[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123369-en":3,"doc-seo-123369-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123369,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data","When estimating heterogeneous treatment effects, missing outcome data can distort subgroup representation and weaken treatment effect learning. The article analyzes the impact of missing-at-random (MAR) outcome data on causal machine learning estimators for the conditional average treatment effect (CATE). It introduces two de-biased estimators, the mDR-learner and mEP-learner, that combine inverse probability of censoring weights with DR-learner and EP-learner structures. Theoretical results establish oracle efficiency under conditions, and simulations plus a GBSG2 breast cancer application demonstrate improved performance and practical implementation guidance.","Biometrics, 2025, 81(3), ujaf098  \n[https://doi.org/10.1093/biomtc/ujaf098](https://doi.org/10.1093/biomtc/ujaf098)[ ](https://doi.org/10.1093/biomtc/ujaf098)Biometric Methodology  \nCausal machine learning for heterogeneous treatment effects in the presence ofmissing outcome data  \nMatthew Pryce 1,*, Karla Diaz-Ordaz 2, Ruth H. Keogh 1, Stijn Vansteelandt 3  \n1Department of Medical Statistics, London School of Hygiene & Tropical Medicine, London WC1E 7HT, United Kingdom, 2Department of Statistical Science, University College London, London WC1E7HB, United Kingdom, 3Department of Applied Mathematics, Computer Science, and  \nStatistics, Ghent University, Ghent, 9000, Belgium  \n* Corresponding author: Matthew Pryce, Department of Medical Statistics, London School of Hygiene & Tropical Medicine, London, WC1E 7HT, United Kingdom  \n([matthew.pryce@lshtm.ac.uk](matthew.pryce@lshtm.ac.uk)).  \nABSTRACT  \nWhen estimating heterogeneous treatment effects, missing outcome data can complicate treatment effect estimation, causing certain subgroups of the population tobe poorly represented. In this work, we discuss this commonly overlooked problem and consider the impact that missing at random outcome data has on causal machine learning estimators for the conditional average treatment effect (CATE). We propose 2 de-biased machine learning estimators for the CATE, the mDR-learner, and mEP-learner, which address the issue of under-representation by integrating inverse probability of censoring weights into the DR-learner and EP-learner, respectively. We show that under reasonable conditions, these estimators are oracle efficient and illustrate their favorable performance through simulated data settings, comparing them to existing CATE estimators, including comparison to estimators that use common missing data techniques. We present an example of their application using the GBSG2 trial, exploring treatment effect heterogeneity when comparing hormonal therapies to non-hormonal therapies among breast cancer patients post surgery, and offer guidance on the decisions a practitioner must make when implementing these estimators.  \nKEYWORDS: causal machine learning; heterogeneous treatment effects; influence functions; missing outcome data.  \n1 INTRODUCTION  \nWhen evaluating the effect of an intervention, investigators are often interested in how the effect may vary within a target population. One approach used to explore treatment effect heterogeneity for a binary intervention is to estimate the conditional average treatment effect (CATE), defined as θ (x) = E [Y (1)|X = x] − E [Y (0)|X = x], where Y(0) and Y(1) are potential outcomes under the 2 levels of the treatment (Rubin, 2005) and X represents the individual (pre-treatment) characteristics in which heterogeneity is of interest.  \nCATEs can be used to explore treatment effect heterogeneity or to derive individualized treatment rules, aiding in the development ofprecision medicine (VanderWeele et al., 2019). Many estimatorsofthe CATE havebeen proposed, with the focus turning toward non-parametric estimators, using machine learning (ML) to estimate complex functions of high dimensional data (Künzel et al., 2019; Nie and Wager, 2021; Kennedy, 2023; van der Laan et al., 2024). Of these estimators, each requires that the training data be fully observed and no data be missing. In this paper, we relax this requirement and propose2 novel CATEestimators, themDR-learner and mEP-learner, which demonstrate how causal ML estimators can be constructed when outcome data is missing at random (MAR).  \nMAR outcome data occur frequently in practice, typically arising when individuals are lost to follow-up. When it occurs,  \nthe observed data may no longer represent the target population, and subgroups that have high levels of drop-out can be under-represented. This presents a challenge for existing nonparametric CATE estimators, which do not address this underrepresentation and are prone to producing biased estimat","cbCaitoEbxfwkKC4","https://ap.wps.com/l/cbCaitoEbxfwkKC4","pdf",1528927,1,11,"English","en",105,"# Abstract\n# Introduction\n## Setting\n# Background\n## Setting","[{\"question\":\"为什么缺失结局数据会影响异质性治疗效应的估计？\",\"answer\":\"缺失会导致目标人群在训练数据中的代表性下降，使具有较高失访率的子群体被低估，从而产生偏的CATE估计。\"},{\"question\":\"文中关注的缺失机制是什么？\",\"answer\":\"文中考虑missing at random（MAR）条件下的缺失结局数据，并分析其对因果机器学习估计器的影响。\"},{\"question\":\"mDR-learner 和 mEP-learner 的核心改进是什么？\",\"answer\":\"两种方法都通过将逆概率删失权重（IPCW）融入DR-learner或EP-learner结构来处理代表性不足问题，从而得到去偏的CATE估计器。\"}]","Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data | PDF",1785816155,28,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"causal-machine-learning-for-heterogeneous-treatment-effects-in-the-presence-of-missing-outcome-data","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/causal-machine-learning-for-heterogeneous-treatment-effects-in-the-presence-of-missing-outcome-data/123369/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"为什么缺失结局数据会影响异质性治疗效应的估计？","Question",{"text":75,"@type":76},"缺失会导致目标人群在训练数据中的代表性下降，使具有较高失访率的子群体被低估，从而产生偏的CATE估计。","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"文中关注的缺失机制是什么？",{"text":80,"@type":76},"文中考虑missing at random（MAR）条件下的缺失结局数据，并分析其对因果机器学习估计器的影响。",{"name":82,"@type":73,"acceptedAnswer":83},"mDR-learner 和 mEP-learner 的核心改进是什么？",{"text":84,"@type":76},"两种方法都通过将逆概率删失权重（IPCW）融入DR-learner或EP-learner结构来处理代表性不足问题，从而得到去偏的CATE估计器。","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]