{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T03:47:55Z","timestamp":1775965675168,"version":"3.50.1"},"reference-count":36,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2018,11,19]],"date-time":"2018-11-19T00:00:00Z","timestamp":1542585600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Genetic Epidemiology"],"published-print":{"date-parts":[[2019,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Single\u2010variant\u2010based genome\u2010wide association studies have successfully detected many genetic variants that are associated with a number of complex traits. However, their power is limited due to weak marginal signals and ignoring potential complex interactions among genetic variants. The set\u2010based strategy was proposed to provide a remedy where multiple genetic variants in a given set (e.g., gene or pathway) are jointly evaluated, so that the systematic effect of the set is considered. Among many, the kernel\u2010based testing (KBT) framework is one of the most popular and powerful methods in set\u2010based association studies. Given a set of candidate kernels, the method has been proposed to choose the one with the smallest\n                    <jats:italic>p<\/jats:italic>\n                    \u2010value. Such a method, however, can yield inflated Type 1 error, especially when the number of variants in a set is large. Alternatively one can get\n                    <jats:italic>p<\/jats:italic>\n                    values by permutations which, however, could be very time\u2010consuming. In this study, we proposed an efficient testing procedure that cannot only control Type 1 error rate but also have power close to the one obtained under the optimal kernel in the candidate kernel set, for quantitative trait association studies. Our method, a maximum kernel\u2010based\n                    <jats:italic>U<\/jats:italic>\n                    \u2010statistic method, is built upon the KBT framework and is based on asymptotic results under a high\u2010dimensional setting. Hence it can efficiently deal with the case where the number of variants in a set is much larger than the sample size. Both simulation and real data analysis demonstrate the advantages of the method compared with its counterparts.\n                  <\/jats:p>","DOI":"10.1002\/gepi.22170","type":"journal-article","created":{"date-parts":[[2018,11,19]],"date-time":"2018-11-19T22:21:35Z","timestamp":1542666095000},"page":"137-149","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["An optimal kernel\u2010based\n                    <i>U<\/i>\n                    \u2010statistic method for quantitative gene\u2010set association analysis"],"prefix":"10.1002","volume":"43","author":[{"given":"Tao","family":"He","sequence":"first","affiliation":[{"name":"Department of Mathematics San Francisco State University San Francisco California"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaoyu","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics University of North Carolina at Charlotte Charlotte North Carolina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping\u2010Shou","family":"Zhong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago Illinois"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8099-1753","authenticated-orcid":false,"given":"Yuehua","family":"Cui","sequence":"additional","affiliation":[{"name":"Department of Statistics &amp; Probability Michigan State University East Lansing Michigan"},{"name":"School of Public Health, Zhengzhou University Zhengzhou China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,11,19]]},"reference":[{"key":"e_1_2_7_1_2_1","doi-asserted-by":"publisher","DOI":"10.1038\/75556"},{"key":"e_1_2_7_1_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/gepi.20609"},{"key":"e_1_2_7_1_4_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2010.tm09560"},{"key":"e_1_2_7_1_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/nar\/gkq1018"},{"key":"e_1_2_7_1_6_1","unstructured":"He T. 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