{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:09:39Z","timestamp":1787018979004,"version":"build-2736575974"},"reference-count":40,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T00:00:00Z","timestamp":1752710400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"National Institute of Mental Health of the National Institutes of Health","award":["R01MH134715"],"award-info":[{"award-number":["R01MH134715"]}]},{"name":"National Institute on Drug Abuse of the National Institutes of Health","award":["DP2DA046856"],"award-info":[{"award-number":["DP2DA046856"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:p>Many public health interventions are conducted in settings where individuals are connected and the intervention assigned to some individuals may spill over to other individuals. In these settings, we can assess: (a) the individual effect on the treated, (b) the spillover effect on untreated individuals through an indirect exposure to the intervention, and (c) the overall effect on the whole population. Here, we consider an egocentric network-based randomized design in which a set of index participants is recruited and randomly assigned to treatment, while data are also collected on their untreated network members. Such a design is common in peer education interventions conceived to leverage behavioral influence among peers. Using the potential outcomes framework, we first clarify the assumptions required to rely on an identification strategy that is commonly used in the well-studied two-stage randomized design. Under these assumptions, causal effects can be jointly estimated using a regression model with a block-diagonal structure. We then develop sample size formulas for detecting individual, spillover, and overall effects for single and joint hypothesis tests, and investigate the role of different parameters. Finally, we illustrate the use of our sample size formulas for an egocentric network-based randomized experiment to evaluate a  peer education intervention\u00a0for HIV prevention.<\/jats:p>","DOI":"10.1177\/09622802251357021","type":"journal-article","created":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T08:28:31Z","timestamp":1752740911000},"page":"2034-2052","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Design of egocentric network-based studies to estimate causal effects under interference"],"prefix":"10.1177","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4766-5590","authenticated-orcid":false,"given":"Junhan","family":"Fang","sequence":"first","affiliation":[{"name":"Hoffmann-La Roche Ltd, Mississauga, ON, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4006-4650","authenticated-orcid":false,"given":"Donna","family":"Spiegelman","sequence":"additional","affiliation":[{"name":"Center for Methods in Implementation and Prevention Science, Department of Biostatistics, Yale School of Public Health, Yale University, New Haven, CT, USA"},{"name":"Department of Biostatistics, Yale School of Public Health, Yale University, New Haven, CT, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4715-3456","authenticated-orcid":false,"given":"Ashley L","family":"Buchanan","sequence":"additional","affiliation":[{"name":"University of Rhode Island"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3721-9826","authenticated-orcid":false,"given":"Laura","family":"Forastiere","sequence":"additional","affiliation":[{"name":"Center for Methods in Implementation and Prevention Science, Department of Biostatistics, Yale School of Public Health, Yale University, New Haven, CT, USA"},{"name":"Department of Biostatistics, Yale School of Public Health, Yale University, New Haven, CT, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,7,17]]},"reference":[{"key":"e_1_3_2_2_2","volume-title":"Planning of Experiments","author":"Cox DR","year":"1958","unstructured":"Cox DR. Planning of Experiments. New York: \u00a0Wiley, 1958."},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000001112"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"key":"e_1_3_2_5_2","first-page":"204","article-title":"An application of the theory of probabilities to the study of a priori pathometry.\u2014part i","volume":"92","author":"Ross R","year":"1916","unstructured":"Ross R. An application of the theory of probabilities to the study of a priori pathometry.\u2014part i. Proc R Soc London Ser A, Contain Papers Math Phys Character 1916; 92: 204\u2013230.","journal-title":"Proc R Soc London Ser A, Contain Papers Math Phys Character"},{"key":"e_1_3_2_6_2","first-page":"1","article-title":"Identification and estimation of treatment and interference effects in observational studies on networks","volume":"116","author":"Forastiere L","year":"2020","unstructured":"Forastiere L, Airoldi EM, Mealli F. Identification and estimation of treatment and interference effects in observational studies on networks. J Am Stat Assoc 2020; 116: 1\u201318.","journal-title":"J Am Stat Assoc"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40471-016-0086-4"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000292"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2013.844698"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asw047"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12184"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-5907.2012.00592.x"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1177\/0962280210386779"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOAS1005"},{"key":"e_1_3_2_15_2","first-page":"2165","article-title":"Estimating causal effects of non-randomized hiv prevention interventions with interference in network-based studies among people who inject drugs","volume":"17","author":"Lee T","year":"2023","unstructured":"Lee T, Buchanan AL, Forastiere KNVL, et al. Estimating causal effects of non-randomized hiv prevention interventions with interference in network-based studies among people who inject drugs. Ann Appl Stat In Press 2023; 17: 2165\u20132191.","journal-title":"Ann Appl Stat In Press"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1162\/rest_a_00818"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13125"},{"key":"e_1_3_2_18_2","unstructured":"Ogburn E Sofrygin O Diaz I et al. Causal inference for social network data. arXiv preprint arXiv:1705.08527 2017."},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1515\/jci-2016-0003"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1214\/20-AOS1973"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1811098"},{"key":"e_1_3_2_22_2","first-page":"2449","article-title":"Assessing individual and disseminated effects in network-randomized studies","volume":"187","author":"Buchanan AL","year":"2018","unstructured":"Buchanan AL, Vermund SH, Friedman SR, et al. Assessing individual and disseminated effects in network-randomized studies. Am J Epidemiol 2018; 187: 2449\u20132459.","journal-title":"Am J Epidemiol"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10461-011-9943-9"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.socscimed.2008.11.019"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1360-0443.2010.03146.x"},{"key":"e_1_3_2_26_2","volume-title":"Design and analysis of cluster randomization trials in health research","author":"Donner A","year":"2000","unstructured":"Donner A, Klar N. Design and analysis of cluster randomization trials in health research. London: \u00a0Arnold, 2000."},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781584888178"},{"key":"e_1_3_2_28_2","article-title":"How to design efficient cluster randomised trials","volume":"358","author":"Hemming K","year":"2017","unstructured":"Hemming K, Eldridge S, Forbes G, et al. How to design efficient cluster randomised trials. BMJ 2017; 358.","journal-title":"BMJ"},{"key":"e_1_3_2_29_2","volume-title":"Design and Analysis of Group-Randomized Trials","author":"Murray D","year":"1998","unstructured":"Murray D. Design and Analysis of Group-Randomized Trials. New York, NY: Oxford University Press, 1998."},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.2.2.173"},{"key":"e_1_3_2_31_2","first-page":"1","article-title":"Sample size estimation for randomised controlled trials with repeated assessment of patient-reported outcomes: what correlation between baseline and follow-up outcomes should we assume?","volume":"20","author":"Walters SJ","year":"2019","unstructured":"Walters SJ, Jacques RM, dos Anjos Henriques-Cadby IB, et al. Sample size estimation for randomised controlled trials with repeated assessment of patient-reported outcomes: what correlation between baseline and follow-up outcomes should we assume?. Trials 2019; 20: 1\u201316.","journal-title":"Trials"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1093\/epirev\/24.1.39"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1162\/rest_a_00716"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13782"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2003.08.009"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1177\/1094428108320370"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1017\/9781316443255"},{"key":"e_1_3_2_38_2","volume-title":"Causal Inference: What If","author":"Hern\u00e1n M","year":"2020","unstructured":"Hern\u00e1n M, Robins J. Causal Inference: What If. Boca Raton: \u00a0Chapman & Hall\/CRC Press, 2020."},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0318-1"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9284"},{"key":"e_1_3_2_41_2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1002\/1521-4036(200102)43:1<75::AID-BIMJ75>3.0.CO;2-N","article-title":"Sample size estimation in cluster randomized studies with varying cluster size","volume":"43","author":"Manatunga AK","year":"2001","unstructured":"Manatunga AK, Hudgens MG, Chen S. Sample size estimation in cluster randomized studies with varying cluster size. Biomet J: J Mathemat Methods Biosci 2001; 43: 75\u201386.","journal-title":"Biomet J: J Mathemat Methods Biosci"}],"container-title":["Statistical Methods in Medical Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09622802251357021","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/09622802251357021","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/09622802251357021","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:19:52Z","timestamp":1761178792000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/09622802251357021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,17]]},"references-count":40,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["10.1177\/09622802251357021"],"URL":"https:\/\/doi.org\/10.1177\/09622802251357021","relation":{},"ISSN":["0962-2802","1477-0334"],"issn-type":[{"value":"0962-2802","type":"print"},{"value":"1477-0334","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,17]]}}}