Abstract
Yu et al. (Breast Cancer Res Treat 117:675–677, 2009) recently stated that testing for deviation from Hardy–Weinberg equilibrium (HWE) is necessary to identify systematic genotyping errors in case–control studies. They criticized a meta-analytic study for the deviation from HWE in the case group of one study. The aim of this article is twofold. First, we derive recommendations on how to test for deviations from HWE in different study designs. Second, we develop a meta-analytic framework for assessing compatibility with HWE or measuring deviation from HWE. The authors sketch the possible reasons behind deviation from HWE and provide guidelines for proper investigation of HWE deviations in different study designs. The authors argue that the standard HWE χ2 lack of fit test is logically flawed and provide a logically unflawed approach for measuring deviation from HWE using confidence intervals. The proposed method is applicable to meta-analyses of both case–control or cohort association studies. The proposed approach is illustrated using the meta-analysis criticized by Yu et al. Heterogeneity between studies can be assessed. The critique of Yu et al. to the article of Frank et al. (Breast Cancer Res Treat 111:139–144, 2008) can be refuted. Even more, validity of HWE can be proven for the pooled control sample. The authors advocate the use of a confidence interval-based approach to assess HWE. The latter should only be investigated in control populations. In multicenter studies or meta-analysis, deviation from HWE should be analyzed using a meta-analytic approach.
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Frank B, Rigas SH, Bermejo JL, Wiestler M, Wagner K, Hemminki K, Reed MW, Sutter C, Wappenschmidt B, Balasubramanian SP, Meindl A, Kiechle M, Bugert P, Schmutzler RK, Bartram CR, Justenhoven C, Ko YD, Bruning T, Brauch H, Hamann U, Pharoah PP, Dunning AM, Pooley KA, Easton DF, Cox A, Burwinkel B (2008) The CASP8–652 6 N del promoter polymorphism and breast cancer risk: a multicenter study. Breast Cancer Res Treat 111:139–144. doi:10.1007/s10549-007-9752-z
Guo SW, Thompson EA (1992) Performing the exact test of Hardy–Weinberg proportion for multiple alleles. Biometrics 48:361–372
Higgins JP, Thompson SG (2002) Quantifying heterogeneity in a meta-analysis. Stat Med 21:1539–1558. doi:10.1002/sim.1186
Hoh J, Wille A, Ott J (2001) Trimming, weighting, and grouping SNPs in human case–control association studies. Genome Res 11:2115–2119. doi:10.1101/gr.204001
Huber M, Chen Y, Dinwoodie I, Dobra A, Nicholas M (2006) Monte Carlo algorithms for Hardy–Weinberg proportions. Biometrics 62:49–53. doi:10.1111/j.1541-0420.2005.00418.x
Huedo-Medina TB, Sanchez-Meca J, Marin-Martinez F, Botella J (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychol Methods 11:193–206. doi:10.1037/1082-989X.11.2.193
Lee WC (2003) Searching for disease-susceptibility loci by testing for Hardy–Weinberg disequilibrium in a gene bank of affected individuals. Am J Epidemiol 158:397–400
Minelli C, Thompson JR, Abrams KR, Thakkinstian A, Attia J (2007) How should we use information about HWE in the meta-analyses of genetic association studies? Int J Epidemiol 37:136–146. doi:10.1093/ije/dym234
Nam JM (1997) Testing a genetic equilibrium across strata. Ann Hum Genet 61:163–170. doi:10.1046/j.1469-1809.1997.6120163.x
Olson JM (1993) Testing the Hardy–Weinberg law across strata. Ann Hum Genet 57:291–295
Olson JM, Foley M (1996) Testing for homogeneity of Hardy–Weinberg disequilibrium using data sampled from several populations. Biometrics 52:971–979
Schaid DJ, Batzler AJ, Jenkins GD, Hildebrandt MA (2006) Exact tests of Hardy–Weinberg equilibrium and homogeneity of disequilibrium across strata. Am J Hum Genet 79:1071–1080. doi:10.1086/510257
Song K, Elston RC (2006) A powerful method of combining measures of association and Hardy–Weinberg disequilibrium for fine-mapping in case–control studies. Stat Med 25:105–126. doi:10.1002/sim.2350
Troendle JF, Yu KF (1994) A note on testing the Hardy–Weinberg law across strata. Ann Hum Genet 58:397–402
Wellek S, Goddard KA, Ziegler A (2010) A confidence-limit-based approach to the assessment of Hardy–Weinberg equilibrium. Biom J 52:253–270. doi:10.1002/bimj.200900249
Wittke-Thompson JK, Pluzhnikov A, Cox NJ (2005) Rational inferences about departures from Hardy–Weinberg equilibrium. Am J Hum Genet 76:967–986. doi:10.1086/430507
Yu KD, Di GH, Fan L, Shao ZM (2009) Test of Hardy–Weinberg equilibrium in breast cancer case–control studies: an issue may influence the conclusions. Breast Cancer Res Treat 117:675–677. doi:10.1007/s10549-009-0353-x
Ziegler A, König IR (2010) A statistical approach to genetic epidemiology: concepts and applications, 2nd edn. Wiley-VCH, Weinheim
Ziegler A, Thompson JR, König IR (2008) Biostatistical aspects of genome-wide association studies. Biom J 50:8–28. doi:10.1002/bimj.200710398
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This study was funded by the German Research Foundation (ZI 591/17-1) and the German Ministry of Education and Research (NGFN-Plus, 01GS0831). This study was completed during the sabbatical of AZ at the University of Liège, Belgium.
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Ziegler, A., Van Steen, K. & Wellek, S. Investigating Hardy–Weinberg equilibrium in case–control or cohort studies or meta-analysis. Breast Cancer Res Treat 128, 197–201 (2011). https://doi.org/10.1007/s10549-010-1295-z
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DOI: https://doi.org/10.1007/s10549-010-1295-z