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1. An Alternative Robust Estimator of Average Treatment Effect in Causal Inference

   https://doi.org/10.1111/biom.12859  

   Liu, Jianxuan; Ma, Yanyuan; Wang, Lan (February 2018, Biometrics)

   Summary The problem of estimating the average treatment effects is important when evaluating the effectiveness of medical treatments or social intervention policies. Most of the existing methods for estimating the average treatment effect rely on some parametric assumptions about the propensity score model or the outcome regression model one way or the other. In reality, both models are prone to misspecification, which can have undue influence on the estimated average treatment effect. We propose an alternative robust approach to estimating the average treatment effect based on observational data in the challenging situation when neither a plausible parametric outcome model nor a reliable parametric propensity score model is available. Our estimator can be considered as a robust extension of the popular class of propensity score weighted estimators. This approach has the advantage of being robust, flexible, data adaptive, and it can handle many covariates simultaneously. Adopting a dimension reduction approach, we estimate the propensity score weights semiparametrically by using a non-parametric link function to relate the treatment assignment indicator to a low-dimensional structure of the covariates which are formed typically by several linear combinations of the covariates. We develop a class of consistent estimators for the average treatment effect and study their theoretical properties. We demonstrate the robust performance of the estimators on simulated data and a real data example of investigating the effect of maternal smoking on babies’ birth weight. 

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2. Covariate adjustment in randomized experiments with missing outcomes and covariates

   https://doi.org/10.1093/biomet/asae017  

   Zhao, Anqi; Ding, Peng; Li, Fan (March 2024, Biometrika)

   Summary Covariate adjustment can improve precision in analysing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis. When some outcomes are missing, we consider combining these two adjustment methods with the inverse probability of observation weighting for handling missing outcomes, and show that the equivalence between the two methods breaks down. Regression adjustment no longer ensures efficiency gain over unadjusted analysis unless the true outcome model is linear in covariates or the outcomes are missing completely at random. Propensity score weighting, in contrast, still guarantees efficiency over unadjusted analysis, and including more covariates in adjustment never harms asymptotic efficiency. Moreover, we establish the value of using partially observed covariates to secure additional efficiency by the missingness indicator method, which imputes all missing covariates by zero and uses the union of the completed covariates and corresponding missingness indicators as the new, fully observed covariates. Based on these findings, we recommend using regression adjustment in combination with the missingness indicator method if the linear outcome model or missing-completely-at-random assumption is plausible and using propensity score weighting with the missingness indicator method otherwise. 

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3. STACKED ENSEMBLE LEARNING FOR PROPENSITY SCORE METHODS IN OBSERVATIONAL STUDIES

   https://doi.org/https://doi.org/10.5281/zenodo.5048425  

   Autenriech, M.; Levine, R.A.; Fan, J.; Guarcello, M. (June 2021, Journal of educational data mining)

   null (Ed.)

   Propensity score methods account for selection bias in observational studies. However, the consistency of the propensity score estimators strongly depends on a correct specification of the propensity score model. Logistic regression and, with increasing popularity, machine learning tools are used to estimate propensity scores. We introduce a stacked generalization ensemble learning approach to improve propensity score estimation by fitting a meta learner on the predictions of a suitable set of diverse base learners. We perform a comprehensive Monte Carlo simulation study, implementing a broad range of scenarios that mimic characteristics of typical data sets in educational studies. The population average treatment effect is estimated using the propensity score in Inverse Probability of Treatment Weighting. Our proposed stacked ensembles, especially using gradient boosting machines as a meta learner trained on a set of 12 base learner predictions, led to superior reduction of bias compared to the current state-of-the-art in propensity score estimation. Further, our simulations imply that commonly used balance measures (averaged standardized absolute mean differences) might be misleading as propensity score model selection criteria. We apply our proposed model - which we call GBM-Stack - to assess the population average treatment effect of a Supplemental Instruction (SI) program in an introductory psychology (PSY 101) course at San Diego State University. Our analysis provides evidence that moving the whole population to SI attendance would on average lead to 1.69 times higher odds to pass the PSY 101 class compared to not offering SI, with a 95% bootstrap confidence interval of (1.31, 2.20). 

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4. 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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5. Benchmarking Estimators for Natural Experiments: A Novel Dataset and a Doubly Robust Algorithm

   Witter, R Teal; Musco, Christopher (December 2024, Advances in Neural Information Processing Systems)

   Estimating the effect of treatments from natural experiments, where treatments are pre-assigned, is an important and well-studied problem. We introduce a novel natural experiment dataset obtained from an early childhood literacy nonprofit. Surprisingly, applying over 20 established estimators to the dataset produces inconsistent results in evaluating the nonprofits efficacy. To address this, we create a benchmark to evaluate estimator accuracy using synthetic outcomes, whose design was guided by domain experts. The benchmark extensively explores performance as real world conditions like sample size, treatment correlation, and propensity score accuracy vary. Based on our benchmark, we observe that the class of doubly robust treatment effect estimators, which are based on simple and intuitive regression adjustment, generally outperform other more complicated estimators by orders of magnitude. To better support our theoretical understanding of doubly robust estimators, we derive a closed form expression for the variance of any such estimator that uses dataset splitting to obtain an unbiased estimate. This expression motivates the design of a new doubly robust estimator that uses a novel loss function when fitting functions for regression adjustment. We release the dataset and benchmark in a Python package; the package is built in a modular way to facilitate new datasets and estimators. https://github.com/rtealwitter/naturalexperiments. 

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