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The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss…

Methodology · Statistics 2021-10-29 Eli Ben-Michael , Avi Feller , David A. Hirshberg , José R. Zubizarreta

Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type…

Methodology · Statistics 2021-09-14 Kangjie Zhou , Jinzhu Jia

In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are…

Methodology · Statistics 2017-01-17 Olli Saarela , Léo R. Belzile , David A. Stephens

Inferring the causal effect of a treatment on an outcome in an observational study requires adjusting for observed baseline confounders to avoid bias. However, adjusting for all observed baseline covariates, when only a subset are…

Methodology · Statistics 2021-02-04 Wen Wei Loh , Stijn Vansteelandt

Bayesian doubly robust (DR) causal inference faces a fundamental dilemma: joint modeling of outcome and propensity score suffers from the feedback problem where outcome information contaminates propensity score estimation, while two-step…

Methodology · Statistics 2026-01-05 Shunichiro Orihara , Tomotaka Momozaki , Shonosuke Sugasawa

With medical tests becoming increasingly available, concerns about over-testing and over-treatment dramatically increase. Hence, it is important to understand the influence of testing on treatment selection in general practice. Most…

Methodology · Statistics 2020-08-11 Yun Li , Irina Bondarenko , Michael R. Elliott , Timothy P. Hofer , Jeremy M. G. Taylor

For many kinds of interventions, such as a new advertisement, marketing intervention, or feature recommendation, it is important to target a specific subset of people for maximizing its benefits at minimum cost or potential harm. However, a…

Methodology · Statistics 2020-11-12 Yanbo Xu , Divyat Mahajan , Liz Manrao , Amit Sharma , Emre Kiciman

The growing availability of large health databases has expanded the use of observational studies for comparative effectiveness research. Unlike randomized trials, observational studies must adjust for systematic differences in patient…

Methodology · Statistics 2026-01-21 Haidong Lu , Fan Li , Laine E. Thomas , Fan Li

The average treatment effect (ATE), the mean difference in potential outcomes under treatment and control, is a canonical causal effect. Overlap, which says that all subjects have non-zero probability of either treatment status, is…

Methodology · Statistics 2026-05-14 Herbert P. Susmann , Alec McClean , Iván Díaz

Propensity score (PS) methods are widely used in observational studies to reduce confounding and estimate causal treatment effects. However, the validity of PS-based causal estimators depends heavily on correct model specification, and…

Estimating the joint effect of a multivariate, continuous exposure is crucial, particularly in environmental health where interest lies in simultaneously evaluating the impact of multiple environmental pollutants on health. We develop novel…

We introduce causal inference reasoning to cross-over trials, with a focus on Thorough QT (TQT) studies. For such trials, we propose different sets of assumptions and consider their impact on the modelling strategy and estimation procedure.…

Methodology · Statistics 2022-05-31 Jeppe Ekstrand Halkjær Madsen , Thomas Scheike , Christian Pipper

Estimating causal effects from observational data is challenging due to selection bias, which leads to imbalanced covariate distributions across treatment groups. Propensity score-based weighting methods are widely used to address this…

Machine Learning · Computer Science 2025-08-08 Ahmad Saeed Khan , Erik Schaffernicht , Johannes Andreas Stork

In this paper, we develop new methods for estimating average treatment effects in observational studies, focusing on settings with more than two treatment levels under unconfoundedness given pre-treatment variables. We emphasize…

Methodology · Statistics 2017-10-11 Shu Yang , Guido W. Imbens , Zhanglin Cui , Douglas Faries , Zbigniew Kadziola

In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for…

Methodology · Statistics 2022-02-21 Yaqian Zhu , Nandita Mitra , Jason Roy

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment…

Methodology · Statistics 2022-03-11 Steve Yadlowsky , Hongseok Namkoong , Sanjay Basu , John Duchi , Lu Tian

When constructing a model to estimate the causal effect of a treatment, it is necessary to control for other factors which may have confounding effects. Because the ignorability assumption is not testable, however, it is usually unclear…

Methodology · Statistics 2022-09-07 Spencer Woody , Carlos M. Carvalho , Jared S. Murray

In sequential causal inference, one estimates the causal net effect of treatment in treatment sequence on an outcome after last treatment in the presence of time-dependent covariates between treatments, improves the estimation by the…

Methodology · Statistics 2014-11-18 Li Yin , Xiaoqin Wang

A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…

Statistics Theory · Mathematics 2019-05-31 Debashis Ghosh , Efrén Cruz-Cortés

The finite sample variance of an inverse propensity weighted estimator is derived in the case of discrete control variables with finite support. The obtained expressions generally corroborate widely-cited asymptotic theory showing that…

Methodology · Statistics 2023-05-19 Andrew Herren , P. Richard Hahn