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They appear in many scientific problems, including non-compliance, truncation by death, mediation, and surrogate endpoint evaluation. Principal stratification is a strategy to address these challenges by adjusting for the potential values of the post-treatment variables, defined as the principal strata. It allows for characterizing treatment effect heterogeneity across principal strata and unveiling the mechanism of the treatment\u2019s impact on the outcome related to post-treatment variables. However, the existing literature has primarily focused on binary post-treatment variables, leaving the case with continuous post-treatment variables largely unexplored. This gap persists due to the complexity of infinitely many principal strata, which present challenges to both the identification and estimation of causal effects. We fill this gap by providing nonparametric identification and semiparametric estimation theory for principal stratification with continuous post-treatment variables. We propose to use working models to approximate the underlying causal effect surfaces and derive the efficient influence functions of the corresponding model parameters. Based on the theory, we construct doubly robust estimators and implement them in the R package continuousPCE.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf049","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T13:16:01Z","timestamp":1752585361000},"page":"239-260","source":"Crossref","is-referenced-by-count":2,"title":["Principal stratification with continuous post-treatment variables: nonparametric identification and semiparametric estimation"],"prefix":"10.1093","volume":"88","author":[{"given":"Sizhu","family":"Lu","sequence":"first","affiliation":[{"name":"Department of Statistics, University of California , Berkeley, CA 94720 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8571-0217","authenticated-orcid":false,"given":"Zhichao","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University , Guangzhou, Guangdong 510275 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2704-2353","authenticated-orcid":false,"given":"Peng","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California , Berkeley, CA 94720 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,7,31]]},"reference":[{"issue":"3","key":"2026021010562006600_qkaf049-B1","doi-asserted-by":"publisher","first-page":"779","DOI":"10.3982\/QE1494","article-title":"A unified framework for efficient estimation of general treatment models","volume":"12","author":"Ai","year":"2021","journal-title":"Quantitative Economics"},{"issue":"434","key":"2026021010562006600_qkaf049-B2","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1080\/01621459.1996.10476902","article-title":"Identification of causal effects using instrumental variables (with 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