{"doi":"10.5705/ss.202022.0228","title":"On Combining Individual-Level Data With Summary Data in Statistical Inferences","abstract":"Statistical models and inferences are typically based on measurements made on individual participants in the study (individual-level data). There is a great interest to improve the statistical inference by taking advantage of aggregated summary level data from other studies, such as those statistics typically used in meta-analyses. The generalized method of moments (GMM) provides a flexible way to achieve such a goal. However, it has been observed that the integration of external summary information does not always lead to efficiency improvement. We provide the necessary and sufficient condition under which the use of external summary information can be beneficial. We further extend the GMM procedure to incorporate summary data that is generated from a Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) population with its covariate distribution being different from the one in the individual-level data. We also establish the connection between the GMM and other integration procedures.","journal":"Statistica Sinica","year":2022,"id":290592,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":4,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9551,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2022-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":973013,"name":"Sheng Fu","orcid":"0000-0002-2441-3120","position":1,"is_corresponding":false},{"id":752531,"name":"Jing Qin","orcid":"0000-0002-7059-0929","position":2,"is_corresponding":false},{"id":302110,"name":"Kai Yu","orcid":"0000-0002-4778-4389","position":3,"is_corresponding":false},{"id":973012,"name":"L. Deng","orcid":"0000-0003-2247-3530","position":0,"is_corresponding":true}],"reference_count":20,"raw_metadata":null,"created_at":"2026-07-19T00:30:30.639224Z","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":[]}