{"id":"https://openalex.org/W4381548436","doi":"https://doi.org/10.1186/s12874-023-01939-z","title":"On the Q statistic with constant weights in meta-analysis of binary outcomes","display_name":"On the Q statistic with constant weights in meta-analysis of binary outcomes","publication_year":2023,"publication_date":"2023-06-21","ids":{"openalex":"https://openalex.org/W4381548436","doi":"https://doi.org/10.1186/s12874-023-01939-z","pmid":"https://pubmed.ncbi.nlm.nih.gov/37344771","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/10286409"},"language":"en","primary_location":{"id":"doi:10.1186/s12874-023-01939-z","doi":"https://doi.org/10.1186/s12874-023-01939-z","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s12874-023-01939-z","pdf_url":"https://bmcmedresmethodol.biomedcentral.com/counter/pdf/10.1186/s12874-023-01939-z","source":{"id":"https://openalex.org/S185874209","display_name":"BMC Medical Research Methodology","issn_l":"1471-2288","issn":["1471-2288"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-b","doyens","jufo-1","ki-jl-1","medline","norway-1","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Medical Research Methodology","raw_type":"journal-article"},"volume":null,"type":"review","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://bmcmedresmethodol.biomedcentral.com/counter/pdf/10.1186/s12874-023-01939-z","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001621375","display_name":"Elena Kulinskaya","orcid":"https://orcid.org/0000-0002-9843-1663","observed_orcids":["https://orcid.org/0000-0002-9843-1663"]},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]},{"id":"https://openalex.org/I2799300731","display_name":"Norwich Research Park","ror":"https://ror.org/0062dz060","country_code":"GB","type":"archive","lineage":["https://openalex.org/I2799300731"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Elena Kulinskaya","raw_affiliation_strings":["School of Computing Sciences, University of East Anglia, Norwich Research Park, NR4 7TJ, Norwich, UK. e.kulinskaya@uea.ac.uk","School of Computing Sciences, University of East Anglia, Norwich Research Park, NR4 7TJ, Norwich, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing Sciences, University of East Anglia, Norwich Research Park, NR4 7TJ, Norwich, UK. e.kulinskaya@uea.ac.uk","institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"]},{"raw_affiliation_string":"School of Computing Sciences, University of East Anglia, Norwich Research Park, NR4 7TJ, Norwich, UK","institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084106675","display_name":"David C. Hoaglin","orcid":"https://orcid.org/0000-0003-1336-181X","observed_orcids":["https://orcid.org/0000-0003-1336-181X"]},"institutions":[{"id":"https://openalex.org/I166722992","display_name":"University of Massachusetts Chan Medical School","ror":"https://ror.org/0464eyp60","country_code":"US","type":"education","lineage":["https://openalex.org/I166722992"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David C. Hoaglin","raw_affiliation_strings":["Department of Population and Quantitative Health Sciences, UMass Chan Medical School, 368 Plantation Street, Worcester, Massachusetts 01605, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Population and Quantitative Health Sciences, UMass Chan Medical School, 368 Plantation Street, Worcester, Massachusetts 01605, USA","institution_ids":["https://openalex.org/I166722992"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001621375"],"corresponding_institution_ids":["https://openalex.org/I1118541","https://openalex.org/I2799300731"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.5647,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.62557924,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"1","first_page":"146","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10206","display_name":"Meta-analysis and systematic reviews","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10206","display_name":"Meta-analysis and systematic reviews","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T14374","display_name":"Statistical Methods in Epidemiology","score":0.0010000000474974513,"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/T11235","display_name":"Statistical Methods in Clinical Trials","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/heterogeneity-test","display_name":"heterogeneity testing","score":0.8460000157356262},{"id":"https://openalex.org/keywords/between-study-variance","display_name":"between-study variance","score":0.7360000014305115},{"id":"https://openalex.org/keywords/log-odds-ratio","display_name":"log odds ratio","score":0.8220000267028809},{"id":"https://openalex.org/keywords/risk-difference","display_name":"risk difference","score":1.0},{"id":"https://openalex.org/keywords/gamma-distribution-approximation","display_name":"Gamma distribution approximation","score":0.8009999990463257},{"id":"https://openalex.org/keywords/chi-square-approximation","display_name":"chi-square approximation","score":0.8849999904632568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6251882910728455},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5656905174255371},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.5653062462806702},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5329958200454712},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.5004525184631348},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4474494457244873},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.43616747856140137},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.42547282576560974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41348594427108765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1613817811012268},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016017","descriptor_name":"Odds Ratio","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D018401","descriptor_name":"Sample Size","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":5,"locations":[{"id":"doi:10.1186/s12874-023-01939-z","doi":"https://doi.org/10.1186/s12874-023-01939-z","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s12874-023-01939-z","pdf_url":"https://bmcmedresmethodol.biomedcentral.com/counter/pdf/10.1186/s12874-023-01939-z","source":{"id":"https://openalex.org/S185874209","display_name":"BMC Medical Research Methodology","issn_l":"1471-2288","issn":["1471-2288"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-b","doyens","jufo-1","ki-jl-1","medline","norway-1","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Medical Research Methodology","raw_type":"journal-article"},{"id":"doi:10.21203/rs.3.rs-2121915/v1","doi":"https://doi.org/10.21203/rs.3.rs-2121915/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-2121915/v1","pdf_url":"https://www.researchsquare.com/article/rs-2121915/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},{"id":"pmh:oai:pubmedcentral.nih.gov:10286409","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10286409","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10286409/pdf/12874_2023_Article_1939.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Med Res Methodol","raw_type":"Text"},{"id":"pmid:37344771","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37344771","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC medical research methodology","raw_type":"Meta-Analysis"},{"id":"pmh:oai:doaj.org/article:1f72b07ab8944ef28026f502f52ca56b","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/1f72b07ab8944ef28026f502f52ca56b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"BMC Medical Research Methodology, Vol 23, Iss 1, Pp 1-18 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1186/s12874-023-01939-z","doi":"https://doi.org/10.1186/s12874-023-01939-z","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s12874-023-01939-z","pdf_url":"https://bmcmedresmethodol.biomedcentral.com/counter/pdf/10.1186/s12874-023-01939-z","source":{"id":"https://openalex.org/S185874209","display_name":"BMC Medical Research Methodology","issn_l":"1471-2288","issn":["1471-2288"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-b","doyens","jufo-1","ki-jl-1","medline","norway-1","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Medical Research Methodology","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3482995644","display_name":"Smart Data Analytics for Business and Local Government","funder_award_id":"ES/L011859/1","funder_id":"https://openalex.org/F4320334630","funder_display_name":"Economic and Social Research Council"},{"id":"https://openalex.org/G8322284704","display_name":null,"funder_award_id":"ES/L011859/1","funder_id":"https://openalex.org/F4320334630","funder_display_name":"Economic and Social Research Council"}],"funders":[{"id":"https://openalex.org/F4320334630","display_name":"Economic and Social Research Council","ror":"https://ror.org/03n0ht308"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4381548436.pdf","grobid_xml":"https://content.openalex.org/works/W4381548436.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1497405457","https://openalex.org/W1591837399","https://openalex.org/W1821872278","https://openalex.org/W1883430110","https://openalex.org/W1967046314","https://openalex.org/W1978127742","https://openalex.org/W1979190635","https://openalex.org/W1996740657","https://openalex.org/W1996843362","https://openalex.org/W2001248225","https://openalex.org/W2016140862","https://openalex.org/W2063119504","https://openalex.org/W2088441249","https://openalex.org/W2164586769","https://openalex.org/W2267047343","https://openalex.org/W2315123323","https://openalex.org/W2743122016","https://openalex.org/W2811026575","https://openalex.org/W2920850085","https://openalex.org/W2983184714","https://openalex.org/W3008542205","https://openalex.org/W3092560382","https://openalex.org/W3131578222","https://openalex.org/W3163649563","https://openalex.org/W3168016381","https://openalex.org/W4210521626","https://openalex.org/W4237559595","https://openalex.org/W4248173958","https://openalex.org/W4283219894","https://openalex.org/W4301040373","https://openalex.org/W6742905407","https://openalex.org/W7071376953"],"related_works":["https://openalex.org/W4283219894","https://openalex.org/W3163649563","https://openalex.org/W4210521626","https://openalex.org/W3134767884","https://openalex.org/W3094327543","https://openalex.org/W7113516440","https://openalex.org/W6977305070","https://openalex.org/W1497405457","https://openalex.org/W2063119504","https://openalex.org/W2021000194"],"abstract_inverted_index":{"BACKGROUND:":[0],"Cochran's":[1],"Q":[2,52,79],"statistic":[3],"is":[4,20,165,264],"routinely":[5],"used":[6],"for":[7,39,126,135,152,167,180,199,206,218,232,236,245,266,288,297],"testing":[8],"heterogeneity":[9,278],"in":[10,46],"meta-analysis.":[11],"Its":[12],"expected":[13],"value":[14],"(under":[15],"an":[16,73,157,161,290],"incorrect":[17],"null":[18],"distribution)":[19],"part":[21],"of":[22,26,41,65,106,115,128,146,163,257,277],"several":[23],"popular":[24],"estimators":[25],"the":[27,42,47,63,89,104,124,144,173,188,221,258,294],"between-study":[28],"variance,":[29],"[Formula:":[30,55,66,81,116,120,147,185,237,260,281],"see":[31,56,67,82,117,121,148,186,238,261,282],"text].":[32],"Those":[33],"applications":[34],"generally":[35],"do":[36],"not":[37],"account":[38],"use":[40,87],"studies'":[43,90],"estimated":[44],"variances":[45],"inverse-variance":[48],"weights":[49,60,86],"that":[50,194],"define":[51],"(more":[53],"explicitly,":[54],"text]).":[57],"Importantly,":[58],"those":[59],"make":[61],"approximating":[62],"distribution":[64,145],"text]":[68,118,149,239,262,283],"rather":[69],"complicated.":[70],"METHODS:":[71],"As":[72],"alternative,":[74],"we":[75,108,273],"are":[76,195],"investigating":[77],"a":[78,139,275],"statistic,":[80],"text],":[83,122,187],"whose":[84],"constant":[85],"only":[88],"arm-level":[91],"sample":[92,154,169,182,248],"sizes.":[93,170,183],"For":[94,171,184],"log-odds-ratio":[95],"(LOR),":[96],"log-relative-risk":[97],"(LRR),":[98],"and":[99,119,137,156,201,203,220,223,284],"risk":[100],"difference":[101],"(RD)":[102],"as":[103,123],"measures":[105],"effect,":[107],"study,":[109],"by":[110],"simulation,":[111],"approximations":[112],"to":[113,143],"distributions":[114],"basis":[125],"tests":[127],"heterogeneity.":[129],"RESULTS:":[130],"The":[131,208,255],"results":[132],"show":[133],"that:":[134],"LOR":[136,200,233],"LRR,":[138],"two-moment":[140],"gamma":[141],"approximation":[142,158,175,191,217,231,263],"works":[150,176],"well":[151,235],"small":[153,181,247,252],"sizes,":[155],"based":[159,279],"on":[160,280],"algorithm":[162],"Farebrother":[164,174],"recommended":[166],"larger":[168],"RD,":[172],"very":[177,246],"well,":[178],"even":[179],"standard":[189,259],"chi-square":[190],"provides":[192],"levels":[193],"much":[196],"too":[197,204],"low":[198],"LRR":[202],"high":[205],"RD.":[207],"Kulinskaya":[209,222],"et":[210],"al.":[211],"(Res":[212],"Synth":[213],"Methods":[214],"2:254-70,":[215],"2011)":[216],"RD":[219],"Dollinger":[224],"(BMC":[225],"Med":[226],"Res":[227],"Methodol":[228],"15:49,":[229],"2015)":[230],"work":[234],"but":[240],"have":[241],"some":[242],"convergence":[243],"issues":[244],"sizes":[249],"combined":[250],"with":[251],"probabilities.":[253],"CONCLUSIONS:":[254],"performance":[256],"inadequate":[265],"all":[267,298],"three":[268,299],"binary":[269],"effect":[270,300],"measures.":[271,301],"Instead,":[272],"recommend":[274],"test":[276,292],"provide":[285],"practical":[286],"guidelines":[287],"choosing":[289],"appropriate":[291],"at":[293],".05":[295],"level":[296]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2023-06-22T00:00:00"}