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In cancer research, a patient's lifespan may dramatically change when a covariate exceeds a threshold. Accurately detecting and estimating this change\u2010point is crucial for predicting the patient's life expectancy and preventing diseases. To address these challenges, we investigate the additive mean residual life model with an unknown change\u2010point in the continuous covariate. The martingale\u2010based smoothed estimating equations are used to estimate the baseline mean residual life function, regression parameters, and the unknown change\u2010point. Furthermore, we establish the large sample properties of the estimator under mild conditions, and propose a maximal Wald test statistic to test the existence of the change\u2010point. Finally, we assess the finite sample performance of our proposed method through extensive simulation studies and apply it to two real data examples from studies on stomach cancer and primary biliary cirrhosis. Supplementary materials for this article are available online.<\/jats:p>","DOI":"10.1002\/sim.70133","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T05:45:44Z","timestamp":1747979144000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Estimation and Inference for the Additive Mean Residual Life Model With Change Point in the Continuous Covariate"],"prefix":"10.1002","volume":"44","author":[{"given":"Yun","family":"Lin","sequence":"first","affiliation":[{"name":"School of Statistics University of International Business and Economics  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoran","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Statistics University of International Business and Economics  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4667-3000","authenticated-orcid":false,"given":"Fangfang","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Statistics University of International Business and Economics  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,5,22]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1973.5216045"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(88)90148-0"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1081\/STA-120024471"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/62.3.585"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/73.1.13"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/77.2.409"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1994.tb01994.x"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.1.19"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/93.2.303"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000000870"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0130"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asr065"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1136\/gut.20.2.137"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1051027876"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.5964"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.8491"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jimonfin.2012.07.004"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2020.109231"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00124"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12623"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280220959118"},{"issue":"1","key":"e_1_2_11_23_1","first-page":"111","article-title":"Threshold Estimation in Proportional Mean Residual Life Model","volume":"34","author":"Wang B.","year":"2024","journal-title":"Statistica Sinica"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001244"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2017.07.005"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.1.149"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7837"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9827"},{"key":"e_1_2_11_29_1","first-page":"625","volume-title":"Counting Processes and Survival Analysis","author":"Fleming T. 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