Studies with staggered entry, in which individuals enroll at different calendar times, are ubiquitous in medicine and related disciplines. Because these studies usually have a fixed administrative end of follow-up, identification of the estimand of interest relies on assumptions about the right-censoring mechanism. The assumptions are often considered plausible only conditional on covariates, including the time an individual entered the study (E). Yet, censoring assumptions formulated conditional on E are ill-posed due to positivity violations. Here, we study the consequences of this issue for common procedures in causal survival analysis, such as those based on marginal structural models. We further give conditions for valid identification and introduce sensitivity analyses to assess practical implications. We illustrate our methodology through two case studies. The first builds on the seminal article by Hernán et al. (2000) on the effect of zidovudine treatment. The second reanalyzes a recent study on the effect of the mRNA vaccine in patients receiving immune checkpoint inhibitors.

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