Utilizing Population Controls in Rare-Variant Case-Parent Association Tests

There is great interest in detecting associations between human traits and rare genetic variation. To address the low power implicit in single-locus tests of rare genetic variants, many rare-variant association approaches attempt to accumulate information across a gene, often by taking linear combinations of single-locus contributions to a statistic. Using the right linear combination is key—an optimal test will up-weight true causal variants, down-weight neutral variants, and correctly assign the direction of effect for causal variants. Here, we propose a procedure that exploits data from population controls to estimate the linear combination to be used in an case-parent trio rare-variant association test. Specifically, we estimate the linear combination by comparing population control allele frequencies with allele frequencies in the parents of affected offspring. These estimates are then used to construct a rare-variant transmission disequilibrium test (rvTDT) in the case-parent data. Because the rvTDT is conditional on the parents’ data, using parental data in estimating the linear combination does not affect the validity or asymptotic distribution of the rvTDT. By using simulation, we show that our new population-control-based rvTDT can dramatically improve power over rvTDTs that do not use population control information across a wide variety of genetic architectures. It also remains valid under population stratification. We apply the approach to a cohort of epileptic encephalopathy (EE) trios and find that dominant (or additive) inherited rare variants are unlikely to play a substantial role within EE genes previously identified through de novo mutation studies.     

Rare-Variant Extensions of the Transmission Disequilibrium Test: Application to Autism Exome Sequence Data

Many population-based rare-variant (RV) association tests, which aggregate variants across a region, have been developed to analyze sequence data. A drawback of analyzing population-based data is that it is difficult to adequately control for population substructure and admixture, and spurious associations can occur. For RVs, this problem can be substantial, because the spectrum of rare variation can differ greatly between populations. A solution is to analyze parent-child trio data, by using the transmission disequilibrium test (TDT), which is robust to population substructure and admixture. We extended the TDT to test for RV associations using four commonly used methods. We demonstrate that for all RV-TDT methods, using proper analysis strategies, type I error is well-controlled even when there are high levels of population substructure or admixture. For trio data, unlike for population-based data, RV allele-counting association methods will lead to inflated type I errors. However type I errors can be properly controlled by obtaining p values empirically through haplotype permutation. The power of the RV-TDT methods was evaluated and compared to the analysis of case-control data with a number of genetic and disease models. The RV-TDT was also used to analyze exome data from 199 Simons Simplex Collection autism trios and an association was observed with variants in ABCA7. Given the problem of adequately controlling for population substructure and admixture in RV association studies and the growing number of sequence-based trio studies, the RV-TDT is extremely beneficial to elucidate the involvement of RVs in the etiology of complex traits.     

Extending rare-variant testing strategies: analysis of noncoding sequence and imputed genotypes

Next Generation Sequencing Technology has revolutionized our ability to study the contribution of rare genetic variation to heritable traits. However, existing single-marker association tests are underpowered for detecting rare risk variants. A more powerful approach involves pooling methods that combine multiple rare variants from the same gene into a single test statistic. Proposed pooling methods can be limited because they generally assume high-quality genotypes derived from deep-coverage sequencing, which may not be available. In this paper, we consider an intuitive and computationally efficient pooling statistic, the cumulative minor-allele test (CMAT). We assess the performance of the CMAT and other pooling methods on datasets simulated with population genetic models to contain realistic levels of neutral variation. We consider study designs ranging from exon-only to whole-gene analyses that contain noncoding variants. For all study designs, the CMAT achieves power comparable to that of previously proposed methods. We then extend the CMAT to probabilistic genotypes and describe application to low-coverage sequencing and imputation data. We show that augmenting sequence data with imputed samples is a practical method for increasing the power of rare-variant studies. We also provide a method of controlling for confounding variables such as population stratification. Finally, we demonstrate that our method makes it possible to use external imputation templates to analyze rare variants imputed into existing GWAS datasets. As proof of principle, we performed a CMAT analysis of more than 8 million SNPs that we imputed into the GAIN psoriasis dataset by using haplotypes from the 1000 Genomes Project.     

A Statistical Approach for Rare-Variant Association Testing in Affected Sibships

Sequencing and exome-chip technologies have motivated development of novel statistical tests to identify rare genetic variation that influences complex diseases. Although many rare-variant association tests exist for case-control or cross-sectional studies, far fewer methods exist for testing association in families. This is unfortunate, because cosegregation of rare variation and disease status in families can amplify association signals for rare variants. Many researchers have begun sequencing (or genotyping via exome chips) familial samples that were either recently collected or previously collected for linkage studies. Because many linkage studies of complex diseases sampled affected sibships, we propose a strategy for association testing of rare variants for use in this study design. The logic behind our approach is that rare susceptibility variants should be found more often on regions shared identical by descent by affected sibling pairs than on regions not shared identical by descent. We propose both burden and variance-component tests of rare variation that are applicable to affected sibships of arbitrary size and that do not require genotype information from unaffected siblings or independent controls. Our approaches are robust to population stratification and produce analytic p values, thereby enabling our approach to scale easily to genome-wide studies of rare variation. We illustrate our methods by using simulated data and exome chip data from sibships ascertained for hypertension collected as part of the Genetic Epidemiology Network of Arteriopathy (GENOA) study.     

Population substructure and control selection in genome-wide association studies

Determination of the relevance of both demanding classical epidemiologic criteria for control selection and robust handling of population stratification (PS) represents a major challenge in the design and analysis of genome-wide association studies (GWAS). Empirical data from two GWAS in European Americans of the Cancer Genetic Markers of Susceptibility (CGEMS) project were used to evaluate the impact of PS in studies with different control selection strategies. In each of the two original case-control studies nested in corresponding prospective cohorts, a minor confounding effect due to PS (inflation factor lambda of 1.025 and 1.005) was observed. In contrast, when the control groups were exchanged to mimic a cost-effective but theoretically less desirable control selection strategy, the confounding effects were larger (lambda of 1.090 and 1.062). A panel of 12,898 autosomal SNPs common to both the Illumina and Affymetrix commercial platforms and with low local background linkage disequilibrium (pair-wise r(2)<0.004) was selected to infer population substructure with principal component analysis. A novel permutation procedure was developed for the correction of PS that identified a smaller set of principal components and achieved a better control of type I error (to lambda of 1.032 and 1.006, respectively) than currently used methods. The overlap between sets of SNPs in the bottom 5% of p-values based on the new test and the test without PS correction was about 80%, with the majority of discordant SNPs having both ranks close to the threshold. Thus, for the CGEMS GWAS of prostate and breast cancer conducted in European Americans, PS does not appear to be a major problem in well-designed studies. A study using suboptimal controls can have acceptable type I error when an effective strategy for the correction of PS is employed.     

Simulation of Finnish Population History,Guided by Empirical Genetic Data,to Assess Power of Rare-Variant Tests in Finland

Finnish samples have been extensively utilized in studying single-gene disorders, where the founder effect has clearly aided in discovery, and more recently in genome-wide association studies of complex traits, where the founder effect has had less obvious impacts. As the field starts to explore rare variants’ contribution to polygenic traits, it is of great importance to characterize and confirm the Finnish founder effect in sequencing data and to assess its implications for rare-variant association studies. Here, we employ forward simulation, guided by empirical deep resequencing data, to model the genetic architecture of quantitative polygenic traits in both the general European and the Finnish populations simultaneously. We demonstrate that power of rare-variant association tests is higher in the Finnish population, especially when variants’ phenotypic effects are tightly coupled with fitness effects and therefore reflect a greater contribution of rarer variants. SKAT-O, variable-threshold tests, and single-variant tests are more powerful than other rare-variant methods in the Finnish population across a range of genetic models. We also compare the relative power and efficiency of exome array genotyping to those of high-coverage exome sequencing. At a fixed cost, less expensive genotyping strategies have far greater power than sequencing; in a fixed number of samples, however, genotyping arrays miss a substantial portion of genetic signals detected in sequencing, even in the Finnish founder population. As genetic studies probe sequence variation at greater depth in more diverse populations, our simulation approach provides a framework for evaluating various study designs for gene discovery.     

Improving data interpretation of fragmentary data-sets on invertebrate dispersal with permutation tests

Biological data often tend to have heterogeneous, discontinuous non-normal distributions. Statistical non-parametric tests, like the Mann–Whitney U-test or the extension for more than two samples, the Kruskal–Wallis test, are often used in these cases, although they assume certain preconditions which are often ignored. We developed a permutation test procedure that uses the ratio of the interquartile distances and the median differences of the original non-classified data to assess the properties of the real distribution more appropriately than the classical methods. We used this test on a heterogeneous, skewed biological data set on invertebrate dispersal and showed how different the reactions of the Kruskal–Wallis test and the permutation approach are. We then evaluated the new testing procedure with reproducible data that were generated from the normal distribution. Here, we tested the influence of four different experimental trials on the new testing procedure in comparison to the Kruskal–Wallis test. These trials showed the impact of data that were varying in terms of (a) negative correlation between variances and means of the samples, (b) changing variances that were not correlated with the means of the samples, (c) constant variances and means, but different sample sizes and in trials (d) we evaluated the testing power of the new procedure. Due to the different test statistics, the permutation test reacted more sensibly to the data presented in trials (a) and c) and non-uniformly in trial (b). In the evaluation of the testing power, no significant differences between the Kruskal–Wallis test and the new permutation testing procedure could be detected. We consider this test to be an alternative for working on heterogeneous data where the preconditions of the classical non-parametric tests are not met.     

A simple and improved correction for population stratification in case-control studies

Population stratification remains an important issue in case-control studies of disease-marker association, even within populations considered to be genetically homogeneous. Campbell et al. (Nature Genetics 2005;37:868-872) illustrated this by showing that stratification induced a spurious association between the lactase gene (LCT) and tall/short status in a European American sample. Furthermore, existing approaches for controlling stratification by use of substructure-informative loci (e.g., genomic control, structured association, and principal components) could not resolve this confounding. To address this problem, we propose a simple two-step procedure. In the first step, we model the odds of disease, given data on substructure-informative loci (excluding the test locus). For each participant, we use this model to calculate a stratification score, which is that participant's estimated odds of disease calculated using his or her substructure-informative-loci data in the disease-odds model. In the second step, we assign subjects to strata defined by stratification score and then test for association between the disease and the test locus within these strata. The resulting association test is valid even in the presence of population stratification. Our approach is computationally simple and less model dependent than are existing approaches for controlling stratification. To illustrate these properties, we apply our approach to the data from Campbell et al. and find no association between the LCT locus and tall/short status. Using simulated data, we show that our approach yields a more appropriate correction for stratification than does principal components or genomic control.     

Exact log-rank tests for unequal follow-up

The asymptotic log-rank and generalized Wilcoxon tests are the standard procedures for comparing samples of possibly censored survival times. For comparison of samples of very different sizes, an exact test is available that is based on a complete permutation of log-rank or Wilcoxon scores. While the asymptotic tests do not keep their nominal sizes if sample sizes differ substantially, the exact complete permutation test requires equal follow-up of the samples. Therefore, we have developed and present two new exact tests also suitable for unequal follow-up. The first of these is an exact analogue of the asymptotic log-rank test and conditions on observed risk sets, whereas the second approach permutes survival times while conditioning on the realized follow-up in each group. In an empirical study, we compare the new procedures with the asymptotic log-rank test, the exact complete permutation test, and an earlier proposed approach that equalizes the follow-up distributions using artificial censoring. Results confirm highly satisfactory performance of the exact procedure conditioning on realized follow-up, particularly in case of unequal follow-up. The advantage of this test over other options of analysis is finally exemplified in the analysis of a breast cancer study.     

Detection of disease genes by use of family data. I. Likelihood-based theory

We present a class of likelihood-based score statistics that accommodate genotypes of both unrelated individuals and families, thereby combining the advantages of case-control and family-based designs. The likelihood extends the one proposed by Schaid and colleagues (Schaid and Sommer 1993, 1994; Schaid 1996; Schaid and Li 1997) to arbitrary family structures with arbitrary patterns of missing data and to dense sets of multiple markers. The score statistic comprises two component test statistics. The first component statistic, the nonfounder statistic, evaluates disequilibrium in the transmission of marker alleles from parents to offspring. This statistic, when applied to nuclear families, generalizes the transmission/disequilibrium test to arbitrary numbers of affected and unaffected siblings, with or without typed parents. The second component statistic, the founder statistic, compares observed or inferred marker genotypes in the family founders with those of controls or those of some reference population. The founder statistic generalizes the statistics commonly used for case-control data. The strengths of the approach include both the ability to assess, by comparison of nonfounder and founder statistics, the potential bias resulting from population stratification and the ability to accommodate arbitrary family structures, thus eliminating the need for many different ad hoc tests. A limitation of the approach is the potential power loss and/or bias resulting from inappropriate assumptions on the distribution of founder genotypes. The systematic likelihood-based framework provided here should be useful in the evaluation of both the relative merits of case-control and various family-based designs and the relative merits of different tests applied to the same design. It should also be useful for genotype-disease association studies done with the use of a dense set of multiple markers.     

A Permutation Test for Oligoset DNA Pooling Studies

Case-control association studies often suffer from population stratification bias. A previous triple combination strategy of stratum matching, genomic controlling, and multiple DNA pooling can correct the bias and save genotyping cost. However the method requires researchers to prepare a multitude of DNA pools—more than 30 case-control pooling sets in total (polyset). In this paper, the authors propose a permutation test for oligoset DNA pooling studies. Monte-Carlo simulations show that the proposed test has a type I error rate under control and a power comparable to that of individual genotyping. For a researcher on a tight budget, oligoset DNA pooling is a viable option.     

Camera: a competitive gene set test accounting for inter-gene correlation

Competitive gene set tests are commonly used in molecular pathway analysis to test for enrichment of a particular gene annotation category amongst the differential expression results from a microarray experiment. Existing gene set tests that rely on gene permutation are shown here to be extremely sensitive to inter-gene correlation. Several data sets are analyzed to show that inter-gene correlation is non-ignorable even for experiments on homogeneous cell populations using genetically identical model organisms. A new gene set test procedure (CAMERA) is proposed based on the idea of estimating the inter-gene correlation from the data, and using it to adjust the gene set test statistic. An efficient procedure is developed for estimating the inter-gene correlation and characterizing its precision. CAMERA is shown to control the type I error rate correctly regardless of inter-gene correlations, yet retains excellent power for detecting genuine differential expression. Analysis of breast cancer data shows that CAMERA recovers known relationships between tumor subtypes in very convincing terms. CAMERA can be used to analyze specified sets or as a pathway analysis tool using a database of molecular signatures.     

Rotation gene set testing for longitudinal expression data

Gene set analysis methods are popular tools for identifying differentially expressed gene sets in microarray data. Most existing methods use a permutation test to assess significance for each gene set. The permutation test's assumption of exchangeable samples is often not satisfied for time‐series data and complex experimental designs, and in addition it requires a certain number of samples to compute p‐values accurately. The method presented here uses a rotation test rather than a permutation test to assess significance. The rotation test can compute accurate p‐values also for very small sample sizes. The method can handle complex designs and is particularly suited for longitudinal microarray data where the samples may have complex correlation structures. Dependencies between genes, modeled with the use of gene networks, are incorporated in the estimation of correlations between samples. In addition, the method can test for both gene sets that are differentially expressed and gene sets that show strong time trends. We show on simulated longitudinal data that the ability to identify important gene sets may be improved by taking the correlation structure between samples into account. Applied to real data, the method identifies both gene sets with constant expression and gene sets with strong time trends.     

A hybrid design for studying genetic influences on risk of diseases with onset early in life

Studies of genetic contributions to risk can be family-based, such as the case-parents design, or population-based, such as the case-control design. Both provide powerful inference regarding associations between genetic variants and risks, but both have limitations. The case-control design requires identifying and recruiting appropriate controls, but it has the advantage that nongenetic risk factors like exposures can be assessed. For a condition with an onset early in life, such as a birth defect, one should also genotype the mothers of cases and the mothers of controls to avoid potential confounding due to maternally mediated genetic effects acting on the fetus during gestation. The case-parents approach is less vulnerable than the case-mother/control-mother approach to biases due to population structure and self-selection. The case-parents approach also allows access to epigenetic phenomena like imprinting, but it cannot evaluate the role of nongenetic cofactors like exposures. We propose a hybrid design based on augmenting a set of affected individuals and their parents with a set of unaffected, unrelated individuals and their parents. The affected individuals and their parents are all genotyped, whereas only the parents of unaffected individuals are genotyped, although exposures are ascertained for both affected and unaffected offspring. The proposed hybrid design, through log-linear, likelihood-based analysis, allows estimation of the relative risk parameters, can provide more power than either the case-parents approach or the case-mother/control-mother approach, permits straightforward likelihood-ratio tests for bias due to mating asymmetry or population stratification, and admits valid alternative analyses when mating is asymmetric or when population stratification is detected.     

A general method for controlling the genome-wide type I error rate in linkage and association mapping experiments in plants

Control of the genome-wide type I error rate (GWER) is an important issue in association mapping and linkage mapping experiments. For the latter, different approaches, such as permutation procedures or Bonferroni correction, were proposed. The permutation test, however, cannot account for population structure present in most association mapping populations. This can lead to false positive associations. The Bonferroni correction is applicable, but usually on the conservative side, because correlation of tests cannot be exploited. Therefore, a new approach is proposed, which controls the genome-wide error rate, while accounting for population structure. This approach is based on a simulation procedure that is equally applicable in a linkage and an association-mapping context. Using the parameter settings of three real data sets, it is shown that the procedure provides control of the GWER and the generalized genome-wide type I error rate (GWER(k)).     

Robust Rare-Variant Association Tests for Quantitative Traits in General Pedigrees

Next-generation sequencing technology has propelled the development of statistical methods to identify rare polygenetic variation associated with complex traits. The majority of these statistical methods are designed for case–control or population-based studies, with few methods that are applicable to family-based studies. Moreover, existing methods for family-based studies mainly focus on trios or nuclear families; there are far fewer existing methods available for analyzing larger pedigrees of arbitrary size and structure. To fill this gap, we propose a method for rare-variant analysis in large pedigree studies that can utilize information from all available relatives. Our approach is based on a kernel machine regression (KMR) framework, which has the advantages of high power, as well as fast and easy calculation of p-values using the asymptotic distribution. Our method is also robust to population stratification due to integration of a QTDT framework (Abecasis et al., Eur J Hum Genet 8(7):545–551, 2000b) with the KMR framework. In our method, we first calculate the expected genotype (between-family component) of a non-founder using all founders’ information and then calculate the deviates (within-family component) of observed genotype from the expectation, where the deviates are robust to population stratification by design. The test statistic, which is constructed using within-family component, is thus robust to population stratification. We illustrate and evaluate our method using simulated data and sequence data from Genetic Analysis Workshop 18.     

Combining association tests across multiple genetic markers in case-control studies

In the search to detect genetic associations between complex traits and DNA variants, a practice is to select a subset of Single Nucleotide Polymorphisms (tag SNPs) in a gene or chromosomal region of interest. This allows study of untyped polymorphisms in this region through the phenomenon of linkage disequilibrium (LD). However, it is crucial in the analysis to utilize such multiple SNP markers efficiently. In this study, we present a robust testing approach (T(C)) that combines single marker association test statistics or p values. This combination is based on the summation of single test statistics or p values, giving greater weight to those with lower p values. We compared the powers of T(C) in identifying common trait loci, using tag SNPs within the same haplotype block that the trait loci reside, with competing published tests, in case-control settings. These competing tests included the Bonferroni procedure (T(B)), the simple permutation procedure (T(P)), the permutation procedure proposed by Hoh et al. (T(P-H)) and its revised version using 'deflated' statistics (T(P-H_def)), the traditional chi(2) procedure (T(CHI)), the regression procedure (Hotelling T(2) test) (T(R)) and the haplotype-based test (T(H)). Results of these comparisons show that our proposed combining procedure (T(C)) is preferred in all scenarios examined. We also apply this new test to a data set from a previously reported association study on airway responsiveness to methacholine.     

Quantitative similarity-based association tests using population samples

Although genetic association studies using unrelated individuals may be subject to bias caused by population stratification, alternative methods that are robust to population stratification, such as family-based association designs, may be less powerful. Furthermore, it is often more feasible and less expensive to collect unrelated individuals. Recently, several statistical methods have been proposed for case-control association tests in a structured population; these methods may be robust to population stratification. In the present study, we propose a quantitative similarity-based association test (QSAT) to identify association between a candidate marker and a quantitative trait of interest, through use of unrelated individuals. For the QSAT, we first determine whether two individuals are from the same subpopulation or from different subpopulations, using genotype data at a set of independent markers. We then perform an association test between the candidate marker and the quantitative trait, through incorporation of such information. Simulation results based on either coalescent models or empirical population genetics data show that the QSAT has a correct type I error rate in the presence of population stratification and that the power of the QSAT is higher than that of family-based association designs.     

Admixture-matched case-control study: a practical approach for genetic association studies in admixed populations

Case-control genetic association studies in admixed populations are known to be susceptible to genetic confounding due to population stratification. The transmission/disequilibrium test (TDT) approach can avoid this problem. However, the TDT is expensive and impractical for late-onset diseases. Case-control study designs, in which, cases and controls are matched by admixture, can be an appealing and a suitable alternative for genetic association studies in admixed populations. In this study, we applied this matching strategy when recruiting our African American participants in the Study of African American, Asthma, Genes and Environments. Group admixture in this cohort consists of 83% African ancestry and 17% European ancestry, which was consistent with reports from other studies. By carrying out several complementary analyses, our results show that there is a substructure in the cohort, but that the admixture distributions are almost identical in cases and controls, and also in cases only. We performed association tests for asthma-related traits with ancestry, and only found that FEV(1), a measure for baseline pulmonary function, was associated with ancestry after adjusting for socio-economic and environmental risk factors (P=0.01). We did not observe an excess of type I error rate in our association tests for ancestry informative markers and asthma-related phenotypes when ancestry was not adjusted in the analyses. Furthermore, using the association tests between genetic variants in a known asthma candidate gene, beta(2) adrenergic receptor (beta(2)AR) and DeltaFEF(25-75), an asthma-related phenotype, as an example, we demonstrated population stratification was not a confounder in our genetic association. Our present work demonstrates that admixture-matched case-control strategies can efficiently control population stratification confounding in admixed populations.     

A note on exact tests of Hardy-Weinberg equilibrium

Deviations from Hardy-Weinberg equilibrium (HWE) can indicate inbreeding, population stratification, and even problems in genotyping. In samples of affected individuals, these deviations can also provide evidence for association. Tests of HWE are commonly performed using a simple chi2 goodness-of-fit test. We show that this chi2 test can have inflated type I error rates, even in relatively large samples (e.g., samples of 1,000 individuals that include approximately 100 copies of the minor allele). On the basis of previous work, we describe exact tests of HWE together with efficient computational methods for their implementation. Our methods adequately control type I error in large and small samples and are computationally efficient. They have been implemented in freely available code that will be useful for quality assessment of genotype data and for the detection of genetic association or population stratification in very large data sets.