{"id":"https://openalex.org/W4394430702","doi":"https://doi.org/10.6084/m9.figshare.7015253","title":"A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies","display_name":"A Geometric Perspective on the Power of Principal Component Association Tests in Multiple Phenotype Studies","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W4394430702","doi":"https://doi.org/10.6084/m9.figshare.7015253"},"language":"en","primary_location":{"id":"pmh:oai:figshare.com:article/7015253","doi":null,"is_oa":true,"landing_page_url":"https://figshare.com/articles/dataset/A_Geometric_Perspective_on_the_Power_of_Principal_Component_Association_Tests_in_Multiple_Phenotype_Studies/7015253","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dataset"},"volume":null,"type":"dataset","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/dataset/A_Geometric_Perspective_on_the_Power_of_Principal_Component_Association_Tests_in_Multiple_Phenotype_Studies/7015253","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100413271","display_name":"Zhonghua Liu","orcid":"https://orcid.org/0000-0003-3048-9823","observed_orcids":["https://orcid.org/0000-0003-3048-9823","https://orcid.org/0009-0001-0313-2506"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zhonghua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030660111","display_name":"Xihong Lin","orcid":"https://orcid.org/0000-0001-7067-7752","observed_orcids":["https://orcid.org/0000-0001-7067-7752"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Xihong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10261","display_name":"Genetic Associations and Epidemiology","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10261","display_name":"Genetic Associations and Epidemiology","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.027000000700354576,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11468","display_name":"Genetic Mapping and Diversity in Plants and Animals","score":0.006099999882280827,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"principal component analysis","score":0.8679999709129333},{"id":"https://openalex.org/keywords/genetic-association-testing","display_name":"genetic association testing","score":0.5979999899864197},{"id":"https://openalex.org/keywords/statistical-power","display_name":"statistical power","score":0.8009999990463257},{"id":"https://openalex.org/keywords/principal-angles","display_name":"principal angles","score":0.9679999947547913},{"id":"https://openalex.org/keywords/omnibus-test","display_name":"omnibus test","score":0.7799999713897705},{"id":"https://openalex.org/keywords/wald-test","display_name":"Wald test","score":0.7269999980926514},{"id":"https://openalex.org/keywords/rejection-region","display_name":"critical region","score":0.5199999809265137},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"dimensionality reduction","score":0.671999990940094},{"id":"https://openalex.org/keywords/metabolic-syndrome","display_name":"metabolic syndrome","score":0.7369999885559082}],"concepts":[{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6966782808303833},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.6710966229438782},{"id":"https://openalex.org/C142853389","wikidata":"https://www.wikidata.org/wiki/Q744778","display_name":"Association (psychology)","level":2,"score":0.570199728012085},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.5558428168296814},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4168219268321991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3589848279953003},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.35697779059410095},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.3007963299751282},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.2973559498786926},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.2234642505645752},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11637136340141296},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08760282397270203},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:figshare.com:article/7015253","doi":null,"is_oa":true,"landing_page_url":"https://figshare.com/articles/dataset/A_Geometric_Perspective_on_the_Power_of_Principal_Component_Association_Tests_in_Multiple_Phenotype_Studies/7015253","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dataset"},{"id":"doi:10.6084/m9.figshare.7015253","doi":"https://doi.org/10.6084/m9.figshare.7015253","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.7015253","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"doi:10.6084/m9.figshare.7015253.v1","doi":"https://doi.org/10.6084/m9.figshare.7015253.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.7015253.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"doi:10.6084/m9.figshare.7015253.v2","doi":"https://doi.org/10.6084/m9.figshare.7015253.v2","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.7015253.v2","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"doi:10.6084/m9.figshare.7015253.v3","doi":"https://doi.org/10.6084/m9.figshare.7015253.v3","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.7015253.v3","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"doi:10.6084/m9.figshare.7015253.v4","doi":"https://doi.org/10.6084/m9.figshare.7015253.v4","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.7015253.v4","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/7015253","doi":null,"is_oa":true,"landing_page_url":"https://figshare.com/articles/dataset/A_Geometric_Perspective_on_the_Power_of_Principal_Component_Association_Tests_in_Multiple_Phenotype_Studies/7015253","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dataset"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3017329137","https://openalex.org/W2028416113","https://openalex.org/W2950943649","https://openalex.org/W4306850923","https://openalex.org/W2407003837","https://openalex.org/W2464054386","https://openalex.org/W2169441372","https://openalex.org/W2738879958","https://openalex.org/W2024193591","https://openalex.org/W6977240797"],"abstract_inverted_index":{"Joint":[0],"analysis":[1,83,179,263],"of":[2,26,53,79,167,173,198,264,279,295],"multiple":[3,36,81],"phenotypes":[4,27,267],"can":[5,55,126,219],"increase":[6],"statistical":[7],"power":[8,178],"in":[9,67,163,196,231,242],"genetic":[10,69],"association":[11,70],"studies.":[12],"Principal":[13],"component":[14],"analysis,":[15],"as":[16,305],"a":[17,85,90,147,164,232,292],"popular":[18],"dimension":[19],"reduction":[20],"method,":[21],"especially":[22],"when":[23],"the":[24,45,50,77,120,143,155,171,174,216,225,257,261,277,280,296,301],"number":[25],"is":[28,99,105,108,114,146,159],"high":[29],"dimensional,":[30],"has":[31,40],"been":[32,41,229],"proposed":[33,175,203,217,226,258,281],"to":[34,260,275],"analyze":[35],"correlated":[37],"phenotypes.":[38],"It":[39],"empirically":[42],"observed":[43],"that":[44,142,154],"first":[46],"PC,":[47],"which":[48],"summarizes":[49],"largest":[51],"amount":[52],"variance,":[54],"be":[56,127,220],"less":[57],"powerful":[58,100,162],"than":[59],"higher-order":[60],"PCs":[61],"and":[62,107,133,161,180,185,209,224,245,252],"other":[63],"commonly":[64],"used":[65],"methods":[66,176,192],"detecting":[68],"signals.":[71],"In":[72],"this":[73,289],"article,":[74,290],"we":[75],"investigate":[76],"properties":[78,172],"PCA-based":[80],"phenotype":[82],"from":[84,271],"geometric":[86],"perspective":[87],"by":[88,137],"introducing":[89],"novel":[91],"concept":[92],"called":[93],"principal":[94,103,112,122],"angle.":[95],"A":[96],"particular":[97],"PC":[98,125,157,191,283],"if":[101,110],"its":[102,111],"angle":[104,113],"0\u00b0":[106],"powerless":[109],"90\u00b0.":[115],"Without":[116],"prior":[117],"knowledge":[118],"about":[119],"true":[121],"angle,":[123],"each":[124],"powerless.":[128],"We":[129,140,152,169,238,255],"propose":[130],"linear,":[131],"nonlinear,":[132],"data-adaptive":[134],"omnibus":[135,156],"tests":[136,204,218,227,259],"combining":[138],"PCs.":[139],"demonstrate":[141,276],"Wald":[144],"test":[145,158],"special":[148],"quadratic":[149],"PC-based":[150],"test.":[151],"show":[153],"robust":[160],"wide":[165],"range":[166],"scenarios.":[168],"study":[170],"using":[177],"eigen-analysis.":[181],"The":[182,213],"subtle":[183],"differences":[184],"close":[186],"connections":[187],"between":[188],"these":[189],"combined":[190,282],"are":[193,211,303],"illustrated":[194],"graphically":[195],"terms":[197],"their":[199],"rejection":[200],"boundaries.":[201],"Our":[202],"have":[205,228],"convex":[206],"acceptance":[207],"regions":[208],"hence":[210],"admissible.":[212],"p-values":[214],"for":[215,288,299],"efficiently":[221],"calculated":[222],"analytically":[223],"implemented":[230],"publicly":[233],"available":[234,298,304],"R":[235],"package":[236],"MPAT.":[237],"conduct":[239],"simulation":[240],"studies":[241],"both":[243],"low-":[244],"high-dimensional":[246],"settings":[247],"with":[248,268],"various":[249],"signal":[250],"vectors":[251],"correlation":[253],"structures.":[254],"apply":[256],"joint":[262],"metabolic":[265],"syndrome-related":[266],"datasets":[269],"collected":[270],"four":[272],"international":[273],"consortia":[274],"effectiveness":[278],"testing":[284],"procedures.":[285],"Supplementary":[286],"materials":[287,297],"including":[291],"standardized":[293],"description":[294],"reproducing":[300],"work,":[302],"an":[306],"online":[307],"supplement.":[308]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2024-04-08T00:00:00"}