in large part to recent advances in genotyping technology. With this change in paradigm for genetic studies of complex diseases, it is vital to develop valid, powerful, and efficient statistical tools and approaches to evaluate such data. Despite a dramatic drop in genotyping costs, it is still expensive to genotype thousands of individuals for hundreds of thousands single nucleotide polymorphisms (SNPs) for large-scale whole genome association studies. A multi-stage (or two-stage) design has been a promising alternative: in the first stage, only a fraction of samples are genotyped and tested using a dense set of SNPs, and only a small subset of markers that show moderate associations with the disease will be genotyped in later stages. Multi-stage designs have also been used in candidate gene association studies, usually in regions that have shown strong signals by linkage studies. To decide which set of SNPs to be genotyped in the next stage, a common practice is to utilize a simple test (such as a chi2 test for case-control data) and a liberal significance level without corrections for multiple testing, to ensure that no true signals will be filtered out. In this paper, I have developed a novel SNP selection procedure within the framework of multi-stage designs. Based on data from stage 1, the method explicitly explores correlations (linkage disequilibrium) among SNPs and their possible interactions in determining the disease phenotype. Comparing with a regular multi-stage design, the approach can select a much reduced set of SNPs with high discriminative power for later stages. Therefore, not only does it reduce the genotyping cost in later stages, it also increases the statistical power by reducing the number of tests. Combined analysis is proposed to further improve power, and the theoretical significance level of the combined statistic is derived. Extensive simulations have been performed, and results have shown that the procedure can reduce the number of SNPs required in later stages, with improved power to detect associations. The procedure has also been applied to a real data set from a genome-wide association study of the sporadic amyotrophic lateral sclerosis (ALS) disease, and an interesting set of candidate SNPs has been identified.     

MaGIC: a program to generate targeted marker sets for genome-wide association studies

High-throughput genotyping technologies such as DNA pooling and DNA microarrays mean that whole-genome screens are now practical for complex disease gene discovery using association studies. Because it is currently impractical to use all available markers, a subset is typically selected on the basis of required saturation density. Restricting markers to those within annotated genomic features of interest (e.g., genes or exons) or within feature-rich regions, reduces workload and cost while retaining much information. We have designed a program (MaGIC) that exploits genome assembly data to create lists of markers correlated with other genomic features. Marker lists are generated at a user-defined spacing and can target features with a user-defined density. Maps are in base pairs or linkage disequilibrium units (LDUs) as derived from the International HapMap data, which is useful for association studies and fine-mapping. Markers may be selected on the basis of heterozygosity and source database, and single nucleotide polymorphism (SNP) markers may additionally be selected on the basis of validation status. The import function means the method can be used for any genomic features such as housekeeping genes, long interspersed elements (LINES), or Alu repeats in humans, and is also functional for other species with equivalent data. The program and source code is freely available at http://cogent.iop.kcl.ac.uk/MaGIC.cogx.     

Improved power offered by a score test for linkage disequilibrium mapping of quantitative-trait loci by selective genotyping

Selective genotyping is used to increase efficiency in genetic association studies of quantitative traits by genotyping only those individuals who deviate from the population mean. However, selection distorts the conditional distribution of the trait given genotype, and such data sets are usually analyzed using case-control methods, quantitative analysis within selected groups, or a combination of both. We show that Hotelling's T(2) test, recently proposed for association studies of one or several tagging single-nucleotide polymorphisms in a prospective (i.e., trait given genotype) design, can also be applied to the retrospective (i.e., genotype given trait) selective-genotyping design, and we use simulation to demonstrate its improved power over existing methods.     

Microarray genotyping resource to determine population stratification in genetic association studies of complex disease

We have developed a robust microarray genotyping chip that will help advance studies in genetic epidemiology. In population-based genetic association studies of complex disease, there could be hidden genetic substructure in the study populations, resulting in false-positive associations. Such population stratification may confound efforts to identify true associations between genotype/haplotype and phenotype. Methods relying on genotyping additional null single nucleotide polymorphism (SNP) markers have been proposed, such as genomic control (GC) and structured association (SA), to correct association tests for population stratification. If there is an association of a disease with null SNPs, this suggests that there is a population subset with different genetic background plus different disease susceptibility. Genotyping over 100 null SNPs in the large numbers of patient and control DNA samples that are required in genetic association studies can be prohibitively expensive. We have therefore developed and tested a resequencing chip based on arrayed primer extension (APEX) from over 2000 DNA probe features that facilitate multiple interrogations of each SNP, providing a powerful, accurate, and economical means to simultaneously determine the genotypes at 110 null SNP loci in any individual. Based on 1141 known genotypes from other research groups, our GC SNP chip has an accuracy of 98.5%, including non-calls.     

ExactFDR: exact computation of false discovery rate estimate in case-control association studies

Genome-wide association studies require accurate and fast statistical methods to identify relevant signals from the background noise generated by a huge number of simultaneously tested hypotheses. It is now commonly accepted that exact computations of association probability value (P-value) are preferred to chi(2) and permutation-based approximations. Following the same principle, the ExactFDR software package improves speed and accuracy of the permutation-based false discovery rate (FDR) estimation method by replacing the permutation-based estimation of the null distribution by the generalization of the algorithm used for computing individual exact P-values. It provides a quick and accurate non-conservative estimator of the proportion of false positives in a given selection of markers, and is therefore an efficient and pragmatic tool for the analysis of genome-wide association studies.     

In situ analysis of cross-hybridisation on microarrays and the inference of expression correlation

Background

When conducting multiple hypothesis tests, it is important to control the number of false positives, or the False Discovery Rate (FDR). However, there is a tradeoff between controlling FDR and maximizing power. Several methods have been proposed, such as the q-value method, to estimate the proportion of true null hypothesis among the tested hypotheses, and use this estimation in the control of FDR. These methods usually depend on the assumption that the test statistics are independent (or only weakly correlated). However, many types of data, for example microarray data, often contain large scale correlation structures. Our objective was to develop methods to control the FDR while maintaining a greater level of power in highly correlated datasets by improving the estimation of the proportion of null hypotheses.

Results

We showed that when strong correlation exists among the data, which is common in microarray datasets, the estimation of the proportion of null hypotheses could be highly variable resulting in a high level of variation in the FDR. Therefore, we developed a re-sampling strategy to reduce the variation by breaking the correlations between gene expression values, then using a conservative strategy of selecting the upper quartile of the re-sampling estimations to obtain a strong control of FDR.

Conclusion

With simulation studies and perturbations on actual microarray datasets, our method, compared to competing methods such as q-value, generated slightly biased estimates on the proportion of null hypotheses but with lower mean square errors. When selecting genes with controlling the same FDR level, our methods have on average a significantly lower false discovery rate in exchange for a minor reduction in the power.     

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.     

Quantification of the power of Hardy-Weinberg equilibrium testing to detect genotyping error

Deviation from Hardy-Weinberg equilibrium has become an accepted test for genotyping error. While it is generally considered that testing departures from Hardy-Weinberg equilibrium to detect genotyping error is not sensitive, little has been done to quantify this sensitivity. Therefore, we have examined various models of genotyping error, including error caused by neighboring SNPs that degrade the performance of genotyping assays. We then calculated the power of chi-square goodness-of-fit tests for deviation from Hardy-Weinberg equilibrium to detect such error. We have also examined the affects of neighboring SNPs on risk estimates in the setting of case-control association studies. We modeled the power of departure from Hardy-Weinberg equilibrium as a test to detect genotyping error and quantified the effect of genotyping error on disease risk estimates. Generally, genotyping error does not generate sufficient deviation from Hardy-Weinberg equilibrium to be detected. As expected, genotyping error due to neighboring SNPs attenuates risk estimates, often drastically. For the moment, the most widely accepted method of detecting genotyping error is to confirm genotypes by sequencing and/or genotyping via a separate method. While these methods are fairly reliable, they are also costly and time consuming.