{"doi":"10.1002/sim.7038","title":"An alternative empirical likelihood method in missing response problems and causal inference","abstract":"<jats:p>Missing responses are common problems in medical, social, and economic studies. When responses are missing at random, a complete case data analysis may result in biases. A popular debias method is inverse probability weighting proposed by Horvitz and Thompson. To improve efficiency, Robins <jats:italic>et al.</jats:italic> proposed an augmented inverse probability weighting method. The augmented inverse probability weighting estimator has a double‐robustness property and achieves the semiparametric efficiency lower bound when the regression model and propensity score model are both correctly specified. In this paper, we introduce an empirical likelihood‐based estimator as an alternative to Qin and Zhang (2007). Our proposed estimator is also doubly robust and locally efficient. Simulation results show that the proposed estimator has better performance when the propensity score is correctly modeled. Moreover, the proposed method can be applied in the estimation of average treatment effect in observational causal inferences. Finally, we apply our method to an observational study of smoking, using data from the Cardiovascular Outcomes in Renal Atherosclerotic Lesions clinical trial. Copyright © 2016 John Wiley &amp; Sons, Ltd.</jats:p>","journal":"Statistics in Medicine","year":2016,"id":30884,"datarank":0.4752133213204445,"base_score":1.791759469228055,"endowment":1.791759469228055,"self_citation_contribution":0.26876392038420827,"citation_network_contribution":0.20644940093623626,"self_endowment_contribution":0.26876392038420827,"citer_contribution":0.20644940093623626,"corpus_percentile":null,"corpus_rank":null,"citation_count":5,"citer_count":5,"citers_with_citation_signal":3,"citers_with_endowment":3,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":166796,"name":"Christopher A. 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Cooper","orcid":null,"position":5,"is_corresponding":false},{"id":166805,"name":"Biao Zhang","orcid":null,"position":6,"is_corresponding":false},{"id":166795,"name":"Kaili Ren","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":1.791759469228055,"endowment":1.791759469228055,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"27417265","pmcid":"PMC5096999","openalex_id":"https://openalex.org/W2512840654","authors":[],"funders":[{"funder_name":"National Heart, Lung, and Blood Institute of the National Institutes of Health","grant_id":"U01HL072734","title":null},{"funder_name":"National Heart, Lung, and Blood Institute of the National Institutes of Health","grant_id":"U01HL072735","title":null},{"funder_name":"National Heart, Lung, and Blood Institute of the National Institutes of Health","grant_id":"U01HL072736","title":null},{"funder_name":"National Heart, Lung, and Blood Institute of the National Institutes of Health","grant_id":"U01HL072737","title":null},{"funder_name":"National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health","grant_id":"5U01HL071556","title":null},{"funder_name":"National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health","grant_id":"1F32DK104615-01","title":null},{"funder_name":"National and Ohio Valley Affiliate of the American Heart Association","grant_id":"13POST16860035","title":null},{"funder_name":"NHLBI, the National Institutes of Health","grant_id":"1R01HL-105649","title":null},{"funder_name":"NHLBI NIH HHS","grant_id":"U01 HL071556","title":null},{"funder_name":"NIDDK NIH HHS","grant_id":"F32 DK104615","title":null},{"funder_name":"NHLBI NIH HHS","grant_id":"R01 HL105649","title":null},{"funder_name":"AstraZeneca","grant_id":"","title":null},{"funder_name":"Cordis","grant_id":"","title":null},{"funder_name":"Pfizer","grant_id":"","title":null}],"total_grants":14,"fwci":0.3623,"citation_percentile":0.69226951,"influential_citations":1,"citation_trend":[{"year":2018,"count":1},{"year":2020,"count":2},{"year":2024,"count":2}],"oa_status":"green","license":"http://doi.wiley.com/10.1002/tdm_license_1.1","oa_locations":[{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5096999","host_type":"repository"},{"url":"https://europepmc.org/articles/pmc5096999?pdf=render","host_type":"GREEN"},{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5096999","host_type":"repository"},{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fsim.7038","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.7038","host_type":"publisher"},{"url":"https://doi.org/10.1002/sim.7038","host_type":"journal"},{"url":"https://pubmed.ncbi.nlm.nih.gov/27417265","host_type":"repository"}],"fields_of_study":["Advanced Causal Inference Techniques","Statistical Methods and Bayesian Inference","Statistical Methods and Inference","Medicine","Mathematics","Economics","Computer Simulation","Data Interpretation, Statistical","Humans","Likelihood Functions","Models, Statistical","Propensity Score"],"mesh_terms":["Computer Simulation","Data Interpretation, Statistical","Humans","Models, Statistical","Likelihood Functions","Propensity Score"],"keywords":["Inverse probability weighting","Inverse probability","Empirical likelihood","Propensity score matching","Estimator","Causal inference","Observational study","Weighting","Statistics","Missing data","Econometrics","Robustness (evolution)","Mathematics","Marginal structural model","Computer science","Medicine","Posterior probability","Bayesian probability","Propensity Score","Missing At Random","Average Treatment Effect"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Good health and well-being"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-09T05:49:18.691713Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}