{"id":27155,"date":"2025-02-07T19:56:48","date_gmt":"2025-02-07T18:56:48","guid":{"rendered":"https:\/\/www.irpet.it\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/"},"modified":"2025-02-17T19:15:17","modified_gmt":"2025-02-17T18:15:17","slug":"bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death","status":"publish","type":"post","link":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/","title":{"rendered":"Bayesian principal stratification with longitudinal data and truncation by death"},"content":{"rendered":"\n<p id=\"metaDataTitle\"><strong>Author:\u00a0<\/strong>Giulio Grossi, <strong>Marco Mariani<\/strong>, Alessandra Mattei, Fabrizia Mealli<\/p>\n\n<p><strong>Publication:\u00a0<\/strong>Econometrics and Statistics<\/p>\n\n<p><strong>Publisher:<\/strong>\u00a0Elsevier<\/p>\n\n<p><strong>Date:<\/strong>\u00a0Available online 6 February 2025<\/p>\n\n<p><a href=\"https:\/\/doi.org\/10.1016\/j.ecosta.2025.01.003\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/doi.org\/10.1016\/j.ecosta.2025.01.003<\/a><\/p>\n\n<h6 class=\"wp-block-heading\">Abstract<\/h6>\n\n<p>In causal studies, outcomes are often \u2018censored by death,\u2019 meaning they are not observed or defined for units that die. These studies typically focus on the stratum of\u2019always survivors\u2019 up to a single fixed time\u00a0s. An extension is proposed for the analysis of longitudinal studies where units may die at different times and outcomes observed and well-defined only up to the respective moment of death. A Bayesian longitudinal principal stratification approach is developed, where units are cross-classified based on their death status over time. This method focuses on causal effects for principal strata of units that would survive until time\u00a0s, regardless of treatment assignment, with these strata varying as a function of s. The approach provides insights into treatment effects by examining the distribution of baseline characteristics within each longitudinal principal stratum and the time trends of both stratum membership and survivor-average causal effects. The methodology is illustrated in a longitudinal observational study assessing the causal effects of a policy promoting start-ups on firms\u2019 survival and hiring decisions, assuming strong ignorability of treatment assignment, where firms\u2019 hiring decisions may be censored by death.<\/p>\n\n<h6 class=\"wp-block-heading\">Keywords<\/h6>\n\n<p>Non-ignorable censoring, Start-ups, Program evaluation, Causal inference<\/p>\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>By G. Grossi, M. Mariani, A. Mattei, F. Mealli<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1033],"tags":[1421,1419,1420],"staff":[985],"temi-pubblicazioni":[1006],"class_list":["post-27155","post","type-post","status-publish","format-standard","hentry","category-articoli-e-riviste-scientifiche","tag-causal-inference-en","tag-non-ignorable-censoring-en","tag-start-ups-en","staff-mariani-marco-en","temi-pubblicazioni-enterprise-and-production-sistems"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Bayesian principal stratification with longitudinal data and truncation by death - Irpet<\/title>\n<meta name=\"description\" content=\"Irpet Bayesian principal stratification with longitudinal data and truncation by death Scientific journal articles\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bayesian principal stratification with longitudinal data and truncation by death - Irpet\" \/>\n<meta property=\"og:description\" content=\"Irpet Bayesian principal stratification with longitudinal data and truncation by death Scientific journal articles\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\" \/>\n<meta property=\"og:site_name\" content=\"Irpet\" \/>\n<meta property=\"article:published_time\" content=\"2025-02-07T18:56:48+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-02-17T18:15:17+00:00\" \/>\n<meta name=\"author\" content=\"zangheri\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"zangheri\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\"},\"author\":{\"name\":\"zangheri\",\"@id\":\"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/cf5629686fc3257bec9f68301d0ad5e2\"},\"headline\":\"Bayesian principal stratification with longitudinal data and truncation by death\",\"datePublished\":\"2025-02-07T18:56:48+00:00\",\"dateModified\":\"2025-02-17T18:15:17+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\"},\"wordCount\":229,\"keywords\":[\"Causal inference\",\"Non-ignorable censoring\",\"Start-ups\"],\"articleSection\":[\"Scientific journal articles\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\",\"url\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\",\"name\":\"Bayesian principal stratification with longitudinal data and truncation by death - Irpet\",\"isPartOf\":{\"@id\":\"https:\/\/irpetwp.netseven.work\/#website\"},\"datePublished\":\"2025-02-07T18:56:48+00:00\",\"dateModified\":\"2025-02-17T18:15:17+00:00\",\"author\":{\"@id\":\"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/cf5629686fc3257bec9f68301d0ad5e2\"},\"description\":\"Irpet Bayesian principal stratification with longitudinal data and truncation by death Scientific journal articles\",\"breadcrumb\":{\"@id\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.irpet.it\/en\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bayesian principal stratification with longitudinal data and truncation by death\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/irpetwp.netseven.work\/#website\",\"url\":\"https:\/\/irpetwp.netseven.work\/\",\"name\":\"Irpet\",\"description\":\"Istituto Regionale Programmazione Economica Toscana\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/irpetwp.netseven.work\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/cf5629686fc3257bec9f68301d0ad5e2\",\"name\":\"zangheri\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/59fa50ff47af9b745c5dc13f1ed25a6e27692b953b37f2381e3ae108b0b21989?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/59fa50ff47af9b745c5dc13f1ed25a6e27692b953b37f2381e3ae108b0b21989?s=96&d=mm&r=g\",\"caption\":\"zangheri\"},\"url\":\"https:\/\/www.irpet.it\/en\/author\/zangheri\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Bayesian principal stratification with longitudinal data and truncation by death - Irpet","description":"Irpet Bayesian principal stratification with longitudinal data and truncation by death Scientific journal articles","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/","og_locale":"en_US","og_type":"article","og_title":"Bayesian principal stratification with longitudinal data and truncation by death - Irpet","og_description":"Irpet Bayesian principal stratification with longitudinal data and truncation by death Scientific journal articles","og_url":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/","og_site_name":"Irpet","article_published_time":"2025-02-07T18:56:48+00:00","article_modified_time":"2025-02-17T18:15:17+00:00","author":"zangheri","twitter_card":"summary_large_image","twitter_misc":{"Written by":"zangheri","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/#article","isPartOf":{"@id":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/"},"author":{"name":"zangheri","@id":"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/cf5629686fc3257bec9f68301d0ad5e2"},"headline":"Bayesian principal stratification with longitudinal data and truncation by death","datePublished":"2025-02-07T18:56:48+00:00","dateModified":"2025-02-17T18:15:17+00:00","mainEntityOfPage":{"@id":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/"},"wordCount":229,"keywords":["Causal inference","Non-ignorable censoring","Start-ups"],"articleSection":["Scientific journal articles"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/","url":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/","name":"Bayesian principal stratification with longitudinal data and truncation by death - Irpet","isPartOf":{"@id":"https:\/\/irpetwp.netseven.work\/#website"},"datePublished":"2025-02-07T18:56:48+00:00","dateModified":"2025-02-17T18:15:17+00:00","author":{"@id":"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/cf5629686fc3257bec9f68301d0ad5e2"},"description":"Irpet Bayesian principal stratification with longitudinal data and truncation by death Scientific journal articles","breadcrumb":{"@id":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.irpet.it\/en\/bayesian-principal-stratification-with-longitudinal-data-and-truncation-by-death\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.irpet.it\/en\/"},{"@type":"ListItem","position":2,"name":"Bayesian principal stratification with longitudinal data and truncation by death"}]},{"@type":"WebSite","@id":"https:\/\/irpetwp.netseven.work\/#website","url":"https:\/\/irpetwp.netseven.work\/","name":"Irpet","description":"Istituto Regionale Programmazione Economica Toscana","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/irpetwp.netseven.work\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/cf5629686fc3257bec9f68301d0ad5e2","name":"zangheri","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/irpetwp.netseven.work\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/59fa50ff47af9b745c5dc13f1ed25a6e27692b953b37f2381e3ae108b0b21989?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/59fa50ff47af9b745c5dc13f1ed25a6e27692b953b37f2381e3ae108b0b21989?s=96&d=mm&r=g","caption":"zangheri"},"url":"https:\/\/www.irpet.it\/en\/author\/zangheri\/"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/posts\/27155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/comments?post=27155"}],"version-history":[{"count":1,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/posts\/27155\/revisions"}],"predecessor-version":[{"id":27156,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/posts\/27155\/revisions\/27156"}],"wp:attachment":[{"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/media?parent=27155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/categories?post=27155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/tags?post=27155"},{"taxonomy":"staff","embeddable":true,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/staff?post=27155"},{"taxonomy":"temi-pubblicazioni","embeddable":true,"href":"https:\/\/www.irpet.it\/en\/wp-json\/wp\/v2\/temi-pubblicazioni?post=27155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}