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One challenge in analysing such data is that the observed residual survival times tend to be longer than those in the target population, since patients who die before experiencing the intermediate event are excluded from the cohort identified. We propose to model jointly the ordered bivariate survival data by using a copula model and appropriately adjusting for the sampling bias. We develop an estimating procedure to estimate simultaneously the parameters for the marginal survival functions and the association parameter in the copula model, and we use a two-stage expectation\u2013maximization algorithm. Using empirical process theory, we prove that the estimators have strong consistency and asymptotic normality. We conduct simulation studies to evaluate the finite sample performance of the method proposed. We apply the method to two cohort studies to evaluate the association between patient characteristics and residual survival.<\/jats:p>","DOI":"10.1111\/rssb.12308","type":"journal-article","created":{"date-parts":[[2019,1,7]],"date-time":"2019-01-07T04:35:07Z","timestamp":1546835707000},"page":"409-429","source":"Crossref","is-referenced-by-count":7,"title":["Semiparametric Model for Bivariate Survival Data Subject to Biased Sampling"],"prefix":"10.1093","volume":"81","author":[{"given":"Jin","family":"Piao","sequence":"first","affiliation":[{"name":"University of Southern California , Los Angeles , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Ning","sequence":"additional","affiliation":[{"name":"University of Texas MD Anderson Cancer Center , Houston , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Shen","sequence":"additional","affiliation":[{"name":"University of Texas MD Anderson Cancer Center , Houston , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,1,6]]},"reference":[{"key":"2023022012281505100_","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1200\/JCO.2011.41.0076","article-title":"Nomogram to predict the benefit of radiation for older patients with breast cancer treated with conservative surgery","volume":"30","author":"Albert","year":"2012","journal-title":"J. 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