A simple and robust TDT-type test against genotyping error with error rates varying across families

The transmission/disequilibrium test (TDT), a family based test of linkage and association, is a popular test for studies of complex inheritance, as it is nonparametric and robust against spurious conclusions induced by hidden genetic structure, such as stratification or admixture. However, the TDT may be biased by genotyping errors. Undetected genotyping errors may be contributing to an inflated type I error rate among reported TDT-derived associations. To adjust for bias, a popular approach is to assume a genotype error model for describing the pattern of errors and propose association tests using likelihood method. However, all model-based approaches tend to perform unsatisfactorily if the related genotyping error rates are not identical across all families. In this paper, we propose a TDT-type association test which is not only simple, robust against population stratification (and hence the assumption of Hardy-Weinberg equilibrium is not required), but also robust against genotyping error with error rates varying across families. Simulation studies confirm that the new test has very reasonable performance.     

Robust genomic control and robust delta centralization tests for case-control association studies

The population-based case-control design is a powerful approach for detecting susceptibility markers of a complex disease. However, this approach may lead to spurious association when there is population substructure: population stratification (PS) or cryptic relatedness (CR). Two simple approaches to correct for the population substructure are genomic control (GC) and delta centralization (DC). GC uses the variance inflation factor to correct for the variance distortion of a test statistic, and the DC centralizes the non-central chi-square distribution of the test statistic. Both GC and DC have been studied for case-control association studies mainly under a specific genetic model (e.g. recessive, additive or dominant), under which an optimal trend test is available. The genetic model is usually unknown for many complex diseases. In this situation, we study the performance of three robust tests based on the GC and DC corrections in the presence of the population substructure. Our results show that, when the genetic model is unknown, the DC- (or GC-) corrected maximum and Pearson's association test are robust and have good control of Type I error and high power relative to the optimal trend tests in the presence of PS (or CR).     

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.     

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.     

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.     

Effect of population stratification on case-control association studies. II. False-positive rates and their limiting behavior as number of subpopulations increases

There has been considerable debate in the literature concerning bias in case-control association mapping studies due to population stratification. In this paper, we perform a theoretical analysis of the effects of population stratification by measuring the inflation in the test's type I error (or false-positive rate). Using a model of stratified sampling, we derive an exact expression for the type I error as a function of population parameters and sample size. We give necessary and sufficient conditions for the bias to vanish when there is no statistical association between disease and marker genotype in each of the subpopulations making up the total population. We also investigate the variation of bias with increasing subpopulations and show, both theoretically and by using simulations, that the bias can sometimes be quite substantial even with a very large number of subpopulations. In a companion simulation-based paper (Heiman et al., Part I, this issue), we have focused on the CRR (confounding risk ratio) and its relationship to the type I error in the case of two subpopulations, and have also quantified the magnitude of the type I error that can occur with relatively low CRR values.     

A unified approach for quantifying, testing and correcting population stratification in case-control association studies

The HapMap project has given case-control association studies a unique opportunity to uncover the genetic basis of complex diseases. However, persistent issues in such studies remain the proper quantification of, testing for, and correction for population stratification (PS). In this paper, we present the first unified paradigm that addresses all three fundamental issues within one statistical framework. Our unified approach makes use of an omnibus quantity (delta), which can be estimated in a case-control study from suitable null loci. We show how this estimated value can be used to quantify PS, to statistically test for PS, and to correct for PS, all in the context of case-control studies. Moreover, we provide guidelines for interpreting values of delta in association studies (e.g., at alpha = 0.05, a delta of size 0.416 is small, a delta of size 0.653 is medium, and a delta of size 1.115 is large). A novel feature of our testing procedure is its ability to test for either strictly any PS or only 'practically important' PS. We also performed simulations to compare our correction procedure with Genomic Control (GC). Our results show that, unlike GC, it maintains good Type I error rates and power across all levels of PS.     

Robust genomic control for association studies

Population-based case-control studies are a useful method to test for a genetic association between a trait and a marker. However, the analysis of the resulting data can be affected by population stratification or cryptic relatedness, which may inflate the variance of the usual statistics, resulting in a higher-than-nominal rate of false-positive results. One approach to preserving the nominal type I error is to apply genomic control, which adjusts the variance of the Cochran-Armitage trend test by calculating the statistic on data from null loci. This enables one to estimate any additional variance in the null distribution of statistics. When the underlying genetic model (e.g., recessive, additive, or dominant) is known, genomic control can be applied to the corresponding optimal trend tests. In practice, however, the mode of inheritance is unknown. The genotype-based chi (2) test for a general association between the trait and the marker does not depend on the underlying genetic model. Since this general association test has 2 degrees of freedom (df), the existing formulas for estimating the variance factor by use of genomic control are not directly applicable. By expressing the general association test in terms of two Cochran-Armitage trend tests, one can apply genomic control to each of the two trend tests separately, thereby adjusting the chi (2) statistic. The properties of this robust genomic control test with 2 df are examined by simulation. This genomic control-adjusted 2-df test has control of type I error and achieves reasonable power, relative to the optimal tests for each model.     

Incorporating individual error rate into association test of unmatched case-control design

OBJECTIVES: Genotyping error commonly occurs and could reduce the power and bias statistical inference in genetics studies. In addition to genotypes, some automated biotechnologies also provide quality measurement of each individual genotype. We studied the relationship between the quality measurement and genotyping error rate. Furthermore, we propose two association tests incorporating the genotyping quality information with the goal to improve statistical power and inference. METHODS: 50 pairs of DNA sample duplicates were typed for 232 SNPs by BeadArray technology. We used scatter plot, smoothing function and generalized additive models to investigate the relationship between genotype quality score (q) and inconsistency rate (?) among duplicates. We constructed two association tests: (1) weighted contingency table test (WCT) and (2) likelihood ratio test (LRT) to incorporate individual genotype error rate (epsilon(i)), in unmatched case-control setting. RESULTS: In the 50 duplicates, we found q and ? were in strong negative association, suggesting the genotypes with low quality score were more likely to be mistyped. The WCT improved the statistical power and partially corrects the bias in point estimation. The LRT offered moderate power gain, but was able to correct the bias in odds ratio estimation. The two new methods also performed favorably in some scenarios when epsilon(i) was mis-specified. CONCLUSIONS: With increasing number of genetic studies and application of automated genotyping technology, there is a growing need to adequately account for individual genotype error rate in statistical analysis. Our study represents an initial step to address this need and points out a promising direction for further research.     

Power and sample size calculations for case-control genetic association tests when errors are present: application to single nucleotide polymorphisms

The purpose of this work is to quantify the effects that errors in genotyping have on power and the sample size necessary to maintain constant asymptotic Type I and Type II error rates (SSN) for case-control genetic association studies between a disease phenotype and a di-allelic marker locus, for example a single nucleotide polymorphism (SNP) locus. We consider the effects of three published models of genotyping errors on the chi-square test for independence in the 2 x 3 table. After specifying genotype frequencies for the marker locus conditional on disease status and error model in both a genetic model-based and a genetic model-free framework, we compute the asymptotic power to detect association through specification of the test's non-centrality parameter. This parameter determines the functional dependence of SSN on the genotyping error rates. Additionally, we study the dependence of SSN on linkage disequilibrium (LD), marker allele frequencies, and genotyping error rates for a dominant disease model. Increased genotyping error rate requires a larger SSN. Every 1% increase in sum of genotyping error rates requires that both case and control SSN be increased by 2-8%, with the extent of increase dependent upon the error model. For the dominant disease model, SSN is a nonlinear function of LD and genotyping error rate, with greater SSN for lower LD and higher genotyping error rate. The combination of lower LD and higher genotyping error rates requires a larger SSN than the sum of the SSN for the lower LD and for the higher genotyping error rate.     

A semiparametric test to detect associations between quantitative traits and candidate genes in structured populations

MOTIVATION: Although population-based association mapping may be subject to the bias caused by population stratification, alternative methods that are robust to population stratification such as family-based linkage analysis have lower mapping resolution. Recently, various statistical methods robust to population stratification were proposed for association studies, using unrelated individuals to identify associations between candidate genes and traits of interest. The association between a candidate gene and a quantitative trait is often evaluated via a regression model with inferred population structure variables as covariates, where the residual distribution is customarily assumed to be from a symmetric and unimodal parametric family, such as a Gaussian, although this may be inappropriate for the analysis of many real-life datasets. RESULTS: In this article, we proposed a new structured association (SA) test. Our method corrects for continuous population stratification by first deriving population structure and kinship matrices through a set of random genetic markers and then modeling the relationship between trait values, genotypic scores at a candidate marker and genetic background variables through a semiparametric model, where the error distribution is modeled as a mixture of Polya trees centered around a normal family of distributions. We compared our model to the existing SA tests in terms of model fit, type I error rate, power, precision and accuracy by application to a real dataset as well as simulated datasets.     

Bias correction with a single null marker for population stratification in candidate gene association studies

Population stratification is a form of confounding by ethnicity that may cause bias to effect estimates and inflate test statistics in genetic association studies. Unlinked genetic markers have been used to adjust for test statistics, but their use in correcting biased effect estimates has not been addressed. We evaluated the potential of bias correction that could be achieved by a single null marker (M) in studies involving one candidate gene (G). When the distribution of M varied greatly across ethnicities, controlling for M in a logistic regression model substantially reduced biases on odds ratio estimates. When M had same distributions as G across ethnicities, biases were further reduced or eliminated by subtracting the regression coefficient of M from the coefficient of G in the model, which was fitted either with or without a multiplicative interaction term between M and G. Correction of bias due to population stratification depended specifically on the distributions of G and M, the difference between baseline disease risks across ethnicities, and whether G had an effect on disease risk or not. Our results suggested that marker choice and the specific treatment of that marker in analysis greatly influenced bias correction.     

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.     

The bias introduced by population stratification in IBD based linkage analysis

The lack of replication of model-free linkage analyses performed on complex diseases raises questions about the robustness of these methods to various biases. The confounding effect of population stratification on a genetic association study has long been recognized in the genetic epidemiology community. Because the estimation of the number of alleles shared identical by descent (IBD) does not depend on the marker allele frequency when founders of families are observed, model-free linkage analysis is usually thought to be robust to population stratification. However, for common complex diseases, the genotypes of founders are often unobserved and therefore population stratification has the potential to impair model-free linkage analysis. Here, we demonstrate that, when some or all of the founder genotypes are missing, population stratification can introduce deleterious effects on various model-free linkage methods or designs. For an affected sib pair design, it can cause excess false-positive discoveries even when the trait distribution is homogeneous among subpopulations. After incorporating a control group of discordant sib pairs or for a quantitative trait, two circumstances must be met for population stratification to be a confounder: the distributions for both the marker and the trait must be heterogeneous among subpopulations. When this occurs, the bias can result in either a liberal, and hence invalid, test or a conservative test. Bias can be eliminated or alleviated by inclusion of founders' or other family members' genotype data. When this is not possible, new methods need to be developed to be robust to population stratification.     

Validation of a cost-efficient multi-purpose SNP panel for disease based research

Background

Here we present convergent methodologies using theoretical calculations, empirical assessment on in-house and publicly available datasets as well as in silico simulations, that validate a panel of SNPs for a variety of necessary tasks in human genetics disease research before resources are committed to larger-scale genotyping studies on those samples. While large-scale well-funded human genetic studies routinely have up to a million SNP genotypes, samples in a human genetics laboratory that are not yet part of such studies may be productively utilized in pilot projects or as part of targeted follow-up work though such smaller scale applications require at least some genome-wide genotype data for quality control purposes such as DNA “barcoding” to detect swaps or contamination issues, determining familial relationships between samples and correcting biases due to population effects such as population stratification in pilot studies.

Principal Findings

Empirical performance in classification of relative types for any two given DNA samples (e.g., full siblings, parental, etc) indicated that for outbred populations the panel performs sufficiently to classify relationship in extended families and therefore also for smaller structures such as trios and for twin zygosity testing. Additionally, familial relationships do not significantly diminish the (mean match) probability of sharing SNP genotypes in pedigrees, further indicating the uniqueness of the “barcode.” Simulation using these SNPs for an African American case-control disease association study demonstrated that population stratification, even in complex admixed samples, can be adequately corrected under a range of disease models using the SNP panel.

Conclusion

The panel has been validated for use in a variety of human disease genetics research tasks including sample barcoding, relationship verification, population substructure detection and statistical correction. Given the ease of genotyping our specific assay contained herein, this panel represents a useful and economical panel for human geneticists.     

Testing gene-gene interactions in the case-parents design

The case-parents design has been widely used to detect genetic associations as it can prevent spurious association that could occur in population-based designs. When examining the effect of an individual genetic locus on a disease, logistic regressions developed by conditioning on parental genotypes provide complete protection from spurious association caused by population stratification. However, when testing gene-gene interactions, it is unknown whether conditional logistic regressions are still robust. Here we evaluate the robustness and efficiency of several gene-gene interaction tests that are derived from conditional logistic regressions. We found that in the presence of SNP genotype correlation due to population stratification or linkage disequilibrium, tests with incorrectly specified main-genetic-effect models can lead to inflated type I error rates. We also found that a test with fully flexible main genetic effects always maintains correct test size and its robustness can be achieved with negligible sacrifice of its power. When testing gene-gene interactions is the focus, the test allowing fully flexible main effects is recommended to be used.     

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.     

Exact tests for the analysis of case-control studies of genetic markers

OBJECTIVES: The association of a candidate gene with disease can be evaluated by a case-control study in which the genotype distribution is compared for diseased cases and unaffected controls. Usually, the data are analyzed with Armitage's test using the asymptotic null distribution of the test statistic. Since this test does not generally guarantee a type I error rate less than or equal to the significance level alpha, tests based on exact null distributions have been investigated. METHODS: An algorithm to generate the exact null distribution for both Armitage's test statistic and a recently proposed modification of the Baumgartner-Weiss-Schindler statistic is presented. I have compared the tests in a simulation study. RESULTS: The asymptotic Armitage test is slightly anticonservative whereas the exact tests control the type I error rate. The exact Armitage test is very conservative, but the exact test based on the modification of the Baumgartner-Weiss-Schindler statistic has a type I error rate close to alpha. The exact Armitage test is the least powerful test; the difference in power between the other two tests is often small and the comparison does not show a clear winner. CONCLUSION: Simulation results indicate that an exact test based on the modification of the Baumgartner-Weiss-Schindler statistic is preferable for the analysis of case-control studies of genetic markers.     

Sample size determination for case-control studies and the comparison of stratified and unstratified analyses.

Woolson, Bean, and Rojas (1986, Biometrics 42, 927-932) present a simple approximation of sample size for Cochran's (1954, Biometrics 10, 417-451) test for detecting association between exposure and disease. It is useful in the design of case-control studies. We derive a sample size formula for Cochran's statistic with continuity correction which guarantees that the actual Type I error rate of the test does not exceed the nominal level. The corrected sample size is necessarily larger than the uncorrected one given by Woolson et al. and the relative difference between the two sample sizes is considerable. Allocation of equal number of cases and controls within each stratum is asymptotically optimal when the costs per case and control are the same. When any effect of stratification is absent, Cochran's stratified test, although valid, is less efficient than the unstratified one except for the important case of a balanced design.     

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.