Selecting tagging SNPs for association studies using power calculations from genotype data

Recent studies have indicated that linkage disequilibrium (LD) between single nucleotide polymorphism (SNP) markers can be used to derive a reduced set of tagging SNPs (tSNPs) for genetic association studies. Previous strategies for identifying tSNPs have focused on LD measures or haplotype diversity, but the statistical power to detect disease-associated variants using tSNPs in genetic studies has not been fully characterized. We propose a new approach of selecting tSNPs based on determining the set of SNPs with the highest power to detect association. Two-locus genotype frequencies are used in the power calculations. To show utility, we applied this power method to a large number of SNPs that had been genotyped in Caucasian samples. We demonstrate that a significant reduction in genotyping efforts can be achieved although the reduction depends on genotypic relative risk, inheritance mode and the prevalence of disease in the human population. The tSNP sets identified by our method are remarkably robust to changes in the disease model when small relative risk and additive mode of inheritance are employed. We have also evaluated the ability of the method to detect unidentified SNPs. Our findings have important implications in applying tSNPs from different data sources in association studies.     

A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

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.     

Analysis of Allelic Association: Estimation of the Power of the TDT

Analysis of allelic associations is an increasingly more widely used approach to fine mapping of genes of various diseases. To interpret the results correctly, it is necessary to estimate the power of the statistical test used. The principle of the analysis of associations and testing of hypothesis are described, and analytically obtained estimates of the power of the transmission disequilibrium test (TDT), one of the most popular methods of analysis of allelic associations, are presented. These estimates are applicable to arbitrary models of inheritance formulated in terms of genotypic relative risk. The proposed method is illustrated by analysis of the associations of idiopathic scoliosis and aggrecan gene alleles.     

Analysis of allelic association: estimation of the criteria power of the TDT

Analysis of allelic associations is an increasingly more widely used approach to fine mapping of genes of various diseases. To interpret the results correctly, it is necessary to estimate the power of the statistical test used. The principle of the analysis of associations and testing of hypothesis are described, and analytically obtained estimates of the power of the transmission disequilibrium test (TDT), one of the most popular methods of analysis of allelic associations, are presented. These estimates are applicable to arbitrary models of inheritance formulated in terms of relative genotypic risk. The proposed method is illustrated by analysis of the associations of idiopathic scoliosis and aggrecan gene alleles.     

A comparison of different linkage statistics in small to moderate sized pedigrees with complex diseases

ABSTRACT: BACKGROUND: In the last years GWA studies have successfully identified common SNPs associated with complex diseases. However, most of the variants found this way account for only a small portion of the trait variance. This fact leads researchers to focus on rare-variant mapping with large scale sequencing, which can be facilitated by using linkage information. The question arises why linkage analysis often fails to identify genes when analyzing complex diseases. Using simulations we have investigated the power of parametric and nonparametric linkage statistics (KC-LOD, NPL, LOD and MOD scores), to detect the effect of genes responsible for complex diseases using different pedigree structures. RESULTS: As expected, a small number of pedigrees with less than three affected individuals has low power to map disease genes with modest effect. Interestingly, the power decreases when unaffected individuals are included in the analysis, irrespective of the true mode of inheritance. Furthermore, we found that the best performing statistic depends not only on the type of pedigrees but also on the true mode of inheritance. CONCLUSIONS: When applied in a sensible way linkage is an appropriate and robust technique to map genes for complex disease. Unlike association analysis, linkage analysis is not hampered by allelic heterogeneity. So, why does linkage analysis often fail with complex diseases? Evidently, when using an insufficient number of small pedigrees, one might miss a true genetic linkage when actually a real effect exists. Furthermore, we show that the test statistic has an important effect on the power to detect linkage as well. Therefore, a linkage analysis might fail if an inadequate test statistic is employed. We provide recommendations regarding the most favorable test statistics, in terms of power, for a given mode of inheritance and type of pedigrees under study, in order to reduce the probability to miss a true linkage.     

Family-Based Bivariate Association Tests for Quantitative Traits

The availability of a large number of dense SNPs, high-throughput genotyping and computation methods promotes the application of family-based association tests. While most of the current family-based analyses focus only on individual traits, joint analyses of correlated traits can extract more information and potentially improve the statistical power. However, current TDT-based methods are low-powered. Here, we develop a method for tests of association for bivariate quantitative traits in families. In particular, we correct for population stratification by the use of an integration of principal component analysis and TDT. A score test statistic in the variance-components model is proposed. Extensive simulation studies indicate that the proposed method not only outperforms approaches limited to individual traits when pleiotropic effect is present, but also surpasses the power of two popular bivariate association tests termed FBAT-GEE and FBAT-PC, respectively, while correcting for population stratification. When applied to the GAW16 datasets, the proposed method successfully identifies at the genome-wide level the two SNPs that present pleiotropic effects to HDL and TG traits.     

Rapid Testing of SNPs and Gene-Environment Interactions in Case-Parent Trio Data Based on Exact Analytic Parameter Estimation

Summary Case-parent trio studies concerned with children affected by a disease and their parents aim to detect single nucleotide polymorphisms (SNPs) showing a preferential transmission of alleles from the parents to their affected offspring. A popular statistical test for detecting such SNPs associated with disease in this study design is the genotypic transmission/disequilibrium test (gTDT) based on a conditional logistic regression model, which usually needs to be fitted by an iterative procedure. In this article, we derive exact closed-form solutions for the parameter estimates of the conditional logistic regression models when testing for an additive, a dominant, or a recessive effect of a SNP, and show that such analytic parameter estimates also exist when considering gene-environment interactions with binary environmental variables. Because the genetic model underlying the association between a SNP and a disease is typically unknown, it might further be beneficial to use the maximum over the gTDT statistics for the possible effects of a SNP as test statistic. We therefore propose a procedure enabling a fast computation of the test statistic and the permutation-based p-value of this MAX gTDT. All these methods are applied to whole-genome scans of the case-parent trios from the International Cleft Consortium. These applications show our procedures dramatically reduce the required computing time compared to the conventional iterative methods allowing, for example, the analysis of hundreds of thousands of SNPs in a few minutes instead of several hours.     

The future is now - will the real disease gene please stand up?

The transmission/disequilibrium test (TDT) [Spielman et al.: Am J Hum Genet 1993;52:506-516] has been postulated as the future of gene mapping for complex diseases, provided one is able to genotype a dense enough map of markers across the genome. Risch and Merikangas [Science 1996;273:1516-1517] suggested a million-marker screen in affected sibpair (ASP) families, demonstrating that the TDT is a more powerful test of linkage than traditional linkage tests based on allele-sharing when there is also association between marker and disease alleles. While the future of genotyping has arrived, successes in family-based association studies have been modest. This is often attributed to excessive false positives in candidate gene studies. This problem is only exacerbated by the increasing numbers of whole genome association (WGA) screens. When applied in ASPs, the TDT statistic, which assumes transmissions to siblings are independent, is not expected to have a constant variance in the presence of variable linkage. This results in generally more extreme statistics, hence will further aggravate the problem of having a large number of positive results to sort through. So an important question is how many positive TDT results will show up on a chromosome containing a disease gene due only to linkage, and will they obfuscate the true disease gene location. To answer this question we combined theory and computer simulations. These studies show that in ASPs the normal version of the TDT statistic has a mean of 0 and a variance of 1 in unlinked regions, but has a variance larger than 1 in linked regions. In contrast, the pedigree disequilibrium test (PDT) statistic adjusts for correlation between siblings due to linkage and maintains a constant variance of 1 at unassociated markers irrespective of linkage. The TDT statistic is generally larger than the PDT statistic across linked regions. This is true for unassociated as well as associated markers. To compare the two tests we ranked both statistics at the disease locus, or an associated marker, among statistics at all other markers. The TDT did better job than PDT placing the score of the associated marker near the top. Though, strictly speaking, the TDT in ASPs should be interpreted as a test of linkage and not a test of association, there is a good chance that if a marker stands out, the marker is associated as well as linked. In conclusion, our results suggest that TDT is an effective screening tool for WGA studies, especially in multiplex families.     

Linkage detection adaptive to linkage disequilibrium: the disequilibrium maximum-likelihood-binomial test for affected-sibship data

It has been demonstrated in the literature that the transmission/disequilibrium test (TDT) has higher power than the affected-sib-pair (ASP) mean test when linkage disequilibrium (LD) is strong but that the mean test has higher power when LD is weak. Thus, for ASP data, it seems clear that the TDT should be used when LD is strong but that the mean test or other linkage tests should be used when LD is weak or absent. However, in practice, it may be difficult to follow such a guideline, because the extent of LD is often unknown. Even with a highly dense genetic-marker map, in which some markers should be located near the disease-predisposing mutation, strong LD is not inevitable. Besides the genetic distance, LD is also affected by many factors, such as the allelic heterogeneity at the disease locus, the initial LD, the allelic frequencies at both disease locus and marker locus, and the age of the mutation. Therefore, it is of interest to develop methods that are adaptive to the extent of LD. In this report, we propose a disequilibrium maximum-binomial-likelihood (DMLB) test that incorporates LD in the maximum-binomial-likelihood (MLB) test. Examination of the corresponding score statistics shows that this method adaptively combines two sources of information: (a) the identity-by-descent (IBD) sharing score, which is informative for linkage regardless of the existence of LD, and (b) the contrast between allele-specific IBD sharing score, which is informative for linkage only in the presence of LD. For ASP data, the proposed test has higher power than either the TDT or the mean test when the extent of LD ranges from moderate to strong. Only when LD is very weak or absent is the DMLB slightly less powerful than the mean test; in such cases, the TDT has essentially no power to detect linkage. Therefore, the DMLB test is an interesting approach to linkage detection when the extent of LD is unknown.     

A log-linear approach to case-parent-triad data: assessing effects of disease genes that act either directly or through maternal effects and that may be subject to parental imprinting.

We describe a log-linear method for analysis of case-parent-triad data, based on maximum likelihood with stratification on parental mating type. The method leads to estimates of association parameters, such as relative risks, for a single allele, and also to likelihood ratio chi2 tests (LRTs) of linkage disequilibrium. Hardy-Weinberg equilibrium need not be assumed. Our simulations suggest that the LRT has power similar to that of the chi2 "score" test proposed by Schaid and Sommer and that both can outperform the transmission/disequilibrium test (TDT), although the TDT can perform better under an additive model of inheritance. Because a restricted version of the LRT is asymptotically equivalent to the TDT, the proposed test can be regarded as a generalization of the TDT. The method that we describe generalizes easily to accommodate maternal effects on risk and, in fact, produces powerful and orthogonal tests of the contribution of fetal versus maternal genetic factors. We further generalize the model to allow for effects of parental imprinting. Imprinting effects can be fitted by a simple, iterative procedure that relies on the expectation-maximization algorithm and that uses standard statistical software for the maximization steps. Simulations reveal that LRT tests for detection of imprinting have very good operating characteristics. When a single allele is under study, the proposed method can yield powerful tests for detection of linkage disequilibrium and is applicable to a broader array of causal scenarios than is the TDT.     

Association Testing Strategy for Data from Dense Marker Panels

Genome wide association studies have been usually analyzed in a univariate manner. The commonly used univariate tests have one degree of freedom and assume an additive mode of inheritance. The experiment-wise significance of these univariate statistics is obtained by adjusting for multiple testing. Next generation sequencing studies, which assay 10-20 million variants, are beginning to come online. For these studies, the strategy of additive univariate testing and multiple testing adjustment is likely to result in a loss of power due to (1) the substantial multiple testing burden and (2) the possibility of a non-additive causal mode of inheritance. To reduce the power loss we propose: a new method (1) to summarize in a single statistic the strength of the association signals coming from all not-very-rare variants in a linkage disequilibrium block and (2) to incorporate, in any linkage disequilibrium block statistic, the strength of the association signals under multiple modes of inheritance. The proposed linkage disequilibrium block test consists of the sum of squares of nominally significant univariate statistics. We compare the performance of this method to the performance of existing linkage disequilibrium block/gene-based methods. Simulations show that (1) extending methods to combine testing for multiple modes of inheritance leads to substantial power gains, especially for a recessive mode of inheritance, and (2) the proposed method has a good overall performance. Based on simulation results, we provide practical advice on choosing suitable methods for applied analyses.     

A Transmission/Disequilibrium Test That Allows for Genotyping Errors in the Analysis of Single-Nucleotide Polymorphism Data

The present study assesses the effects of genotyping errors on the type I error rate of a particular transmission/disequilibrium test (TDT(std)), which assumes that data are errorless, and introduces a new transmission/disequilibrium test (TDT(ae)) that allows for random genotyping errors. We evaluate the type I error rate and power of the TDT(ae) under a variety of simulations and perform a power comparison between the TDT(std) and the TDT(ae), for errorless data. Both the TDT(std) and the TDT(ae) statistics are computed as two times a log-likelihood difference, and both are asymptotically distributed as chi(2) with 1 df. Genotype data for trios are simulated under a null hypothesis and under an alternative (power) hypothesis. For each simulation, errors are introduced randomly via a computer algorithm with different probabilities (called "allelic error rates"). The TDT(std) statistic is computed on all trios that show Mendelian consistency, whereas the TDT(ae) statistic is computed on all trios. The results indicate that TDT(std) shows a significant increase in type I error when applied to data in which inconsistent trios are removed. This type I error increases both with an increase in sample size and with an increase in the allelic error rates. TDT(ae) always maintains correct type I error rates for the simulations considered. Factors affecting the power of the TDT(ae) are discussed. Finally, the power of TDT(std) is at least that of TDT(ae) for simulations with errorless data. Because data are rarely error free, we recommend that researchers use methods, such as the TDT(ae), that allow for errors in genotype data.     

Screening and replication using the same data set: testing strategies for family-based studies in which all probands are affected

For genome-wide association studies in family-based designs, we propose a powerful two-stage testing strategy that can be applied in situations in which parent-offspring trio data are available and all offspring are affected with the trait or disease under study. In the first step of the testing strategy, we construct estimators of genetic effect size in the completely ascertained sample of affected offspring and their parents that are statistically independent of the family-based association/transmission disequilibrium tests (FBATs/TDTs) that are calculated in the second step of the testing strategy. For each marker, the genetic effect is estimated (without requiring an estimate of the SNP allele frequency) and the conditional power of the corresponding FBAT/TDT is computed. Based on the power estimates, a weighted Bonferroni procedure assigns an individually adjusted significance level to each SNP. In the second stage, the SNPs are tested with the FBAT/TDT statistic at the individually adjusted significance levels. Using simulation studies for scenarios with up to 1,000,000 SNPs, varying allele frequencies and genetic effect sizes, the power of the strategy is compared with standard methodology (e.g., FBATs/TDTs with Bonferroni correction). In all considered situations, the proposed testing strategy demonstrates substantial power increases over the standard approach, even when the true genetic model is unknown and must be selected based on the conditional power estimates. The practical relevance of our methodology is illustrated by an application to a genome-wide association study for childhood asthma, in which we detect two markers meeting genome-wide significance that would not have been detected using standard methodology.     

Testing for Genetic Association in the Presence of Linkage and Gene–Covariate Interactions

In order to study family‐based association in the presence of linkage, we extend a generalized linear mixed model proposed for genetic linkage analysis (Lebrec and van Houwelingen (2007), Human Heredity 64 , 5–15) by adding a genotypic effect to the mean. The corresponding score test is a weighted family‐based association tests statistic, where the weight depends on the linkage effect and on other genetic and shared environmental effects. For testing of genetic association in the presence of gene–covariate interaction, we propose a linear regression method where the family‐specific score statistic is regressed on family‐specific covariates. Both statistics are straightforward to compute. Simulation results show that adjusting the weight for the within‐family variance structure may be a powerful approach in the presence of environmental effects. The test statistic for genetic association in the presence of gene–covariate interaction improved the power for detecting association. For illustration, we analyze the rheumatoid arthritis data from GAW15. Adjusting for smoking and anti‐cyclic citrullinated peptide increased the significance of the association with the DR locus.     

Undetected genotyping errors cause apparent overtransmission of common alleles in the transmission/disequilibrium test

The transmission/disequilibrium test (TDT), a family-based test of linkage and association, is a popular and intuitive statistical test for studies of complex inheritance, as it is nonparametric and robust to population stratification. We carried out a literature search and located 79 significant TDT-derived associations between a microsatellite marker allele and a disease. Among these, there were 31 (39%) in which the most common allele was found to exhibit distorted transmission to affected offspring, implying that the allele may be associated with either susceptibility to or protection from a disease. In 27 of these 31 studies (87%), the most common allele appeared to be overtransmitted to affected offspring (a risk factor), and, in the remaining 4 studies, the most common allele appeared to be undertransmitted (a protective factor). In a second literature search, we identified 92 case-control studies in which a microsatellite marker allele was found to have significantly different frequencies in case and control groups. Of these, there were 37 instances (40%) in which the most common allele was involved. In 12 of these 37 studies (32%), the most common allele was enriched in cases relative to controls (a risk factor), and, in the remaining 25 studies, the most common allele was enriched in controls (a protective factor). Thus, the most common allele appears to be a risk factor when identified through the TDT, and it appears to be protective when identified through case-control analysis. To understand this phenomenon, we incorporated an error model into the calculation of the TDT statistic. We show that undetected genotyping error can cause apparent transmission distortion at markers with alleles of unequal frequency. We demonstrate that this distortion is in the direction of overtransmission for common alleles. Therefore, we conclude that undetected genotyping errors may be contributing to an inflated false-positive rate among reported TDT-derived associations and that genotyping fidelity must be increased.     

Nonlinear tests for genomewide association studies

As millions of single-nucleotide polymorphisms (SNPs) have been identified and high-throughput genotyping technologies have been rapidly developed, large-scale genomewide association studies are soon within reach. However, since a genomewide association study involves a large number of SNPs it is therefore nearly impossible to ensure a genomewide significance level of 0.05 using the available statistics, although the multiple-test problems can be alleviated, but not sufficiently, by the use of tagging SNPs. One strategy to circumvent the multiple-test problem associated with genome-wide association tests is to develop novel test statistics with high power. In this report, we introduce several nonlinear tests, which are based on nonlinear transformation of allele or haplotype frequencies. We investigate the power of the nonlinear test statistics and demonstrate that under certain conditions, some nonlinear test statistics have much higher power than the standard chi2-test statistic. Type I error rates of the nonlinear tests are validated using simulation studies. We also show that a class of similarity measure-based test statistics is based on the quadratic function of allele or haplotype frequencies, and thus they belong to nonlinear tests. To evaluate their performance, the nonlinear test statistics are also applied to three real data sets. Our study shows that nonlinear test statistics have great potential in association studies of complex diseases.     

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.     

Development and Application of Genomic Control Methods for Genome-Wide Association Studies Using Non-Additive Models

Genome-wide association studies (GWAS) comprise a powerful tool for mapping genes of complex traits. However, an inflation of the test statistic can occur because of population substructure or cryptic relatedness, which could cause spurious associations. If information on a large number of genetic markers is available, adjusting the analysis results by using the method of genomic control (GC) is possible. GC was originally proposed to correct the Cochran-Armitage additive trend test. For non-additive models, correction has been shown to depend on allele frequencies. Therefore, usage of GC is limited to situations where allele frequencies of null markers and candidate markers are matched. In this work, we extended the capabilities of the GC method for non-additive models, which allows us to use null markers with arbitrary allele frequencies for GC. Analytical expressions for the inflation of a test statistic describing its dependency on allele frequency and several population parameters were obtained for recessive, dominant, and over-dominant models of inheritance. We proposed a method to estimate these required population parameters. Furthermore, we suggested a GC method based on approximation of the correction coefficient by a polynomial of allele frequency and described procedures to correct the genotypic (two degrees of freedom) test for cases when the model of inheritance is unknown. Statistical properties of the described methods were investigated using simulated and real data. We demonstrated that all considered methods were effective in controlling type 1 error in the presence of genetic substructure. The proposed GC methods can be applied to statistical tests for GWAS with various models of inheritance. All methods developed and tested in this work were implemented using R language as a part of the GenABEL package.