An official website of the United States government
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.
more »
« less
Soft calibration for selection bias problems under mixed-effects models
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.
more »
« less
- Award ID(s):
- 1931380
- PAR ID:
- 10491690
- Publisher / Repository:
- Biometrika
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 110
- Issue:
- 4
- ISSN:
- 0006-3444
- Page Range / eLocation ID:
- 897 to 911
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Complementary features of randomized controlled trials (RCTs) and observational studies (OSs) can be used jointly to estimate the average treatment effect of a target population. We propose a calibration weighting estimator that enforces the covariate balance between the RCT and OS, therefore improving the trial-based estimator's generalizability. Exploiting semiparametric efficiency theory, we propose a doubly robust augmented calibration weighting estimator that achieves the efficiency bound derived under the identification assumptions. A nonparametric sieve method is provided as an alternative to the parametric approach, which enables the robust approximation of the nuisance functions and data-adaptive selection of outcome predictors for calibration. We establish asymptotic results and confirm the finite sample performances of the proposed estimators by simulation experiments and an application on the estimation of the treatment effect of adjuvant chemotherapy for early-stage non-small-cell lung patients after surgery.more » « less
-
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.more » « less
-
In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based U-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits.more » « less
-
Abstract We provide a novel characterization of augmented balancing weights, also known as automatic debiased machine learning. These popular doubly robust estimators combine outcome modelling with balancing weights—weights that achieve covariate balance directly instead of estimating and inverting the propensity score. When the outcome and weighting models are both linear in some (possibly infinite) basis, we show that the augmented estimator is equivalent to a single linear model with coefficients that combine those of the original outcome model with those from unpenalized ordinary least-squares (OLS). Under certain choices of regularization parameters, the augmented estimator in fact collapses to the OLS estimator alone. We then extend these results to specific outcome and weighting models. We first show that the augmented estimator that uses (kernel) ridge regression for both outcome and weighting models is equivalent to a single, undersmoothed (kernel) ridge regression—implying a novel analysis of undersmoothing. When the weighting model is instead lasso-penalized, we demonstrate a familiar ‘double selection’ property. Our framework opens the black box on this increasingly popular class of estimators, bridges the gap between existing results on the semiparametric efficiency of undersmoothed and doubly robust estimators, and provides new insights into the performance of augmented balancing weights.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/biomet/asad016
