Genomics & Informatics

Korea Genome Organization (한국유전체학회)
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Comparison of Two Meta-Analysis Methods: Inverse-Variance-Weighted Average and Weighted Sum of Z-Scores

  • Lee, Cue Hyunkyu (Asan Institute for Life Sciences, Asan Medical Center) ;
  • Cook, Seungho (Asan Institute for Life Sciences, Asan Medical Center) ;
  • Lee, Ji Sung (Asan Institute for Life Sciences, Asan Medical Center) ;
  • Han, Buhm (Asan Institute for Life Sciences, Asan Medical Center)
  • Received : 2016.10.18
  • Accepted : 2016.12.03
  • Published : 2016.12.31
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Abstract

The meta-analysis has become a widely used tool for many applications in bioinformatics, including genome-wide association studies. A commonly used approach for meta-analysis is the fixed effects model approach, for which there are two popular methods: the inverse variance-weighted average method and weighted sum of z-scores method. Although previous studies have shown that the two methods perform similarly, their characteristics and their relationship have not been thoroughly investigated. In this paper, we investigate the optimal characteristics of the two methods and show the connection between the two methods. We demonstrate that the each method is optimized for a unique goal, which gives us insight into the optimal weights for the weighted sum of z-scores method. We examine the connection between the two methods both analytically and empirically and show that their resulting statistics become equivalent under certain assumptions. Finally, we apply both methods to the Wellcome Trust Case Control Consortium data and demonstrate that the two methods can give distinct results in certain study designs.

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References

  1. Evangelou E, Ioannidis JP. Meta-analysis methods for genome-wide association studies and beyond. Nat Rev Genet 2013;14:379-389. https://doi.org/10.1038/nrg3472
  2. de Bakker PI, Ferreira MA, Jia X, Neale BM, Raychaudhuri S, Voight BF. Practical aspects of imputation-driven meta-analysis of genome-wide association studies. Hum Mol Genet 2008; 17:R122-R128. https://doi.org/10.1093/hmg/ddn288
  3. Zeggini E, Ioannidis JP. Meta-analysis in genome-wide association studies. Pharmacogenomics 2009;10:191-201. https://doi.org/10.2217/14622416.10.2.191
  4. Cantor RM, Lange K, Sinsheimer JS. Prioritizing GWAS results: a review of statistical methods and recommendations for their application. Am J Hum Genet 2010;86:6-22. https://doi.org/10.1016/j.ajhg.2009.11.017
  5. Borenstein M, Hedges LV, Higgins JP, Rothstein HR. A basic introduction to fixed-effect and random-effects models for meta-analysis. Res Synth Methods 2010;1:97-111. https://doi.org/10.1002/jrsm.12
  6. Zeggini E, Weedon MN, Lindgren CM, Frayling TM, Elliott KS, Lango H, et al. Replication of genome-wide association signals in UK samples reveals risk loci for type 2 diabetes. Science 2007;316:1336-1341. https://doi.org/10.1126/science.1142364
  7. Traylor M, Makela KM, Kilarski LL, Holliday EG, Devan WJ, Nalls MA, et al. A novel MMP12 locus is associated with large artery atherosclerotic stroke using a genome-wide age-at-onset informed approach. PLoS Genet 2014;10:e1004469. https://doi.org/10.1371/journal.pgen.1004469
  8. Lee MN, Ye C, Villani AC, Raj T, Li W, Eisenhaure TM, et al. Common genetic variants modulate pathogen-sensing responses in human dendritic cells. Science 2014;343:1246980. https://doi.org/10.1126/science.1246980
  9. Raj T, Rothamel K, Mostafavi S, Ye C, Lee MN, Replogle JM, et al. Polarization of the effects of autoimmune and neurodegenerative risk alleles in leukocytes. Science 2014;344: 519-523. https://doi.org/10.1126/science.1249547
  10. Zaitlen N, Eskin E. Imputation aware meta-analysis of genome-wide association studies. Genet Epidemiol 2010;34:537-542. https://doi.org/10.1002/gepi.20507
  11. Zeggini E, Scott LJ, Saxena R, Voight BF, Marchini JL, Hu T, et al. Meta-analysis of genome-wide association data and large-scale replication identifies additional susceptibility loci for type 2 diabetes. Nat Genet 2008;40:638-645. https://doi.org/10.1038/ng.120
  12. Furlotte NA, Kang EY, Van Nas A, Farber CR, Lusis AJ, Eskin E. Increasing association mapping power and resolution in mouse genetic studies through the use of meta-analysis for structured populations. Genetics 2012;191:959-967. https://doi.org/10.1534/genetics.112.140277
  13. Nalls MA, Pankratz N, Lill CM, Do CB, Hernandez DG, Saad M, et al. Large-scale meta-analysis of genome-wide association data identifies six new risk loci for Parkinson's disease. Nat Genet 2014;46:989-993. https://doi.org/10.1038/ng.3043
  14. Goodkind M, Eickhoff SB, Oathes DJ, Jiang Y, Chang A, Jones-Hagata LB, et al. Identification of a common neurobiological substrate for mental illness. JAMA Psychiatry 2015;72:305-315. https://doi.org/10.1001/jamapsychiatry.2014.2206
  15. Sul JH, Han B, Ye C, Choi T, Eskin E. Effectively identifying eQTLs from multiple tissues by combining mixed model and meta-analytic approaches. PLoS Genet 2013;9:e1003491. https://doi.org/10.1371/journal.pgen.1003491
  16. Fisher RA. Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd, 1925.
  17. Han B, Eskin E. Random-effects model aimed at discovering associations in meta-analysis of genome-wide association studies. Am J Hum Genet 2011;88:586-598. https://doi.org/10.1016/j.ajhg.2011.04.014
  18. Fleiss JL. The statistical basis of meta-analysis. Stat Methods Med Res 1993;2:121-145. https://doi.org/10.1177/096228029300200202
  19. Liptak T. On the combination of independent events. Magyar Tud Akad Mat Kutato Int Kozl 1958;3:171-197.
  20. Zaykin DV. Optimally weighted Z-test is a powerful method for combining probabilities in meta-analysis. J Evol Biol 2011;24:1836-1841. https://doi.org/10.1111/j.1420-9101.2011.02297.x
  21. Zhou B, Shi J, Whittemore AS. Optimal methods for metaanalysis of genome-wide association studies. Genet Epidemiol 2011;35:581-591. https://doi.org/10.1002/gepi.20603
  22. Cochran WG. The combination of estimates from different experiments. Biometrics 1954;10:101-129. https://doi.org/10.2307/3001666
  23. Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst 1959;22:719-748.
  24. Won S, Morris N, Lu Q, Elston RC. Choosing an optimal method to combine P-values. Stat Med 2009;28:1537-1553. https://doi.org/10.1002/sim.3569
  25. Birch MW. The detection of partial association, I: the 2 $\times$ 2 case. J R Stat Soc Series B 1964;26:313-324.
  26. Pereira TV, Patsopoulos NA, Salanti G, Ioannidis JP. Discovery properties of genome-wide association signals from cumulatively combined data sets. Am J Epidemiol 2009;170:1197-1206. https://doi.org/10.1093/aje/kwp262
  27. Greene WH. Econometric Analysis. Harlow: Pearson Education, 2011.
  28. Wellcome Trust Case Control Consortium. Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 2007;447:661-678. https://doi.org/10.1038/nature05911

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