{"id":"https://openalex.org/W4409045944","doi":"https://doi.org/10.1007/s10994-026-07054-6","title":"Regression-Based Estimation of Causal Effects in the Presence of Selection Bias and Confounding","display_name":"Regression-Based Estimation of Causal Effects in the Presence of Selection Bias and Confounding","publication_year":2026,"publication_date":"2026-05-01","ids":{"openalex":"https://openalex.org/W4409045944","doi":"https://doi.org/10.1007/s10994-026-07054-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-026-07054-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-026-07054-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-026-07054-6.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","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":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10994-026-07054-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116866539","display_name":"Marlies Hafer","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marlies Hafer","raw_affiliation_strings":["Department of Statistics, TU Dortmund University, Dortmund, Germany","Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Dortmund, North Rhine-Westphalia, Germany"],"raw_orcid":"https://orcid.org/0009-0006-0222-0025","affiliations":[{"raw_affiliation_string":"Department of Statistics, TU Dortmund University, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Dortmund, North Rhine-Westphalia, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053408235","display_name":"Alexander Marx","orcid":"https://orcid.org/0000-0002-1575-824X"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexander Marx","raw_affiliation_strings":["Department of Statistics, TU Dortmund University, Dortmund, Germany","Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Dortmund, North Rhine-Westphalia, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1575-824X","affiliations":[{"raw_affiliation_string":"Department of Statistics, TU Dortmund University, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Dortmund, North Rhine-Westphalia, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053408235"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01557751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"115","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10845","display_name":"Advanced Causal Inference Techniques","score":0.6710000038146973,"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/T10845","display_name":"Advanced Causal Inference Techniques","score":0.6710000038146973,"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/confounding","display_name":"Confounding","score":0.8623948097229004},{"id":"https://openalex.org/keywords/selection-bias","display_name":"Selection bias","score":0.7472924590110779},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.6069886088371277},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5532776117324829},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.5308963656425476},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5190815925598145},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5001556873321533},{"id":"https://openalex.org/keywords/causal-inference","display_name":"Causal inference","score":0.43332988023757935},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.42759978771209717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3114638924598694},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2639290392398834},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.19163978099822998},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.128420889377594}],"concepts":[{"id":"https://openalex.org/C77350462","wikidata":"https://www.wikidata.org/wiki/Q1125472","display_name":"Confounding","level":2,"score":0.8623948097229004},{"id":"https://openalex.org/C40423286","wikidata":"https://www.wikidata.org/wiki/Q284172","display_name":"Selection bias","level":2,"score":0.7472924590110779},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.6069886088371277},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5532776117324829},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5308963656425476},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5190815925598145},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5001556873321533},{"id":"https://openalex.org/C158600405","wikidata":"https://www.wikidata.org/wiki/Q5054566","display_name":"Causal inference","level":2,"score":0.43332988023757935},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.42759978771209717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3114638924598694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2639290392398834},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.19163978099822998},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.128420889377594},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10994-026-07054-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-026-07054-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-026-07054-6.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","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":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2503.20546","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.20546","pdf_url":"https://arxiv.org/pdf/2503.20546","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2503.20546","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2503.20546","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s10994-026-07054-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-026-07054-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-026-07054-6.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","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":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320329559","display_name":"Technische Universit\u00e4t Dortmund","ror":"https://ror.org/01k97gp34"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409045944.pdf","grobid_xml":"https://content.openalex.org/works/W4409045944.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3023719900","https://openalex.org/W4287798354","https://openalex.org/W3035083705","https://openalex.org/W2030287811","https://openalex.org/W3002087755","https://openalex.org/W4386534229","https://openalex.org/W4386150491","https://openalex.org/W2806152055","https://openalex.org/W3086603641","https://openalex.org/W4286896224"],"abstract_inverted_index":{"Abstract":[0],"We":[1,143,175],"consider":[2],"the":[3,7,61,67,98,119],"problem":[4],"of":[5,140,162],"estimating":[6],"expected":[8],"causal":[9,99,141],"effect":[10,100],"$$E[Y|do(X)]$$":[11,87],"for":[12,78,115,118,168,173,199],"a":[13,146,190],"target":[14],"variable":[15],"$$Y$$":[16],"when":[17,51,184],"treatment":[18],"$$X$$":[19],"is":[20,92,104,179,186],"set":[21],"by":[22,55,66,95],"intervention,":[23],"focusing":[24],"on":[25],"continuous":[26],"random":[27],"variables.":[28,210],"In":[29],"settings":[30],"without":[31],"selection":[32,56,68,79,120,169,204],"bias":[33,80,170,205],"or":[34,58],"confounding,":[35,96],"$$E[Y|do(X)]":[36],"=":[37],"E[Y|X]$$":[38],",":[39,84,88],"which":[40,152],"can":[41,153],"be":[42,74,154],"estimated":[43],"using":[44],"standard":[45],"regression":[46,49,149],"methods.":[47],"However,":[48],"fails":[50],"systematic":[52],"missingness":[53],"induced":[54],"bias,":[57],"confounding":[59,116,185,207],"distorts":[60],"data.":[62],"Proxy":[63],"variables":[64,165],"unaffected":[65],"process":[69],"can,":[70],"under":[71],"certain":[72],"constraints,":[73],"used":[75],"to":[76,81,110,112,124,166],"correct":[77,114],"recover":[82],"$$E[Y|X]$$":[83],"and":[85,107,117,138,206],"hence":[86],"reliably.":[89],"When":[90],"data":[91,103],"additionally":[93],"affected":[94],"recovering":[97],"from":[101,127],"selection-biased":[102],"more":[105],"challenging":[106],"requires":[108],"access":[109,123],"proxies":[111,126],"both":[113,203],"mechanism.":[121],"Assuming":[122],"such":[125],"external":[128],"unbiased":[129],"observational":[130],"data,":[131],"we":[132],"derive":[133],"theoretical":[134],"conditions":[135],"ensuring":[136],"identifiability":[137],"recoverability":[139],"effects.":[142],"further":[144],"introduce":[145],"linear":[147],"two-step":[148],"estimator":[150],"(TSR),":[151],"extended":[155],"through":[156],"adding":[157],"non-linear":[158],"basis":[159],"functions,":[160],"capable":[161],"exploiting":[163],"proxy":[164,209],"adjust":[167],"while":[171],"accounting":[172],"confounding.":[174],"show":[176],"that":[177,201],"TSR":[178],"consistent":[180],"with":[181,208],"previous":[182],"estimators":[183],"absent,":[187],"but":[188],"achieves":[189],"lower":[191],"variance.":[192],"Extensive":[193],"simulation":[194],"studies":[195],"validate":[196],"TSR\u2019s":[197],"correctness":[198],"scenarios":[200],"include":[202]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}