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Traditionally, GWAS tests the association between a single variant and a single trait. Gene\u2010based methods utilize the fact that multiple SNPs function as a gene to affect traits, extending GWAS to test the association between a trait and multiple variants. Nowadays, only summary statistics instead of individual\u2010level data from GWAS are publicly available due to privacy limits. Existing summary statistics for gene\u2010based methods may lead to power loss under the opposite signs of effect coefficients. In this paper, we develop a novel gene\u2010based transformed test addressing this defect. Instead of directly building test statistics using Wald test statistics, we transform Wald test statistics back into true effect coefficients based on their relationship. Then, we propose an ensemble test to produce robustness under various alternative hypotheses. Extensive simulations show that our proposed method demonstrates high power compared to existing methods. Analysis of real data on polyunsaturated fatty acids shows that our method can identify additional genetic markers previously undetected by other methods.<\/jats:p>","DOI":"10.1002\/sam.70065","type":"journal-article","created":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T06:12:17Z","timestamp":1769753537000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Transformation\u2010Based Direction Combination Association Test for\n                    <scp>GWAS<\/scp>\n                    Summary Statistics"],"prefix":"10.1002","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1664-0333","authenticated-orcid":false,"given":"Yingfang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Statistics, Capital University of Economics and Business  Beijing China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deliang","family":"Bu","sequence":"additional","affiliation":[{"name":"School of Statistics, Capital University of Economics and Business  Beijing China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanbo","family":"Pei","sequence":"additional","affiliation":[{"name":"School of Statistics, Capital University of Economics and Business  Beijing China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,1,29]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1086\/498651"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1093\/cvr\/cvaa088"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1038\/ng.784"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1038\/nature08494"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1038\/ng0508-489"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1038\/nrg2809"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1086\/423901"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mrfmmm.2006.09.003"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1159\/000336982"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1159\/000288704"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/gepi.20402"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2011.05.029"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1001322"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.2147\/AABC.S4095"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2019.01.002"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.xgen.2021.100004"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2011.01.019"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2010.06.009"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1534\/genetics.114.165035"},{"key":"e_1_2_9_21_1","volume-title":"Testing Statistical Hypotheses","author":"Lehmann E. 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