Volume 3 Supplement 7
Accommodating population stratification in case-control association analysis: a new test and its application to genome-wide study on rheumatoid arthritis
© Zhang et al; licensee BioMed Central Ltd. 2009
Published: 15 December 2009
It is well known that conventional association tests can lead to excessive false positives when there is population stratification. We propose a new test for detecting genetic association with a case-control study design. Unlike some other methods for handling population stratification, we treat the cases as a population and the controls as another one even though each of them may be a mixture of several sub-populations. A likelihood-ratio test is used to test whether the allele frequency of a testing single-nucleotide polymorphism in the case population is the same as that in the control population. This new test is applied to the Genetic Analysis Workshop 16 Problem 1 data on rheumatoid arthritis. Compared with the Pearson chi-square genotype test, the association strength of many single-nucleotide polymorphisms is decreased while the signal at the HLA region on 6p21 is maintained.
One well known drawback of case-control study design in genetic association studies is that it may be affected by population stratification. Population stratification is an ethnic confounder. If a sample population is from a recent mixture of different ethnic subpopulations, it may make the cases and controls have different genetic background and spurious association may occur. In order to control the effect of population stratification, genome control , structured association , and principal components  are usually used. These methods try to gather information on population structure from markers not associated with the phenotype (null markers). In this paper, we introduce a likelihood-ratio test for genetic association in the presence of population stratification. This method does not make assumptions on the number of sub-populations in cases or in controls, nor does it make use of null markers. This method is then applied to the Genetic Analysis Workshop 16 (GAW16) Problem 1 data set.
Genotype frequencies in cases and controls
p12 = F1p1+(1-F1)p12
p11 = 2(1-F1)p1(1-p1)
p10 = F1(1-p1)+(1-F1)(1-p1)2
P22 = F2p2+(1-F2)p22
p21 = 2(1-F2)p2(1-p2)
p20 = F2(1-p2)+(1-F2)(1-p2)2
in which i = 1 or 2 for cases or controls; for each marker genotype, j = 0, 1, or 2 for zero A allele, one A allele, or two A alleles, respectively. n ij are observed genotype counts and p ij are genotype frequencies as listed in Table 1.
The maximization of the likelihood function L(p1, p2, F1, F2) under the alternative hypothesis is straightforward. The maximized estimate of each genotype frequency happens to be the observed genotype frequency in cases and controls. However, there is no explicit solution to the maximization problem under the null hypothesis. To maximize the log-likelihood function under H0, we take the first-order partial derivatives of the log-likelihood function under the null with respect to F1 and F2 and set them to zero. Each of the two equations gives an expression of F1 or F2 in terms of p. Then a grid search (step size 0.001) over p ranging from 0.001 to 0.999 is used to find the best value of p maximizing the null log-likelihood function.
According to standard statistical theory, it asymptotically follows a chi-square distribution with 1 degree of freedom.
We proposed a test for genetic association study in the presence of population stratification. Population stratification is a confounder to the difference of genotype frequencies between cases and controls. Unlike some other methods such as the structured association, the proposed test does not try to classify each individual. Instead, it allows for the difference in the composition of cases and controls by using two of FST coefficients, one for cases and one for controls. Population genetics suggests that the FST for a natural population may be small (for instance, 0.001 or 0.01). This may be true for controls, but no longer true for a selected sample such as cases. It is easy to construct a case sample for which the FST is 0.8 or higher. Our test provides a simple way to reduce the confounding impact of population stratification compared with the Pearson chi-square statistic.
The proposed method attributes any deficiency in heterozygosity in cases or controls to population stratification. Its power to detect association can be compromised when there is no population stratification, especially when the trait is recessive . Because population stratification affects not only FST but also allele frequencies in cases and controls, the proposed method cannot completely eliminate the confounding effect of population stratification. Due to the page limitation, no simulation results comparing the proposed method and the Pearson's chi-square statistic are reported. One reviewer pointed out that this may make it difficult to interpret the difference between these two methods observed in current study. In our unreported simulation studies, the proposed method is still more robust to population stratification than Pearson's chi-square statistic.
A method for detecting association in the presence of population stratification is proposed. Analysis of the GAW16 Problem 1 data on rheumatoid arthritis suggests it is more robust to population stratification than the Pearson's chi-square statistic. The proposed test is implemented in two computer languages, C++ and R. Both versions are available from the authors upon request.
List of abbreviations used
Genetic Analysis Workshop 16.
We thank Drs. Deborah Dawson, Trudy Burns, and Jian Huang, GAW16 Group 13 Editors Tony Hinrichs, PhD and Brian Suarez, PhD, and two anonymous reviewers for their valuable comments and suggestions.
This article has been published as part of BMC Proceedings Volume 3 Supplement 7, 2009: Genetic Analysis Workshop 16. The full contents of the supplement are available online at http://www.biomedcentral.com/1753-6561/3?issue=S7.
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