{"id":"https://openalex.org/W4365454113","doi":"https://doi.org/10.1080/03610918.2023.2201413","title":"Extending the Liu estimator for the Cox proportional hazards regression model with multicollinearity","display_name":"Extending the Liu estimator for the Cox proportional hazards regression model with multicollinearity","publication_year":2023,"publication_date":"2023-04-12","ids":{"openalex":"https://openalex.org/W4365454113","doi":"https://doi.org/10.1080/03610918.2023.2201413"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2023.2201413","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2023.2201413","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112601641","display_name":"Sonia Ahmad","orcid":null},"institutions":[{"id":"https://openalex.org/I127670440","display_name":"Bahauddin Zakariya University","ror":"https://ror.org/05x817c41","country_code":"PK","type":"education","lineage":["https://openalex.org/I127670440"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sonia Ahmad","raw_affiliation_strings":["Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan","institution_ids":["https://openalex.org/I127670440"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011827406","display_name":"Muhammad Aslam","orcid":"https://orcid.org/0000-0003-2290-2307"},"institutions":[{"id":"https://openalex.org/I127670440","display_name":"Bahauddin Zakariya University","ror":"https://ror.org/05x817c41","country_code":"PK","type":"education","lineage":["https://openalex.org/I127670440"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Aslam","raw_affiliation_strings":["Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan","institution_ids":["https://openalex.org/I127670440"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100676606","display_name":"Shakeel Ahmad","orcid":"https://orcid.org/0000-0002-5164-6448"},"institutions":[{"id":"https://openalex.org/I127670440","display_name":"Bahauddin Zakariya University","ror":"https://ror.org/05x817c41","country_code":"PK","type":"education","lineage":["https://openalex.org/I127670440"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shakeel Ahmad","raw_affiliation_strings":["Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan","institution_ids":["https://openalex.org/I127670440"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011827406"],"corresponding_institution_ids":["https://openalex.org/I127670440"],"apc_list":null,"apc_paid":null,"fwci":1.3937,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.81300855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"53","issue":"12","first_page":"5828","last_page":"5841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9998000264167786,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9922000169754028,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9822999835014343,"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/multicollinearity","display_name":"Multicollinearity","score":0.9321016073226929},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7624642848968506},{"id":"https://openalex.org/keywords/covariate","display_name":"Covariate","score":0.6259719133377075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5784409642219543},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.5510362982749939},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5478699207305908},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.5300443172454834},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5183392763137817},{"id":"https://openalex.org/keywords/proportional-hazards-model","display_name":"Proportional hazards model","score":0.49015912413597107},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.4321167469024658},{"id":"https://openalex.org/keywords/minimax-estimator","display_name":"Minimax estimator","score":0.42225825786590576},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.3496546149253845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3306569457054138}],"concepts":[{"id":"https://openalex.org/C189285262","wikidata":"https://www.wikidata.org/wiki/Q1332350","display_name":"Multicollinearity","level":3,"score":0.9321016073226929},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7624642848968506},{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.6259719133377075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5784409642219543},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.5510362982749939},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5478699207305908},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5300443172454834},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5183392763137817},{"id":"https://openalex.org/C50382708","wikidata":"https://www.wikidata.org/wiki/Q223218","display_name":"Proportional hazards model","level":2,"score":0.49015912413597107},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.4321167469024658},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.42225825786590576},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.3496546149253845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3306569457054138}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2023.2201413","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2023.2201413","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W221489729","https://openalex.org/W1598266570","https://openalex.org/W1684869656","https://openalex.org/W1781898551","https://openalex.org/W1969650641","https://openalex.org/W1986705681","https://openalex.org/W1988825111","https://openalex.org/W1990655238","https://openalex.org/W1992277956","https://openalex.org/W1999187230","https://openalex.org/W2001424819","https://openalex.org/W2012658469","https://openalex.org/W2016484575","https://openalex.org/W2020364685","https://openalex.org/W2021335009","https://openalex.org/W2023093304","https://openalex.org/W2030172320","https://openalex.org/W2046217136","https://openalex.org/W2047428920","https://openalex.org/W2050418356","https://openalex.org/W2058495667","https://openalex.org/W2062793108","https://openalex.org/W2067239684","https://openalex.org/W2070394662","https://openalex.org/W2081458895","https://openalex.org/W2136916987","https://openalex.org/W2139766869","https://openalex.org/W2143305792","https://openalex.org/W2143421694","https://openalex.org/W2154576538","https://openalex.org/W2159483927","https://openalex.org/W2274232034","https://openalex.org/W2314246804","https://openalex.org/W2338509365","https://openalex.org/W2342519913","https://openalex.org/W2547273949","https://openalex.org/W2771101472","https://openalex.org/W2774382334","https://openalex.org/W2801490189","https://openalex.org/W2946792909","https://openalex.org/W3083952971","https://openalex.org/W3124631997","https://openalex.org/W3147894994","https://openalex.org/W3180133856","https://openalex.org/W3191134718","https://openalex.org/W4205502812","https://openalex.org/W4213021730","https://openalex.org/W4226186974","https://openalex.org/W4234698323","https://openalex.org/W4256170606","https://openalex.org/W4295835860","https://openalex.org/W6720304639"],"related_works":["https://openalex.org/W2160772450","https://openalex.org/W2036696807","https://openalex.org/W1976770238","https://openalex.org/W2161339348","https://openalex.org/W3021510379","https://openalex.org/W2350206592","https://openalex.org/W4386830465","https://openalex.org/W4283751653","https://openalex.org/W2737279617","https://openalex.org/W2014640816"],"abstract_inverted_index":{"In":[0,92],"this":[1,67],"article,":[2,95],"we":[3,96],"present":[4,94],"the":[5,9,27,30,39,53,62,69,73,80,83,88,93,98,105,109,120,127,131,138,150],"Liu":[6,99],"estimator":[7,19,75,122],"for":[8,24,61,82,108,149],"Cox":[10,31,84,110],"proportional":[11],"hazards":[12],"(PH)":[13],"model.":[14,33],"The":[15,34,117],"maximum":[16],"partial":[17],"likelihood":[18],"(MPLE)":[20],"is":[21,55],"commonly":[22],"used":[23],"estimation":[25],"of":[26,29,90,104,119],"coefficients":[28],"PH":[32,85,111],"MPLE":[35,54,81],"performs":[36],"well":[37],"if":[38],"covariates":[40,47],"are":[41],"uncorrelated.":[42],"However,":[43],"in":[44,87],"many":[45],"situations,":[46],"become":[48],"seriously":[49],"correlated,":[50],"and":[51,113],"then":[52],"inept":[56],"to":[57,79],"produce":[58],"stable":[59],"estimates":[60],"unknown":[63],"coefficients.":[64],"To":[65],"overcome":[66],"situation,":[68],"literature":[70],"suggests":[71],"using":[72,130],"ridge":[74,106],"as":[76],"an":[77],"alternative":[78],"model":[86,112],"presence":[89],"multicollinearity.":[91],"extend":[97],"estimator,":[100,107],"a":[101],"popular":[102],"superseder":[103],"discuss":[114],"its":[115],"properties.":[116],"performance":[118],"proposed":[121],"has":[123,145],"been":[124,147],"compared":[125],"with":[126],"available":[128],"estimators":[129],"scalar":[132],"mean":[133],"squared":[134],"error":[135],"criterion":[136],"through":[137],"Monte":[139],"Carlo":[140],"simulations.":[141],"A":[142],"numerical":[143],"example":[144],"also":[146],"provided":[148],"illustration.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
