{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T21:31:10Z","timestamp":1789594270444,"version":"build-2803163510"},"reference-count":32,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,11,23]],"date-time":"2016-11-23T00:00:00Z","timestamp":1479859200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2017,3]]},"abstract":"<jats:p>In follow\u2010up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left\u2010truncated and right\u2010censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum\u2010likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput\u2010wall distance event for patients with ankylosing spondylitis.<\/jats:p>","DOI":"10.1002\/bimj.201500267","type":"journal-article","created":{"date-parts":[[2016,11,23]],"date-time":"2016-11-23T07:58:41Z","timestamp":1479887921000},"page":"270-290","source":"Crossref","is-referenced-by-count":12,"title":["A semiparametric mixture cure survival model for left\u2010truncated and right\u2010censored data"],"prefix":"10.1002","volume":"59","author":[{"given":"Chyong\u2010Mei","family":"Chen","sequence":"first","affiliation":[{"name":"Institute of Public Health School of Medicine, National Yang\u2010Ming University Taipei City Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pao\u2010Sheng","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Statistics Tunghai University Taichung City Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James Cheng\u2010Chung","family":"Wei","sequence":"additional","affiliation":[{"name":"Division of Allergy, Immunology and Rheumatology Department of Medicine, Chung Shan Medical University Hospital Taichung City Taiwan"},{"name":"Division of Allergy Immunology and Rheumatology, Chung Shan Medical University Hospital Taichung City Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lichi","family":"Lin","sequence":"additional","affiliation":[{"name":"Division of Allergy Immunology and Rheumatology, Chung Shan Medical University Hospital Taichung City Taiwan"},{"name":"Department of Statistics Oklahoma State University Stillwater OK 74074 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2016,11,23]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4348-9"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780020223"},{"key":"e_1_2_8_4_1","unstructured":"Chen C. 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