Simultaneously correcting for population stratification and for genotyping error in case-control association studies

In population-based case-control association studies, the regular chi (2) test is often used to investigate association between a candidate locus and disease. However, it is well known that this test may be biased in the presence of population stratification and/or genotyping error. Unlike some other biases, this bias will not go away with increasing sample size. On the contrary, the false-positive rate will be much larger when the sample size is increased. The usual family-based designs are robust against population stratification, but they are sensitive to genotype error. In this article, we propose a novel method of simultaneously correcting for the bias arising from population stratification and/or for the genotyping error in case-control studies. The appropriate corrections depend on sample odds ratios of the standard 2x3 tables of genotype by case and control from null loci. Therefore, the test is simple to apply. The corrected test is robust against misspecification of the genetic model. If the null hypothesis of no association is rejected, the corrections can be further used to estimate the effect of the genetic factor. We considered a simulation study to investigate the performance of the new method, using parameter values similar to those found in real-data examples. The results show that the corrected test approximately maintains the expected type I error rate under various simulation conditions. It also improves the power of the association test in the presence of population stratification and/or genotyping error. The discrepancy in power between the tests with correction and those without correction tends to be more extreme as the magnitude of the bias becomes larger. Therefore, the bias-correction method proposed in this article should be useful for the genetic analysis of complex traits.     

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.     

An improved delta-centralization method for population stratification

Dadd et al. [Hum Hered 2010;69:285-294] recently criticized our delta-centralization (DC) method of controlling for population stratification (PS) and concluded that DC does not work. To explore our method, the authors simulated data under the Balding-Nichols (BN) model, which is more general than the model we had used in our simulations. They determined that the DC method underestimated the PS parameter (δ) and inflated the type I error rates when applied to BN-simulated data, and from this they concluded that the DC method is invalid. However, we argue that this conclusion is premature. In this paper, we (1) show why δ is underestimated and type I error rates are inflated when BN-simulated data are used, and (2) present a simple adjustment to DC that works reasonably well for data from both kinds of simulations. We also show that the adjusted DC method has appropriate power under a range of scenarios.     

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 randomization test for controlling population stratification in whole-genome association studies

Population stratification can be a serious obstacle in the analysis of genomewide association studies. We propose a method for evaluating the significance of association scores in whole-genome cohorts with stratification. Our approach is a randomization test akin to a standard permutation test. It conditions on the genotype matrix and thus takes into account not only the population structure but also the complex linkage disequilibrium structure of the genome. As we show in simulation experiments, our method achieves higher power and significantly better control over false-positive rates than do existing methods. In addition, it can be easily applied to whole-genome association studies.     

A flexible approach to measurement error correction in case-control studies

SUMMARY: We investigate the use of prospective likelihood methods to analyze retrospective case-control data where some of the covariates are measured with error. We show that prospective methods can be applied and the case-control sampling scheme can be ignored if one adequately models the distribution of the error-prone covariates in the case-control sampling scheme. Indeed, subject to this, the prospective likelihood methods result in consistent estimates and information standard errors are asymptotically correct. However, the distribution of such covariates is not the same in the population and under case-control sampling, dictating the need to model the distribution flexibly. In this article, we illustrate the general principle by modeling the distribution of the continuous error-prone covariates using the skewnormal distribution. The performance of the method is evaluated through simulation studies, which show satisfactory results in terms of bias and coverage. Finally, the method is applied to the analysis of two data sets which refer, respectively, to a cholesterol study and a study on breast cancer.     

Testing for population subdivision and association in four case-control studies

Population structure has been presumed to cause many of the unreplicated disease-marker associations reported in the literature, yet few actual case-control studies have been evaluated for the presence of structure. Here, we examine four moderate case-control samples, comprising 3,472 individuals, to determine if detectable population subdivision is present. The four population samples include: 500 U.S. whites and 236 African Americans with hypertension; and 500 U.S. whites and 500 Polish whites with type 2 diabetes, all with matched control subjects. Both diabetes populations were typed for the PPARg Pro12Ala polymorphism, to replicate this well-supported association (Altshuler et al. 2000). In each of the four samples, we tested for structure, using the sum of the case-control allele frequency chi(2) statistics for 9 STR and 35 SNP markers (Pritchard and Rosenberg 1999). We found weak evidence for population structure in the African American sample only, but further refinement of the sample, to include only individuals with U.S.-born parents and grandparents, eliminated the stratification. Our examples provide insight into the factors affecting the replication of association studies and suggest that carefully matched, moderate-sized case-control samples in cosmopolitan U.S. and European populations are unlikely to contain levels of structure that would result in significantly inflated numbers of false-positive associations. We explore the role that extreme differences in power among studies, due to sample size and risk-allele frequency differences, may play in the replication problem.     

Correction of population stratification in large multi-ethnic association studies

Background

The vast majority of genetic risk factors for complex diseases have, taken individually, a small effect on the end phenotype. Population-based association studies therefore need very large sample sizes to detect significant differences between affected and non-affected individuals. Including thousands of affected individuals in a study requires recruitment in numerous centers, possibly from different geographic regions. Unfortunately such a recruitment strategy is likely to complicate the study design and to generate concerns regarding population stratification.

Methodology/Principal Findings

We analyzed 9,751 individuals representing three main ethnic groups - Europeans, Arabs and South Asians - that had been enrolled from 154 centers involving 52 countries for a global case/control study of acute myocardial infarction. All individuals were genotyped at 103 candidate genes using 1,536 SNPs selected with a tagging strategy that captures most of the genetic diversity in different populations. We show that relying solely on self-reported ethnicity is not sufficient to exclude population stratification and we present additional methods to identify and correct for stratification.

Conclusions/Significance

Our results highlight the importance of carefully addressing population stratification and of carefully “cleaning” the sample prior to analyses to obtain stronger signals of association and to avoid spurious results.     

人类复杂疾病关联研究中群体分层的检出和校正

病例对照研究是鉴定多基因疾病易感位点重要的遗传流行病学方法, 而群体分层是导致病例对照研究关联研究结果出现偏倚甚至是假关联的重要原因之一。文章对人群分层的检出及校正的方法和原理进行了阐述, 包括基于核心家系的传递/不平衡检验(TDT)以及基于不相关基因组遗传标记的基因组对照(GC)和结构化关联(SA)等, 并且对这几种方法进行了比较。     

MAX-rank: a simple and robust genome-wide scan for case-control association studies

In genome-wide association studies (GWAS), single-marker analysis is usually employed to identify the most significant single nucleotide polymorphisms (SNPs). The trend test has been proposed for analysis of case-control association. Three trend tests, optimal for the recessive, additive and dominant models respectively, are available. When the underlying genetic model is unknown, the maximum of the three trend test results (MAX) has been shown to be robust against genetic model misspecification. Since the asymptotic distribution of MAX depends on the allele frequency of the SNP, using the P-value of MAX for ranking may be different from using the MAX statistic. Calculating the P-value of MAX for 300,000 (300 K) or more SNPs is computationally intensive and the software and program to obtain the P-value of MAX are not widely available. On the other hand, the MAX statistic is very easy to calculate without complex computer programs. Thus, we study whether or not one could use the MAX statistic instead of its P-value to rank SNPs in GWAS. The approaches using the MAX and its P-value to rank SNPs are referred to as MAX-rank and P-rank. By applying MAX-rank and P-rank to simulated and four real datasets from GWAS, we found the ranks of SNPs with true association are very similar using both approaches. Thus, we recommend to use MAX-rank for genome-wide scans. After the top-ranked SNPs are identified, their P-values based on MAX can be calculated and compared with the significance level. The work of Q. Li was partially supported by the Knowledge Innovation Program of the Chinese Academy of Sciences, No. 30465W0 and 30475V0. The research of Z Li was partially sponsored by NIH grant EY014478.     

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.     

随机SNP在全基因组关联研究人群分层分析中的应用

在复杂疾病的全基因组关联研究中,人群分层现象会增加结果的假阳性率,因此考虑人群遗传结构、控制人群分层是很有必要的。而在人群分层研究中,使用随机选择的SNP的效果还有待进一步探讨。文章利用HapMap Phase2人群中无关个体的Affymetrix SNP 6.0芯片分型数据,在全基因组上随机均匀选择不同数量的SNP,同时利用f值和Fisher精确检验方法筛选祖先信息标记（Ancestry Informative Markers,AIMs）。然后利用HapMap Phase3中的无关个体的数据,以F-statistics和STRUCTURE分析两种方法评估所选出的不同SNP组合对人群的区分效果。研究发现,随机均匀分布于全基因组的SNP可用于识别人群内部存在的遗传结构。文章进一步提示,在全基因组关联研究中,当没有针对特定人群的AIMs时,可在全基因组上随机选择3000以上均匀分布的SNP来控制人群分层。     

A simple and rapid method for electromagnetic field distortion correction when using two Fastrak sensors for biomechanical studies

The article presents a simple and rapid method for the correction of electromagnetic distortions when using electromagnetic Fastrak (Polhemus, USA) sensors. It is based on the minimization of objective functions composed of derivative polynomial functions, hence estimating the distortion of the electromagnetic field. The polynomial functions composing the objective function each contain 35 deformation coefficients. These coefficients are then used to correct the electromagnetic measures in position and orientation. Preliminary results on the efficacy of the method are presented for two subjects who walked on a treadmill, and for whom relative movement of the lower leg with respect to the thigh was recorded using two Fastrak sensors. The corrected Fastrak measurements were compared with optoelectronic measurements (Vicon, USA), which are not affected by distortions as electromagnetic sensors are. Results showed that after 3 min of calibrating a volume of approximately 1m(3), the method proved to be efficient in correcting errors in orientation (56% (2.72-1.12 degrees ), 78% (4.4-0.89 degrees ), and 56% (2.25-0.90 degrees ) of error reduction in the respective flexion/extension, ab/adduction and tibial internal/external rotation) and position (53% (18.9-8.9 mm), 21% (6.6-4.6mm), and 48% (15.9-8.1mm) of error reduction in the respective medial/lateral, anterior/posterior and proximal/distal translations) (values are overall means for two subjects and four calibration procedures). That amount of correction compared favorably with values presented in the literature.     

A tracking system for conducting epidemiological case-control studies

The automated-respondent tracking system (ARTS) is an event-driven management system developed to monitor data collection during large epidemiological case-control studies. ARTS facilitates the conduct and management of these studies by eliminating the problems and limitations of manually monitoring subjects. This system, developed on an IBM 3032, consists of a series of programs linked by a general update program. Data captured on each subject for every study phase are used to generate lists of subjects requiring further action by the study staff. Additionally, ARTS produces reports reflecting a study's progress. Improved study management and reduced clerical load justify the system's costs. Concepts and programming principles applied to ARTS can be generalized to other epidemiological study designs.     

A Bayesian hierarchical approach for combining case-control and prospective studies

Motivated by the absolute risk predictions required in medical decision making and patient counseling, we propose an approach for the combined analysis of case-control and prospective studies of disease risk factors. The approach is hierarchical to account for parameter heterogeneity among studies and among sampling units of the same study. It is based on modeling the retrospective distribution of the covariates given the disease outcome, a strategy that greatly simplifies both the combination of prospective and retrospective studies and the computation of Bayesian predictions in the hierarchical case-control context. Retrospective modeling differentiates our approach from most current strategies for inference on risk factors, which are based on the assumption of a specific prospective model. To ensure modeling flexibility, we propose using a mixture model for the retrospective distributions of the covariates. This leads to a general nonlinear regression family for the implied prospective likelihood. After introducing and motivating our proposal, we present simple results that highlight its relationship with existing approaches, develop Markov chain Monte Carlo methods for inference and prediction, and present an illustration using ovarian cancer data.     

Use of unlinked genetic markers to detect population stratification in association studies.

We examine the issue of population stratification in association-mapping studies. In case-control studies of association, population subdivision or recent admixture of populations can lead to spurious associations between a phenotype and unlinked candidate loci. Using a model of sampling from a structured population, we show that if population stratification exists, it can be detected by use of unlinked marker loci. We show that the case-control-study design, using unrelated control individuals, is a valid approach for association mapping, provided that marker loci unlinked to the candidate locus are included in the study, to test for stratification. We suggest guidelines as to the number of unlinked marker loci to use.