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1. Propensity Score Weighting for Causal Inference with Clustered Data

   https://doi.org/10.1515/jci-2017-0027  

   Yang, Shu (September 2018, Journal of Causal Inference)

   Abstract Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-level covariates that are related to both the treatment assignment and outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a calibration technique for propensity score estimation under the latent ignorable treatment assignment mechanism, i. e., the treatment-outcome relationship is unconfounded given the observed covariates and the latent cluster-specific confounders. We impose novel balance constraints which imply exact balance of the observed confounders and the unobserved cluster-level confounders between the treatment groups. We show that the proposed calibrated propensity score weighting estimator is doubly robust in that it is consistent for the average treatment effect if either the propensity score model is correctly specified or the outcome follows a linear mixed effects model. Moreover, the proposed weighting method can be combined with sampling weights for an integrated solution to handle confounding and sampling designs for causal inference with clustered survey data. In simulation studies, we show that the proposed estimator is superior to other competitors. We estimate the effect of School Body Mass Index Screening on prevalence of overweight and obesity for elementary schools in Pennsylvania. 

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2. Soft calibration for selection bias problems under mixed-effects models

   https://doi.org/10.1093/biomet/asad016  

   Gao, Chenyin; Yang, Shu; Kim, Jae Kwang (March 2023, Biometrika)

   Abstract Calibration weighting has been widely used to correct selection biases in nonprobability sampling, missing data and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights. However, hard calibration can produce enormous weights when an exact calibration is enforced on a large set of extraneous covariates. This article proposes a soft calibration scheme, where the outcome and the selection indicator follow mixed-effect models. The scheme imposes an exact calibration on the fixed effects and an approximate calibration on the random effects. On the one hand, our soft calibration has an intrinsic connection with best linear unbiased prediction, which results in a more efficient estimation compared to hard calibration. On the other hand, soft calibration weighting estimation can be envisioned as penalized propensity score weight estimation, with the penalty term motivated by the mixed-effect structure. The asymptotic distribution and a valid variance estimator are derived for soft calibration. We demonstrate the superiority of the proposed estimator over other competitors in simulation studies and using a real-world data application on the effect of BMI screening on childhood obesity. 

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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. 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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5. The LOOP Estimator: Adjusting for Covariates in Randomized Experiments

   https://doi.org/10.1177/0193841X18808003  

   Wu, Edward; Gagnon-Bartsch, Johann_A (November 2018, Evaluation Review)

   Background:When conducting a randomized controlled trial, it is common to specify in advance the statistical analyses that will be used to analyze the data. Typically, these analyses will involve adjusting for small imbalances in baseline covariates. However, this poses a dilemma, as adjusting for too many covariates can hurt precision more than it helps, and it is often unclear which covariates are predictive of outcome prior to conducting the experiment. Objectives:This article aims to produce a covariate adjustment method that allows for automatic variable selection, so that practitioners need not commit to any specific set of covariates prior to seeing the data. Results:In this article, we propose the “leave-one-out potential outcomes” estimator. We leave out each observation and then impute that observation’s treatment and control potential outcomes using a prediction algorithm such as a random forest. In addition to allowing for automatic variable selection, this estimator is unbiased under the Neyman–Rubin model, generally performs at least as well as the unadjusted estimator, and the experimental randomization largely justifies the statistical assumptions made. 

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