Principal components analysis corrects for stratification in genome-wide association studies Alkes L Price 1,2 , Nick J Patterson 2 , Robert M Plenge 2,3 , Michael E Weinblatt 3 , Nancy A Shadick 3 & David Reich 1,2 Population stratification—allele frequency differences between cases and controls due to systematic ancestry differences—can cause spurious associations in disease studies. We describe a method that enables explicit detection and correction of population stratification on a genome-wide scale. Our method uses principal components analysis to explicitly model ancestry differences between cases and controls. The resulting correction is specific to a candidate marker’s variation in frequency across ancestral populations, minimizing spurious associations while maximizing power to detect true associations. Our simple, efficient approach can easily be applied to disease studies with hundreds of thousands of markers. Population stratification—allele frequency differences between cases and controls due to systematic ancestry differences—can cause spur- ious associations in disease studies 1–8 . Because the effects of stratifica- tion vary in proportion to the number of samples 9 , stratification will be an increasing problem in the large-scale association studies of the future, which will analyze thousands of samples in an effort to detect common genetic variants of weak effect. The two prevailing methods for dealing with stratification are genomic control and structured association 9–14 . Although genomic control and structured association have proven useful in a variety of contexts, they have limitations. Genomic control corrects for stratifi- cation by adjusting association statistics at each marker by a uniform overall inflation factor. However, some markers differ in their allele frequencies across ancestral populations more than others. Thus, the uniform adjustment applied by genomic control may be insufficient at markers having unusually strong differentiation across ancestral populations and may be superfluous at markers devoid of such differentiation, leading to a loss in power. Structured association uses a program such as STRUCTURE 15 to assign the samples to discrete subpopulation clusters and then aggregates evidence of association within each cluster. If fractional membership in more than one cluster is allowed, the method cannot currently be applied to genome-wide association studies because of its intensive computa- tional cost on large data sets. Furthermore, assignments of individuals to clusters are highly sensitive to the number of clusters, which is not well defined 14,16 . We propose a method to detect and correct for population stratification that addresses these limitations. Our method, EIGEN- STRAT, consists of three steps (Fig. 1). First, we apply principal components analysis 17 to genotype data to infer continuous axes of genetic variation. Intuitively, the axes of variation reduce the data to a small number of dimensions, describing as much variability as possible; they are defined as the top eigenvectors of a covariance matrix between samples (see Methods). In data sets with ancestry differences between samples, axes of variation often have a geographic interpretation: for example, an axis describing a northwest-southeast cline in Europe would have values that gradually range from positive for samples from northwest Europe, to near zero in central Europe, to negative in southeast Europe. Second, we continuously adjust genotypes and phenotypes by amounts attributable to ancestry along each axis, via computing residuals of linear regressions; intuitively, this creates a virtual set of matched cases and controls. Third, we compute association statistics using ancestry-adjusted genotypes and phenotypes. The EIGENSTRAT method has arisen out of our systematic exploration of the use of principal components analysis in a more general population genetic context. Principal components analysis was originally applied to genetic data to infer worldwide axes of human genetic variation from the allele frequencies of various popula- tions 18,19 . We have further developed this approach in a parallel paper (N.J.P., A.L.P. and D.R., unpublished data), focusing instead on individual genotype data and placing the method on a firm statistical footing by rigorously assigning statistical significance to each axis of variation 20–22 . EIGENSTRAT applies this toolkit to analyze population structure in the context of disease studies. Correcting for stratification using continuous axes of variation has several advantages. Continuous axes provide the most useful descrip- tion of within-continent genetic variation, according to recent stu- dies 23 . Because our continuous axes are constructed to be orthogonal, results are insensitive to the number of axes inferred, as we verify Received 23 March; accepted 21 June; published online 23 July 2006; doi:10.1038/ng1847 1 Department of Genetics, Harvard Medical School, Boston, Massachusetts 02115, USA. 2 Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, 7 Cambridge Center, Cambridge, Massachusetts 02142, USA. 3 Division of Rheumatology, Immunology and Allergy, Brigham and Women’s Hospital, Boston, Massachusetts 02115, USA. Correspondence should be addressed to A.L.P. (aprice@broad.mit.edu). 904 VOLUME 38 [ NUMBER 8 [ AUGUST 2006 NATURE GENETICS ARTICLES © 2006 Nature Publishing Group http://www.nature.com/naturegenetics