{"id":345,"date":"2026-06-08T10:30:39","date_gmt":"2026-06-08T08:30:39","guid":{"rendered":"https:\/\/ideas.stat.unipd.it\/?page_id=345"},"modified":"2026-07-20T11:19:24","modified_gmt":"2026-07-20T09:19:24","slug":"causal-inference","status":"publish","type":"page","link":"https:\/\/ideas.stat.unipd.it\/index.php\/publications\/causal-inference\/","title":{"rendered":"Causal Inference"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"345\" class=\"elementor elementor-345\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2324aa1 e-flex e-con-boxed e-con e-parent\" data-id=\"2324aa1\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-09153a5 elementor-widget elementor-widget-html\" data-id=\"09153a5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<style>\r\npa {\r\n    font-size: 18px;\r\n        text-align: justify;\r\n}\r\n\r\n@media (min-width: 1025px) {\r\n  .mio-spazio {\r\n    height: 40px;\r\n  }\r\n}\r\n\r\n<\/style>\r\n\r\n<section class=\"Research lines\">\r\n    \r\n    <div class=\"mio-spazio\"><\/div>\r\n    \r\n    \r\n    <h1>Publications on Causal Inference<\/h1>\r\n\r\n\r\n<\/section>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8bc3dda elementor-widget elementor-widget-html\" data-id=\"8bc3dda\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<style>\r\n\r\n.publication-list{\r\n    max-width:950px;\r\n    margin:40px auto;\r\n    font-family:Arial,sans-serif;\r\n}\r\n\r\n.publication{\r\n    border:1px solid #d9d9d9;\r\n    border-radius:10px;\r\n    margin-bottom:25px;\r\n    background:#fff;\r\n    overflow:hidden;\r\n    box-shadow:0 2px 8px rgba(0,0,0,.05);\r\n}\r\n\r\n.publication summary{\r\n    list-style:none;\r\n    cursor:pointer;\r\n    padding:22px 25px 0;\r\n}\r\n\r\n.publication summary::-webkit-details-marker{\r\n    display:none;\r\n}\r\n\r\n.pub-title{\r\n    font-size:22px;\r\n    font-weight:700;\r\n    margin-bottom:10px;\r\n    color:#222;\r\n}\r\n\r\n.pub-authors{\r\n    font-size:17px;\r\n    color:#555;\r\n    margin-bottom:10px;\r\n}\r\n\r\n.pub-journal{\r\n    font-size:15px;\r\n    color:#777;\r\n    margin-bottom:18px;\r\n}\r\n\r\n.pub-toolbar{\r\n    display:flex;\r\n    justify-content:space-between;\r\n    align-items:center;\r\n    flex-wrap:wrap;\r\n    border-top:1px solid #ececec;\r\n    margin-left:-25px;\r\n    margin-right:-25px;\r\n    padding:14px 25px;\r\n}\r\n\r\n.pub-links{\r\n    display:flex;\r\n    gap:18px;\r\n    flex-wrap:wrap;\r\n}\r\n\r\n.pub-links a{\r\n    text-decoration:none;\r\n    color:#444;\r\n    font-size:15px;\r\n}\r\n\r\n.pub-type{\r\n    font-size:13px;\r\n    font-weight:600;\r\n    color:#666;\r\n    text-transform:uppercase;\r\n    letter-spacing:.6px;\r\n    margin-bottom:8px;\r\n}\r\n\r\n.pub-links a:hover{\r\n    color:#0056b3;\r\n}\r\n\r\n.right-tools{\r\n    display:flex;\r\n    align-items:center;\r\n    gap:12px;\r\n}\r\n\r\n.bibtex-btn{\r\n    border:1px solid #d6d6d6;\r\n    background:white;\r\n    padding:8px 14px;\r\n    border-radius:8px;\r\n    cursor:pointer;\r\n    transition:.2s;\r\n}\r\n\r\n.bibtex-btn:hover{\r\n    background:#f3f3f3;\r\n}\r\n\r\n.arrow{\r\n    font-size:20px;\r\n    transition:.3s;\r\n}\r\n\r\n.publication[open] .arrow{\r\n    transform:rotate(180deg);\r\n}\r\n\r\n.abstract{\r\n    border-top:1px solid #ececec;\r\n    padding:25px;\r\n    background:#fafafa;\r\n}\r\n\r\n.abstract h4{\r\n    margin-top:0;\r\n}\r\n\r\n.abstract p{\r\n    line-height:1.7;\r\n    text-align:justify;\r\n}\r\n\r\n@media(max-width:768px){\r\n\r\n.pub-toolbar{\r\n    flex-direction:column;\r\n    align-items:flex-start;\r\n    gap:15px;\r\n}\r\n\r\n.right-tools{\r\n    width:100%;\r\n    justify-content:space-between;\r\n}\r\n\r\n}\r\n\r\n<\/style>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n<div class=\"publication-list\">\r\n\r\n<details class=\"publication\">\r\n\r\n<summary>\r\n    \r\n    <div class=\"pub-type\"> Scientific article <\/div>\r\n\r\n<div class=\"pub-title\">\r\nMatching on poset\u2010based average rank for multiple treatments to compare many unbalanced groups\r\n<\/div>\r\n\r\n<div class=\"pub-authors\">\r\nMargherita Silan, Giovanna Boccuzzo, Bruno Arpino\r\n<\/div>\r\n\r\n<div class=\"pub-journal\">\r\nStatistics in Medicine \u2022 2021 \u2022 Vol.40(28), pp. 6443-6458\r\n<\/div>\r\n\r\n<div class=\"pub-toolbar\">\r\n\r\n<div class=\"pub-links\">\r\n\r\n<a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/full\/10.1002\/sim.9192\" target=\"_blank\">\r\n\ud83d\udd17 URL\r\n<\/a>\r\n\r\n<a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/epdf\/10.1002\/sim.9192\" target=\"_blank\">\r\n\ud83d\udcdd PDF\r\n<\/a>\r\n\r\n<a href=\"https:\/\/scholar.google.com\/scholar?hl=it&as_sdt=0%2C5&q=Matching+on+poset%E2%80%90based+average+rank+for+multiple+treatments+to+compare+many+unbalanced+groups&btnG=\" target=\"_blank\">\r\n\ud83c\udf93 Scholar\r\n<\/a>\r\n\r\n<a>\r\n\ud83d\udcc4 DOI: 10.1002\/sim.9192\r\n<\/a>\r\n\r\n<\/div>\r\n\r\n<div class=\"right-tools\">\r\n\r\n<button class=\"bibtex-btn\" onclick=\"copyBibtex(event,'bib19')\">\r\n    \ud83d\udccb <span>Copy BibTeX<\/span>\r\n<\/button>\r\n\r\n<div class=\"arrow\">\r\n\u25bc\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/summary>\r\n\r\n<div class=\"abstract\">\r\n\r\n<h4>Abstract<\/h4>\r\n\r\n<p>\r\n\r\nIn this article, we propose an original matching procedure for multiple treatment frameworks based on partially ordered set theory (poset). In our proposal, called matching on poset-based average rank for multiple treatments (MARMoT), poset theory is used to summarize individuals' confounders and the relative average rank is used to balance confounders and match individuals in different treatment groups. This approach proves to be particularly useful for balancing confounders when the number of treatments considered is high. We apply our approach to the estimation of neighborhood effect on the fractures among older people in Turin (a city in northern Italy).\r\n<\/p>\r\n\r\n<\/div>\r\n\r\n<pre id=\"bib19\" style=\"display:none;\">\r\n@article{silan2021matching,\r\n  title={Matching on poset-based average rank for multiple treatments to compare many unbalanced groups},\r\n  author={Silan, Margherita and Boccuzzo, Giovanna and Arpino, Bruno},\r\n  journal={Statistics in Medicine},\r\n  volume={40},\r\n  number={28},\r\n  pages={6443--6458},\r\n  year={2021},\r\n  publisher={Wiley Online Library}\r\n}\r\n<\/pre>\r\n\r\n<\/details>\r\n\r\n<\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n<div class=\"publication-list\">\r\n\r\n<details class=\"publication\">\r\n\r\n<summary>\r\n    \r\n    <div class=\"pub-type\"> Scientific article <\/div>\r\n\r\n<div class=\"pub-title\">\r\nEvaluating inverse propensity score weighting in the presence of many treatments. An application to the estimation of the neighbourhood effect\r\n<\/div>\r\n\r\n<div class=\"pub-authors\">\r\nMargherita Silan, Bruno Arpino, Giovanna Boccuzzo\r\n<\/div>\r\n\r\n<div class=\"pub-journal\">\r\nJournal of Statistical Computation and Simulation \u2022 2021 \u2022 Vol.91(4), pp. 836-859\r\n<\/div>\r\n\r\n<div class=\"pub-toolbar\">\r\n\r\n<div class=\"pub-links\">\r\n\r\n<a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00949655.2020.1832092\" target=\"_blank\">\r\n\ud83d\udd17 URL\r\n<\/a>\r\n\r\n<a href=\"https:\/\/www.research.unipd.it\/bitstream\/11577\/3442418\/1\/working_paper_5_SilanArpinoBoccuzzo-1.pdf?utm_source=consensus\" target=\"_blank\">\r\n\ud83d\udcdd PDF\r\n<\/a>\r\n\r\n<a href=\"https:\/\/scholar.google.com\/scholar?hl=it&as_sdt=0%2C5&q=Evaluating+inverse+propensity+score+weighting+in+the+presence+of+many+treatments.+An+application+to+the+estimation+of+the+neighbourhood+effect&btnG=\" target=\"_blank\">\r\n\ud83c\udf93 Scholar\r\n<\/a>\r\n\r\n<a>\r\n\ud83d\udcc4 DOI: 10.1080\/00949655.2020.1832092\r\n<\/a>\r\n\r\n<\/div>\r\n\r\n<div class=\"right-tools\">\r\n\r\n<button class=\"bibtex-btn\" onclick=\"copyBibtex(event,'bib18')\">\r\n    \ud83d\udccb <span>Copy BibTeX<\/span>\r\n<\/button>\r\n\r\n<div class=\"arrow\">\r\n\u25bc\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/summary>\r\n\r\n<div class=\"abstract\">\r\n\r\n<h4>Abstract<\/h4>\r\n\r\n<p>\r\n\r\nIn this paper we consider the problem of estimating causal effects in a framework with many treatments through a simulation study. We engage in Monte Carlo simulations to evaluate the performance of inverse probability of treatment weighting (IPTW) with 10 treatments, estimating the propensity scores using Generalized Boosted Models. We assess the performance of IPTW under three different scenarios representing treatment allocations, and compare it with a simple parametric approach, i.e. logistic regression. IPTW's estimates are less biased, even though they exhibit a higher variance than those based on logistic regression. Moreover, we apply IPTW to the estimation of the neighbourhood effect on the probability of older people experiencing at least one fracture requiring hospitalization during the year 2002 by comparing 10 neighbourhoods in the city of Turin (Italy). Our paper demonstrates that IPTW can be successfully applied to the estimation of neighbourhood effects, and, more generally, to the estimation of causal effects in the presence of many treatments.\r\n<\/p>\r\n\r\n<\/div>\r\n\r\n<pre id=\"bib18\" style=\"display:none;\">\r\n@article{silan2021evaluating,\r\n  title={Evaluating inverse propensity score weighting in the presence of many treatments. An application to the estimation of the neighbourhood effect},\r\n  author={Silan, Margherita and Arpino, Bruno and Boccuzzo, Giovanna},\r\n  journal={Journal of Statistical Computation and Simulation},\r\n  volume={91},\r\n  number={4},\r\n  pages={836--859},\r\n  year={2021},\r\n  publisher={Taylor \\& Francis}\r\n}\r\n<\/pre>\r\n\r\n<\/details>\r\n\r\n<\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n<script>\r\n\r\nfunction copyBibtex(event,id){\r\n\r\nevent.preventDefault();\r\nevent.stopPropagation();\r\n\r\nconst testo=document.getElementById(id).textContent;\r\n\r\nnavigator.clipboard.writeText(testo);\r\n\r\nconst btn=event.target;\r\n\r\nconst old=btn.innerHTML;\r\n\r\nbtn.innerHTML=\"\u2713 Copied!\";\r\n\r\nsetTimeout(function(){\r\n\r\nbtn.innerHTML=old;\r\n\r\n},1500);\r\n\r\n}\r\n\r\n<\/script>\r\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Publications on Causal Inference Scientific article Matching on poset\u2010based average rank for multiple treatments to compare many unbalanced groups Margherita Silan, Giovanna Boccuzzo, Bruno Arpino<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":53,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-345","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/pages\/345","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/comments?post=345"}],"version-history":[{"count":4,"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/pages\/345\/revisions"}],"predecessor-version":[{"id":1378,"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/pages\/345\/revisions\/1378"}],"up":[{"embeddable":true,"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/pages\/53"}],"wp:attachment":[{"href":"https:\/\/ideas.stat.unipd.it\/index.php\/wp-json\/wp\/v2\/media?parent=345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}