{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T21:13:34Z","timestamp":1769116414985,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T00:00:00Z","timestamp":1768694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["72025405, 72421002, 92467302, 72474223, 72301285"],"award-info":[{"award-number":["72025405, 72421002, 92467302, 72474223, 72301285"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"The National Science and Technology Major Project for Brain Science and Brain-like Intelligence Technology","award":["2025ZD0215700"],"award-info":[{"award-number":["2025ZD0215700"]}]},{"name":"The Hunan Science and Technology Plan Project","award":["2023JJ40685, 2024RC3133"],"award-info":[{"award-number":["2023JJ40685, 2024RC3133"]}]},{"name":"The Major Program of Xiangjiang Laboratory","award":["24XJJCYJ01001"],"award-info":[{"award-number":["24XJJCYJ01001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Ego-Centric Sampling Method (ECM) leverages individual-level reports about peers to estimate population proportions within social networks, offering strong privacy protection without requiring full network data. However, the conventional ECM estimator is unbiased only under the restrictive assumption of a homogeneous network, where node degrees are uniform and uncorrelated with attributes. To overcome this limitation, we introduce the Activity Ratio Corrected ECM estimator (ECMac), which exploits network reciprocity to recast the population\u2013proportion problem into an equivalent formulation in edge space. This reformulation relies solely on ego\u2013peer data and explicitly corrects for degree\u2013attribute dependencies, yielding unbiased and stable estimates even in highly heterogeneous networks. Simulations and analyses on real-world networks show that ECMac reduces estimation error by up to 70% compared with the conventional ECM. Our results establish a theoretically grounded and practically scalable framework for unbiased inference in network-based sampling designs.<\/jats:p>","DOI":"10.3390\/e28010116","type":"journal-article","created":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T08:23:56Z","timestamp":1768811036000},"page":"116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Peer Reporting: Sampling Design and Unbiased Estimates"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-2719-4557","authenticated-orcid":false,"given":"Kang","family":"Wen","sequence":"first","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6654-7741","authenticated-orcid":false,"given":"Jianhong","family":"Mou","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3547-6493","authenticated-orcid":false,"given":"Xin","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/S0140-6736(12)60821-6","article-title":"Global Epidemiology of HIV Infection in Men Who Have Sex with Men","volume":"380","author":"Beyrer","year":"2012","journal-title":"Lancet"},{"key":"ref_2","first-page":"100002","article-title":"Informatics in the Era of AI","volume":"1","author":"Lu","year":"2025","journal-title":"Innov. 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