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In causal inference, it is common to estimate the causal effect of a single treatment variable on an outcome. However, practitioners may also be interested in the effect of simultaneous interventions on multiple covariates of a fixed target…

Methodology · Statistics 2022-11-24 Jaime Roquero Gimenez , Dominik Rothenhäusler

This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the…

Econometrics · Economics 2018-08-20 Chunrong Ai , Oliver Linton , Kaiji Motegi , Zheng Zhang

Learning causal effects from observational data greatly benefits a variety of domains such as health care, education and sociology. For instance, one could estimate the impact of a new drug on specific individuals to assist the clinic plan…

Machine Learning · Computer Science 2021-05-19 Xin Du , Lei Sun , Wouter Duivesteijn , Alexander Nikolaev , Mykola Pechenizkiy

This paper deals with the problem of evaluating the causal effect using observational data in the presence of an unobserved exposure/ outcome variable, when cause-effect relationships between variables can be described as a directed acyclic…

Methodology · Statistics 2012-06-18 Manabu Kuroki , Zhihong Cai

Randomized controlled trials are considered the gold standard to evaluate the treatment effect (estimand) for efficacy and safety. According to the recent International Council on Harmonisation (ICH)-E9 addendum (R1), intercurrent events…

Methodology · Statistics 2021-11-24 Junxiang Luo , Stephen J. Ruberg , Yongming Qu

In settings where interference is present, direct effects are commonly defined as the average effect of a unit's treatment on their own outcome while fixing the treatment status or probability among interfering units, and spillover effects…

Methodology · Statistics 2025-06-10 Fei Fang , Edoardo M Airoldi , Laura Forastiere

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of…

Methodology · Statistics 2022-10-25 Fan Li , Peng Ding , Fabrizia Mealli

We address the estimation of conditional average treatment effects (CATEs) for structured treatments (e.g., graphs, images, texts). Given a weak condition on the effect, we propose the generalized Robinson decomposition, which (i) isolates…

Machine Learning · Computer Science 2021-10-29 Jean Kaddour , Yuchen Zhu , Qi Liu , Matt J. Kusner , Ricardo Silva

Selection bias is pervasive in observational studies. For example, large scale biobanks data can exhibit ``healthy volunteer bias'' when respondents are healthier and of higher socio-economic status than the population they are meant to…

Methodology · Statistics 2026-05-14 Yiwen Qiu , Filip Kovacevic , Shimeng Huang , Peter Spirtes , Francesco Locatello

When making treatment selection decisions, it is essential to include a causal effect estimation analysis to compare potential outcomes under different treatments or controls, assisting in optimal selection. However, merely estimating…

Machine Learning · Statistics 2024-10-08 Sherly Alfonso-Sánchez , Kristina P. Sendova , Cristián Bravo

Caliper matching is used to estimate causal effects of a binary treatment from observational data by comparing matched treated and control units. Units are matched when their propensity scores, the conditional probability of receiving…

Statistics Theory · Mathematics 2023-04-18 Máté Kormos , Stéphanie van der Pas , Aad van der Vaart

It is valuable for any decision maker to know the impact of decisions (treatments) on average and for subgroups. The causal machine learning literature has recently provided tools for estimating group average treatment effects (GATE) to…

Econometrics · Economics 2025-01-10 Nora Bearth , Michael Lechner

Conventional causal estimands, such as the average treatment effect (ATE), capture how the mean outcome in a population or subpopulation would change if all units were assigned to treatment versus control. Real-world policy changes,…

Methodology · Statistics 2025-12-12 Xiang Zhou , Aleksei Opacic

Causal inference is best understood using potential outcomes. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. The topic of this…

Statistics Theory · Mathematics 2007-06-13 Donald B. Rubin

Estimating causal effects in a target population with unmeasured confounders is challenging, especially when instrumental variables (IVs) are unavailable. However, IVs from auxiliary populations with similar problems can help infer causal…

Methodology · Statistics 2025-08-06 Wei Li , Jiapeng Liu , Peng Ding , Zhi Geng

Factorial experiments are ubiquitous in the social and biomedical sciences, but when units fail to comply with each assigned factors, identification and estimation of the average treatment effects become impossible without strong…

Methodology · Statistics 2025-08-06 Matthew Blackwell , Nicole E. Pashley

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

Estimating individualised treatment effect (ITE) -- that is the causal effect of a set of variables (also called exposures, treatments, actions, policies, or interventions), referred to as \textit{composite treatments}, on a set of outcome…

Machine Learning · Computer Science 2025-12-19 Vinod Kumar Chauhan , Lei Clifton , Gaurav Nigam , David A. Clifton

In the context of having an instrumental variable, the standard practice in causal inference begins by targeting an effect of interest and proceeds by formulating assumptions enabling its identification. We turn this around by adhering to…

Statistics Theory · Mathematics 2026-05-25 Carlos García Meixide , Mark J. van der Laan

Causal inference is to estimate the causal effect in a causal relationship when intervention is applied. Precisely, in a causal model with binary interventions, i.e., control and treatment, the causal effect is simply the difference between…

Machine Learning · Computer Science 2022-07-19 Zhenyu Lu , Yurong Cheng , Mingjun Zhong , George Stoian , Ye Yuan , Guoren Wang