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RMST is the patient's life expectancy until time <jats:italic>t<\/jats:italic> and can be estimated nonparametrically by the area under the Kaplan\u2010Meier curve up to <jats:italic>t<\/jats:italic>. In a comparative study, the difference or ratio of two RMSTs has been utilized to quantify the between\u2010group\u2010difference as a clinically interpretable alternative summary to the hazard ratio. The choice of the time window [0, <jats:italic>t<\/jats:italic>] may be prespecified at the design stage of the study based on clinical considerations. On the other hand, after the survival data have been collected, the choice of time point <jats:italic>t<\/jats:italic> could be data\u2010dependent. The standard inferential procedures for the corresponding RMST, which is also data\u2010dependent, ignore this subtle yet important issue. In this paper, we clarify how to make inference about a random \u201cparameter.\u201d Moreover, we demonstrate that under a rather mild condition on the censoring distribution, one can make inference about the RMST up to <jats:italic>t<\/jats:italic>, where <jats:italic>t<\/jats:italic> is less than or even equal to the largest follow\u2010up time (either observed or censored) in the study. This finding reduces the subjectivity of the choice of <jats:italic>t<\/jats:italic> empirically. The proposal is illustrated with the survival data from a primary biliary cirrhosis study, and its finite sample properties are investigated via an extensive simulation\u00a0study.<\/jats:p>","DOI":"10.1111\/biom.13237","type":"journal-article","created":{"date-parts":[[2020,2,15]],"date-time":"2020-02-15T12:49:07Z","timestamp":1581770947000},"page":"1157-1166","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":109,"title":["On the empirical choice of the time window for restricted mean survival time"],"prefix":"10.1093","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5893-0169","authenticated-orcid":false,"given":"Lu","family":"Tian","sequence":"first","affiliation":[{"name":"Department of Biomedical Data Science Stanford University Stanford California"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4511-6165","authenticated-orcid":false,"given":"Hua","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences South China Normal University Guangzhou P. 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China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0622-8471","authenticated-orcid":false,"given":"Hajime","family":"Uno","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Computational Biology Dana\u2010Farber Cancer Institute Boston Massachusetts"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7698-8962","authenticated-orcid":false,"given":"Ying","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Biomedical Data Science Stanford University Stanford California"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3088-9328","authenticated-orcid":false,"given":"Bo","family":"Huang","sequence":"additional","affiliation":[{"name":"Pfizer Inc Groton Connecticut"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3218-1363","authenticated-orcid":false,"given":"Keaven M.","family":"Anderson","sequence":"additional","affiliation":[{"name":"Merck &amp; Co., Inc. North Wales Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8582-920X","authenticated-orcid":false,"given":"LJ","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Harvard University Boston Massachusetts"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,2,26]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Counting Processes and Survival Analysis","author":"Fleming T.R.","year":"2011"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346055"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.1846"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022172400014443"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1958.10501452"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478555"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531201"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.1878"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1001\/jamaoncol.2017.2797"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1470-2045(09)70284-0"},{"key":"e_1_2_8_12_1","first-page":"2409","article-title":"The use of restricted mean survival time to estimate the treatment effect in randomized clincial trials when the proportional hazards assumption is in doubt","volume":"30","author":"Royston P.","year":"2011","journal-title":"Journal of American Statistical Association"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176324528"},{"key":"e_1_2_8_14_1","volume-title":"Modeling Survival Data: Extending the Cox Model","author":"Therneau T.M.","year":"2013"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12770"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxt050"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1200\/JCO.2015.64.2488"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1200\/JCO.2014.55.2208"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.7326\/M14-1741"},{"key":"e_1_2_8_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8440"},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-7152(89)90113-2"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12384"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774512455464"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1998.10473722"}],"container-title":["Biometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/biom.13237","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/biom.13237","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1111\/biom.13237","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/biom.13237","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T18:09:59Z","timestamp":1706292599000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biometrics\/article\/76\/4\/1157-1166\/7425683"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,26]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1111\/biom.13237"],"URL":"https:\/\/doi.org\/10.1111\/biom.13237","archive":["Portico"],"relation":{},"ISSN":["0006-341X","1541-0420"],"issn-type":[{"value":"0006-341X","type":"print"},{"value":"1541-0420","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,26]]},"assertion":[{"value":"2018-09-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-01-27","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-02-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}