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Due to the properties of Brownian motion, a theoretical derivation of the highest confidence density region cannot be obtained in closed form. Instead, we provide confidence bands derived from a related optimization problem with local time processes. These bands can be applied to the one-sample problem regarding both cumulative hazard and survival functions. In addition, we present a solution to the two-sample problem for testing differences in cumulative hazard functions. The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies. The proposed bands are applied to clinical trial data to assess survival times for primary biliary cirrhosis patients treated with D-penicillamine.<\/jats:p>","DOI":"10.1007\/s10985-021-09522-8","type":"journal-article","created":{"date-parts":[[2021,4,13]],"date-time":"2021-04-13T13:26:22Z","timestamp":1618320382000},"page":"481-498","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["OptBand: optimization-based confidence bands for functions to characterize time-to-event distributions"],"prefix":"10.1007","volume":"27","author":[{"given":"T.","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7057-0832","authenticated-orcid":false,"given":"S.","family":"Tracy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Uno","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,13]]},"reference":[{"issue":"3","key":"9522_CR1","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1093\/biomet\/asz016","volume":"106","author":"Y Cui","year":"2019","unstructured":"Cui Y, Hannig J (2019a) Nonparametric generalized fiducial inference for survival functions under censoring. 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