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1. Bounds on Causal Effects and Application to High Dimensional Data

   A. Li and J. Pearl (March 2022, Proceedings of the Thirty-Sixth AAAI Conference on Artificial Intelligence (AAAI-22))

   Vasant Honavar and Matthijs Spaan (Ed.)

   This paper addresses the problem of estimating causal effects when adjustment variables in the back-door or front-door criterion are partially observed. For such scenarios, we derive bounds on the causal effects by solving two non-linear optimization problems, and demonstrate that the bounds are sufficient. Using this optimization method, we propose a framework for dimensionality reduction that allows one to trade bias for estimation power, and demonstrate its performance using simulation studies. 

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2. A Within-Group Approach to Ensemble Machine Learning Methods for Causal Inference in Multilevel Studies

   https://doi.org/10.3102/10769986231162096  

   Suk, Youmi (April 2023, Journal of Educational and Behavioral Statistics)

   Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level unmeasured confounding. We focus on one particular ML-based causal inference method based on the targeted maximum likelihood estimation (TMLE) with an ensemble learner called SuperLearner. Through our simulation studies, we observe that training TMLE within groups of similar clusters helps remove bias from cluster-level unmeasured confounders. Also, using within-group propensity scores estimated from fixed effects logistic regression increases the robustness of the proposed within-group TMLE method. Even if the propensity scores are partially misspecified, the within-group TMLE still produces robust ATE estimates due to double robustness with flexible modeling, unlike parametric-based inverse propensity weighting methods. We demonstrate our proposed methods and conduct sensitivity analyses against the number of groups and individual-level unmeasured confounding to evaluate the effect of taking an eighth-grade algebra course on math achievement in the Early Childhood Longitudinal Study. 

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3. Two‐step estimation in ratio‐of‐mediator‐probability weighted causal mediation analysis

   https://doi.org/10.1002/sim.7581  

   Bein, Edward; Deutsch, Jonah; Hong, Guanglei; Porter, Kristin E.; Qin, Xu; Yang, Cheng (January 2018, Statistics in Medicine)

   This study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score‐based weighting. Such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator. Ratio‐of‐mediator‐probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score‐based weighting. In step 1, a propensity score model is estimated. In step 2, the causal effects of interest are estimated using weights derived from the prior step's regression coefficient estimates. Statistical inferences obtained from this 2‐step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights. This study extends to ratio‐of‐mediator‐probability weighting analysis a solution to the 2‐step estimation problem by stacking the score functions from both steps. We derive the asymptotic variance‐covariance matrix for the indirect effect and direct effect 2‐step estimators, provide simulation results, and illustrate with an application study. Our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored. The standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation. We discuss broad implications of this approach for causal analysis involving propensity score‐based weighting. 

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4. Multisite causal mediation analysis in the presence of complex sample and survey designs and non-random nonresponse

   Qin, X.; Hong, G.; Deutsch, J.; & Bein, E. (January 2019, Journal of the Royal Statistical Society)

   This study provides a template for multisite causal mediation analysis using a comprehensive weighting-based analytic procedure that enhances external and internal validity. The template incorporates a sample weight to adjust for complex sample and survey designs, adopts an IPTW weight to adjust for differential treatment assignment probabilities, employs an estimated nonresponse weight to account for non-random nonresponse, and utilizes a propensity score-based weighting strategy to flexibly decompose not only the population average but also the between-site heterogeneity of the total program impact. Because the identification assumptions are not always warranted, a weighting-based balance checking procedure assesses the remaining overt bias, while a weighting-based sensitivity analysis further evaluates the potential bias related to omitted confounding or to propensity score model misspecification. We derive the asymptotic variance of the estimators for the causal effects that account for the sampling uncertainty in the estimated weights. The method is applied to a re-analysis of the data from the National Job Corps Study. 

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5. Analysis of regression discontinuity designs with censored data

   Cho, Youngjoo; Hu, Chen; Ghosh, Debashis (January 2021, Journal of statistical research University of Dacca Institute of Statistical Research and Training)

   In many medical and scientific settings, the choice of treatment or intervention may be de-termined by a covariate threshold. For example, elderly men may receive more thoroughdiagnosis if their prostate-specific antigen (PSA) level is high. In these cases, the causaltreatment effect is often of great interest, especially when there is a lack of evidence fromrandomized clinical trials. From the social science literature, a class of methods known asregression discontinuity (RD) designs can be used to estimate the treatment effect in thissituation. Under certain assumptions, such an estimand enjoys a causal interpretation. Weshow how to estimate causal effects under the regression discontinuity design for censoreddata. The proposed estimation procedure employs a class of censoring unbiased transfor-mations that includes inverse probability censored weighting and doubly robust transfor-mation schemes. Simulation studies are used to evaluate the finite-sample properties of theproposed estimator. We also illustrate the proposed method by evaluating the causal effectof PSA-dependent screening strategies 

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