1. Bender R, Lange S (2001) Adjusting for multiple testing—when and how? J Clin Epidemiol 54:343–349. https://doi.org/10.1016/S0895-4356(00)00314-0
2. Botev ZI (2017) The normal law under linear restrictions: simulation and estimation via minimax tilting. J R Stat Soc B 79:125–148. https://doi.org/10.1111/rssb.12162
3. Bush WS, Moore JH (2012) Chapter 11: genome-wide association studies. PLOS Comput Biol 8(12):e1002822. https://doi.org/10.1371/journal.pcbi.1002822
4. Chen SY, Feng Z, Yi X (2017) A general introduction to adjustment for multiple comparisons. J Thorac Dis 9:1725–1729. https://doi.org/10.21037/jtd.2017.05.34
5. Cuadras CM, Cuadras D (2006) A parametric approach to correspondence analysis. Linear Algebra Appl 417:64–74. https://doi.org/10.1016/j.laa.2005.10.029
6. Gao X, Starmer J, Martin ER (2008) A multiple testing correction method for genetic association studies using correlated single nucleotide polymorphisms. Genet Epidemiol 32:361–369. https://doi. org/10.1002/gepi.20310
7. González JR, Carrasco JL, Dudbridge F, Armengol L, Estivill X, Moreno V (2008) Maximizing association statistics over genetic models. Genet Epidemiol 32:246–254. https://doi.org/10.1002/ gepi.20299
8. Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London
9. Hirosawa K, Kawaguchi T, Matsuda F, Yamada R (2010) Estimation of p-value of MAX test with double triangle diagram for 2×3 SNP case-control tables. Genet Epidemiol 34:543–551. https://doi. org/10.1093/nar/gkt1229
10. Higasa K, Miyake N, Yoshimura J et al (2016) Human genetic variation database, a reference database of genetic variations in the Japanese population. J Human Genet 61:547–553. https://doi. org/10.1038/jhg.2016.12
11. Hoh J, Wille A, Ott J (2001) Trimming, weighting, and grouping SNPs in human case-control association studies. Genome Res 11:2115–2119. https://doi.org/10.1101/gr.204001
12. Hsu JC (1996) Multiple comparisons: theory and methods. Chapman & Hall, CRC Press, London
13. Johnson RC, Nelson GW, Troyer JL, Lautenberger JA, Kessing BD, Winkler CA, O’Brien SJ (2010) Accounting for multiple comparisons in a genome-wide association study (GWAS). BMC Genom 11:724. https://doi.org/10.1186/1471-2164-11-724
14. Knijnenburg TA, Wessels LFA, Reinders MJT, Shmulevich I (2009) Fewer permutations, more accurate p-values. Bioinformatics 25:i161–i168. https://doi.org/10.1093/bioinformatics/btp211
15. Lamparter D, Marbach D, Rueedi R, Kutalik Z, Bergmann S (2016) Fast and rigorous computation of gene and pathway scores from SNP-based summary statistics. PLOS Comput Biol 12(1):e1004714. https://doi.org/10.1371/journal.pcbi.1004714
16. Li MX, Gui HS, Kwan JSH et al (2011) GATES: a rapid and powerful gene-based association test using extended simes procedure. Am J Hum Genet 88:283–293. https://doi.org/10.1016/j. ajhg.2011.01.019
17. Mahalanobis PC (1936) On the generalized distance in statistics. Proc Natl Inst Sci India 2:49–55
18. McDonald JH (2014) Handbook of biolological statistics. Sparky House Publishing, Baltimore
19. Nyholt DR (2004) A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with each other. Am J Hum Genet 74:765–769. https://doi.org/10.1086/38325 1
20. Ritchie MD, Hahn LW, Roodi N, Bailey LR, Dupont WD, Parl FF, Moore JH (2001) Multifactordimensionality reduction reveals high-order interactions among estrogen-metabolism genes in sporadic breast cancer. Am J Hum Genet 69:138–147. https://doi.org/10.1086/321276
21. Slavković AB, Fienberg SE (2010) Algebraic and geometric methods in statistics. In: Gibilisco P, Riccomagno E, Rogantin MP, Wynn HP (eds) Algebraic geometry of 2 × 2 contingency tables. Cambridge University Press, Cambridge, pp 63–81
22. Yamada R, Okada Y (2009) An optimal dose-efect mode trend test for SNP genotype tables. Genet Epidemiol 33:114–127. https://doi.org/10.1002/gepi.20362
23. Yoshimura K, Nakayama T, Sekine A et al (2012) B-type natriuretic peptide as an independent correlate of nocturnal voiding in Japanese women. Neurourol Urodyn 31:1266–1271. https://doi. org/10.1002/nau.22250