{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T16:08:52Z","timestamp":1750781332003,"version":"3.40.5"},"reference-count":28,"publisher":"Wiley","issue":"16","license":[{"start":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T00:00:00Z","timestamp":1618272000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2021,7,20]]},"abstract":"<jats:p>Time\u2010to\u2010event outcomes are common in clinical studies. For example, the time to a first major adverse cardiovascular event (MACE, defined as CVD death, nonfatal myocardial infarction, or stroke) is a commonly used outcome in cardiovascular outcome trials. Owing to the lengthy time frame and other factors, the high costs of conducting such studies has been identified as one of the major obstacles in conducting clinical trials in the United States. However, typical approaches for designing clinical trials with time\u2010to\u2010event outcomes do not consider study costs. For a given effect size (eg, hazard ratio), the power to detect differences between two groups is typically a function of the total number of events observed in the study. Therefore, the same level of power will be achieved based on various combinations of the total number of participants, length of enrollment and total follow\u2010up times, and group allocation probability. Herein, we provide a general framework for designing cost\u2010efficient studies comparing treatments with respect to continuous time\u2010to\u2010event outcomes. Among the various designs that achieve the desired level of power to detect a given effect size for a fixed type\u2010I error level, the optimal cost\u2010efficient design is the design that minimizes the expected total study cost. The method is general and can be used for Cox proportional hazards models or Aalen additive models, and under various recruitment and censoring assumptions. The proposed approach for designing cost\u2010efficient studies is illustrated for a Weibull time\u2010to\u2010event outcome with uniform recruitment and exponentially distributed censoring time. The case of an additive hazards model is also described. A Shiny web application implementation of the proposed methods is presented.<\/jats:p>","DOI":"10.1002\/sim.8992","type":"journal-article","created":{"date-parts":[[2021,4,14]],"date-time":"2021-04-14T08:19:14Z","timestamp":1618388354000},"page":"3682-3694","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Cost\u2010efficient clinical studies with continuous time survival outcomes"],"prefix":"10.1002","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3601-6712","authenticated-orcid":false,"given":"Grecio J.","family":"Sandoval","sequence":"first","affiliation":[{"name":"The Biostatistics Center, Department of Biostatistics and Bioinformatics The George Washington University  Rockville Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4944-7968","authenticated-orcid":false,"given":"Ionut","family":"Bebu","sequence":"additional","affiliation":[{"name":"The Biostatistics Center, Department of Biostatistics and Bioinformatics The George Washington University  Rockville Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9838-2841","authenticated-orcid":false,"given":"John M.","family":"Lachin","sequence":"additional","affiliation":[{"name":"The Biostatistics Center, Department of Biostatistics and Bioinformatics The George Washington University  Rockville Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,4,13]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-019-3900-8"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2019.09.009"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774518820060"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9681(71)90094-4"},{"issue":"1","key":"e_1_2_6_6_1","first-page":"15","article-title":"Planning the size and duration of a clinical trial studying the time to some critical event","volume":"27","author":"George SL","year":"1974","journal-title":"J Clin Epidemiol"},{"issue":"9","key":"e_1_2_6_7_1","first-page":"469","article-title":"Planning the duration of a comparative clinical trial with loss to follow\u2010up and a period of continued observation","volume":"34","author":"Rubinstein LV","year":"1981","journal-title":"J Clin Epidemiol"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531201"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780060204"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531593"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780110810"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/68.1.316"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.2.1.20"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.2307\/2529679"},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9681(83)90092-9"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9681(85)90099-2"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531541"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0197-2456(87)90045-6"},{"key":"e_1_2_6_19_1","doi-asserted-by":"publisher","DOI":"10.2337\/dc13-0356"},{"key":"e_1_2_6_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2012.11.006"},{"key":"e_1_2_6_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2013.02.005"},{"key":"e_1_2_6_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6569"},{"volume-title":"Modelling Survival Data in Medical Research","year":"2003","author":"Collett D","key":"e_1_2_6_23_1"},{"key":"e_1_2_6_24_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531021"},{"volume-title":"Numerical Optimization","year":"2006","author":"Nocedal J","key":"e_1_2_6_25_1"},{"key":"e_1_2_6_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780080803"},{"key":"e_1_2_6_27_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774515614542"},{"key":"e_1_2_6_28_1","doi-asserted-by":"publisher","DOI":"10.1137\/0916069"},{"key":"e_1_2_6_29_1","unstructured":"ChenX YinX. 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