[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-201890-105":59,"doc-detail-201890-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","estimating-weighted-quantile-treatment-effects-with-missing-outcome-data-by-double-sampling","Estimating Weighted Quantile Treatment Effects with Missing Outcome Data by Double Sampling","","Causal weighted quantile treatment effects (WQTEs) extend mean-based causal comparisons to characterize treatment impacts at the tails of the counterfactual outcome distribution. Existing causal WQTE methods rely on complete data for all relevant factors, a condition often violated in practice, especially when using observational sources such as electronic health records and disease registries where outcomes may be missing not at random (MNAR). The paper develops a double-sampling approach, proposes an inverse-probability weighted estimator, derives asymptotic properties for pointwise and uniform quantile inference, and validates performance via simulation and an EHR bariatric surgery example.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/estimating-weighted-quantile-treatment-effects-with-missing-outcome-data-by-double-sampling/201890/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/estimating-weighted-quantile-treatment-effects-with-missing-outcome-data-by-double-sampling/201890.png","ImageObject",300,407,{"name":92,"@type":93},"Levi","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does the paper address in estimating causal weighted quantile treatment effects?","Question",{"text":113,"@type":114},"It addresses bias when estimating causal WQTEs using data with missing outcomes, particularly under missing-not-at-random (MNAR) mechanisms.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the proposed double-sampling method work conceptually?",{"text":118,"@type":114},"It ascertains the otherwise missing data for a sub-sample of study units, and uses these additional observations to reduce MNAR-related bias in WQTE estimation.",{"name":120,"@type":111,"acceptedAnswer":121},"What methods and results does the paper provide for inference?",{"text":122,"@type":114},"It introduces a novel inverse-probability weighted estimator, derives asymptotic properties for pointwise and uniform inference across quantiles, and develops a bootstrap procedure to support practical inference.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},201890,1788539865,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":41,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},7971461740909,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","arXiv :2310 .09239v3 [ stat .ME] 14 Mar 2025  \nBiometrics 64, 1–21 DOI: 10.1111/j.1541-0420.2005.00454.x  \nDecember 2008  \nEstimating weighted quantile treatment e􀀋ects with missing outcome data by  \ndouble sampling  \nShuo Sun1 ,􀀃 , Sebastien Haneuse1 , Alexander W. Levis2 , Catherine Lee3 , David E Arterburn4 , Heidi Fischer5 , Susan Shortreed4 ,6 , and Rajarshi Mukherjee 1  \n1 Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA  \n2 Department of Statistics & Data Science, Carnegie Mellon University, Pittsburgh, PA, USA  \n3 Division of Research, Kaiser Permanente Northern California, Oakland, CA, USA  \n4 Health Research Institute, Kaiser Permanente Washington, Seattle, WA, USA  \n5 Department of Research and Evaluation, Kaiser Permanente Southern California, Pasadena, CA, USA  \n6 Department of Biostatistics, University of Washington, Seattle, WA  \n*email: [shuosun@hsph.harvard.edu](shuosun@hsph.harvard.edu)  \nSummary: Causal weighted quantile treatment e􀀋ects (WQTEs) complement standard mean-focused causal contrasts when interest lies at the tails of the counterfactual distribution. However, existing methods for estimating and inferring causal WQTEs assume complete data on all relevant factors, which is often not the case in practice, particularly when the data are not collected for research purposes, such as electronic health records (EHRs) and disease registries. Furthermore, these data may be particularly susceptible to the outcome data being missing-notat-random (MNAR) . This paper proposes to use double-sampling, through which the otherwise missing data are ascertained on a sub-sample of study units, as a strategy to mitigate bias due to MNAR data in estimating causal WQTEs. With the additional data, we present identifying conditions that do not require missingness assumptions in the original data. We then propose a novel inverse-probability weighted estimator and derive its asymptotic properties, both pointwise at speci􀀌c quantiles and uniformly across quantiles over some compact subset of (0, 1), allowing the propensity score and double-sampling probabilities to be estimated. For practical inference, we develop a bootstrap method that can be used for both pointwise and uniform inference. A simulation study is conducted to examine the 􀀌nite sample performance of the proposed estimators. We illustrate the proposed method using EHR data examining the relative e􀀋ects of two bariatric surgery procedures on BMI loss three years post-surgery.  \nKey words: Bootstrap, Causal inference, Heterogeneous treatment e􀀋ect, Missing not at random, Quantile regression process, Uniform inference.  \nThis paper has been submitted for consideration for publication in Biometrics  \nQuantile treatment e􀀋ects with missing data 1  \n1. Introduction  \nModern causal inference conceptualizes causation via a comparison of counterfactuals across interventions or treatment strategies (Hern􀀓an and Robins, 2020) . As causation for individuals cannot be directly observed, analysis typically focuses on contrasts of some summary statistic of the treatment-speci􀀌c counterfactual distributions. The most common contrast, arguably, is the average treatment e􀀋ect (ATE), although related contrasts have been considered including the ATE on the treated (e.g., Imbens, 2004), the survivor ATE (e.g., Tchetgen Tchetgen, 2014), and average e􀀋ects of modi􀀌ed treatment policies (e.g. , Mu˜noz and van der Laan, 2012; Haneuse and Rotnitzky, 2013) . That each of these contrasts focuses on the mean of the counterfactual distribution, in one way or another, is natural since the mean is standard measure of centrality. In some settings, however, particularly when lowprobability but high-impact outcomes are anticipated, understanding the causal e􀀋ect of a given treatment beyond the ‘center’, including at the tails of the counterfactual distributions, may be more relevant to decision-making (Sun et al., 2021; Meyerson et al., 2023) . In such setti","cbCaitKaUWP6IOtD","https://ap.wps.com/l/cbCaitKaUWP6IOtD","pdf",480675,"English","# Introduction\n## Motivation and background\n## Missing data problem and assumptions\n## Estimation strategy for causal QTEs\n## Double-sampling and inverse-probability weighting\n## Inference methods and bootstrap\n## Simulation study and data application","[{\"question\":\"What problem does the paper address in estimating causal weighted quantile treatment effects?\",\"answer\":\"It addresses bias when estimating causal WQTEs using data with missing outcomes, particularly under missing-not-at-random (MNAR) mechanisms.\"},{\"question\":\"How does the proposed double-sampling method work conceptually?\",\"answer\":\"It ascertains the otherwise missing data for a sub-sample of study units, and uses these additional observations to reduce MNAR-related bias in WQTE estimation.\"},{\"question\":\"What methods and results does the paper provide for inference?\",\"answer\":\"It introduces a novel inverse-probability weighted estimator, derives asymptotic properties for pointwise and uniform inference across quantiles, and develops a bootstrap procedure to support practical inference.\"}]","Estimating Weighted Quantile Treatment Effects with Missing Outcome Data by Double Sampling | PDF",76]