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The standard inverse probability weighting method under the model hinges on a propensity score model for the treatment assignment and a censoring model that incorporates both the treatment and the covariates. In such settings model misspecification can often occur, and the Cox regression model\u2019s non-collapsibility has historically posed challenges when striving to guard against model misspecification through augmentation. We introduce a novel joint augmentation to the martingale-based full-data estimating functions and develop rate double robustness, which allows the use of machine learning and nonparametric methods to overcome the challenges of non-collapsibility. We closely examine its theoretical properties to guarantee root-$ n $ inference for the estimand. The estimator extends naturally to estimating a time-average treatment effect when the proportional hazards assumption fails, and we show that it satisfies both the assumption-lean and the well-specification criteria in the context of a causal estimand for censoring survival data; that is, it is a functional of the potential outcome distributions only and does not depend on the treatment assignment mechanism, the covariate distribution or the censoring mechanism. The martingale-based augmentation approach is also applicable to many semiparametric failure time models. Finally, its application to a dataset provides insights into the impact of mid-life alcohol consumption on mortality in later life.<\/jats:p>","DOI":"10.1093\/biomet\/asae065","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T23:26:19Z","timestamp":1732058779000},"source":"Crossref","is-referenced-by-count":6,"title":["Doubly robust estimation under a possibly misspecified marginal structural Cox model"],"prefix":"10.1093","volume":"112","author":[{"given":"Jiyu","family":"Luo","sequence":"first","affiliation":[{"name":"Herbert Wertheim School of Public Health, University of California , San Diego, 9500 Gilman Drive, La Jolla , California 92093,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denise","family":"Rava","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California , San Diego, 9500 Gilman Drive, La Jolla , California 92093,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8974-6807","authenticated-orcid":false,"given":"Jelena","family":"Bradic","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California , San Diego, 9500 Gilman Drive, La Jolla , California 92093,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2822-0561","authenticated-orcid":false,"given":"Ronghui","family":"Xu","sequence":"additional","affiliation":[{"name":"Herbert Wertheim School of Public Health, University of California , San Diego, 9500 Gilman Drive, La Jolla , California 92093,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2024,11,22]]},"reference":[{"key":"2025112120015840800_asae065-B1","first-page":"153","article-title":"Non- and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process","volume":"18","author":"Andersen","year":"1991","journal-title":"Scand. 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