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Objective. To provide step-by-step guidance and STATA and R code for using propensity score (PS) weighting to estimate moderation effects. Research Design. Tutorial illustrating the key steps for estimating and testing moderation using…

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

This paper investigates the theoretical foundation and develops analytical formulas for sample size and power calculations for causal inference with observational data. By analyzing the variance of an inverse probability weighting estimator…

Methodology · Statistics 2026-05-19 Bo Liu , Chengxin Yang , Fan Li

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

Propensity Score Matching (PSM) stands as a widely embraced method in comparative effectiveness research. PSM crafts matched datasets, mimicking some attributes of randomized designs, from observational data. In a valid PSM design where all…

Methodology · Statistics 2024-11-15 Fei Wan

Propensity score methods are increasingly being used to reduce estimation bias of treatment effects for observational studies. Previous research has shown that propensity score methods consistently estimate the marginal hazard ratio for…

Methodology · Statistics 2019-11-19 Haodi Liang , Cecilia Cotton

In estimating the average treatment effect in observational studies, the influence of confounders should be appropriately addressed. To this end, the propensity score is widely used. If the propensity scores are known for all the subjects,…

Methodology · Statistics 2023-12-08 Chengyao Tang , Yi Zhou , Ao Huang , Satoshi Hattori

We propose a Bayesian propensity score-augmented latent factor model for causal inference with time-series cross-sectional data. The framework explicitly models the treatment assignment mechanism by incorporating latent factor loadings,…

Methodology · Statistics 2026-03-27 Licheng Liu

Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…

Methodology · Statistics 2022-08-23 Mark Tygert

Scholars frequently use covariate balance tests to test the validity of natural experiments and related designs. Unfortunately, when measured covariates are unrelated to potential outcomes, balance is uninformative about key identification…

Methodology · Statistics 2025-10-15 Clara Bicalho , Adam Bouyamourn , Thad Dunning

We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work,…

Methodology · Statistics 2024-04-12 Yuhao Wang , Rajen D. Shah

There is growing interest in a hybrid control design in which a randomized controlled trial is augmented with an external control arm from a previous trial or real world data. Existing methods for analyzing hybrid control studies include…

Methodology · Statistics 2025-01-30 Zhiwei Zhang , Jialuo Liu , Wei Liu

We introduce inference methods for score decompositions, which partition scoring functions for predictive assessment into three interpretable components: miscalibration, discrimination, and uncertainty. Our estimation and inference relies…

Econometrics · Economics 2026-03-05 Timo Dimitriadis , Marius Puke

Propensity score matching (PSM) is a pseudo-experimental method that uses statistical techniques to construct an artificial control group by matching each treated unit with one or more untreated units of similar characteristics. To date,…

Statistics Theory · Mathematics 2022-05-27 Yukun Liu , Jing Qin

Propensity Score Matching (PSM) is an useful method to reduce the impact ofTreatment - Selection Bias in the estimation of causal effects in observational studies. After matching, the PSM significantly reduces the sample under…

Methodology · Statistics 2019-02-01 Daniel García Iglesias

Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect…

Methodology · Statistics 2020-08-14 Shuxi Zeng , Fan Li , Rui Wang , Fan Li

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…

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

Estimating average causal effect (ACE) is useful whenever we want to know the effect of an intervention on a given outcome. In the absence of a randomized experiment, many methods such as stratification and inverse propensity weighting have…

Machine Learning · Computer Science 2019-07-11 Rathin Desai , Amit Sharma

Many spatial phenomena exhibit treatment interference where treatments at one location may affect the response at other locations. Because interference violates the stable unit treatment value assumption, standard methods for causal…

Methodology · Statistics 2020-07-02 Andrew Giffin , Brian Reich , Shu Yang , Ana Rappold