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Explore causal inference methods for analyzing recurrent events when terminal events are present in this mathematical research seminar. Learn about a comprehensive efficiency theory developed for causal inference in recurrent event data with terminal failure times, where the estimand is defined as a vector comprising both the expected number of recurrent events and the failure survival function evaluated along landmark times. Discover how this estimand can be identified under weaker conditions than conditionally independent censoring and examine the derivation of nonparametric efficient influence functions under general censoring and failure distributions without assuming absolute continuity. See practical application of these methods through a case study assessing the causal effect of air pollution exposure on cardiovascular disease-related hospitalization recurrence using Medicare data from Arizona, presented by Ashkan Ertefaie from the University of Pennsylvania as part of the Colloque des sciences mathématiques du Québec.