augmented ipw estimation

This paper investigates the impact of covariate balancing on average treatment effect (ATE) and average treatment effect on the treated (ATT) estimation, and establishes the theoretical foundation for numerical equivalence among inverse probability weighting (IPW), augmented IPW (AIPW), and IPW-regression adjustment (IPWRA) estimators. We rigorously prove that when propensity scores are estimated via covariate balancing methods—such as inverse probability tilting (IPT) for ATE or covariate-balancing propensity score (CBPS) for ATT—the three estimators are algebraically identical, and their weights are automatically normalized. This equivalence unifies the theoretical frameworks of weighted and doubly robust estimation, substantially improving finite-sample stability and precision. Moreover, the result enables a novel analytical pathway for identifying the local average treatment effect (LATE) under unmeasured confounding, thereby advancing model robustness and computational consistency in causal inference.

This paper addresses unbiased estimation of the marginal counterfactual cumulative incidence function (CIF) in observational studies under competing risks. We propose a modified Nelson–Aalen estimator based on inverse probability weighting (IPW), incorporating estimated propensity scores. Our key contribution is the first rigorous asymptotic theory for such an adjusted estimator within the competing risks framework: we explicitly characterize the additional variability induced by propensity score estimation and prove its asymptotically negligible impact on final inference. Leveraging counting process theory and influence function analysis, we derive influence functions for both the counterfactual cumulative hazard and the CIF, establishing consistency and asymptotic normality of the estimator. Simulation studies and real-data analyses demonstrate low bias, robust performance across scenarios, and accurate standard error estimation. The proposed method thus provides a theoretically sound and practically viable tool for causal inference in competing risks settings.

To address the dual limitations of the Augmented Inverse Probability Weighting (AIPW) estimator—instability under extreme propensity scores (near 0 or 1) and the Propensity Score Matching (PSM) estimator—dependence on correct model specification and lack of semiparametric efficiency—this paper proposes the Augmented Matching Weighting (AMW) estimator. AMW innovatively replaces inverse-propensity weights with adaptive matching weights based on a non-fixed number of matches $K$, and introduces a cross-validation procedure guided by unbiasedness to select $K$. Theoretically, AMW achieves double robustness and semiparametric efficiency, and supports valid inference via the naïve bootstrap. Simulation and empirical studies demonstrate that AMW significantly outperforms both AIPW and PSM in stability under extreme propensity scores, yields more accurate variance estimation, and maintains computational simplicity.

This paper addresses the “weak paradox” of inverse probability weighting (IPW) estimators—highlighted by Basu (1988) and Wasserman (2004)—in survey sampling, causal inference, and Bayesian evidence estimation. We propose two Bayesian remedies: an IPW correction framework based on Bayesian sieves (binning plus nonparametric smoothing) and one built upon conjugate hierarchical models. We provide the first systematic theoretical comparison, proving posterior consistency for both under MCAR, with substantially weaker assumptions on inclusion probabilities than classical IPW. Monte Carlo simulations demonstrate that both estimators drastically reduce mean squared error in Wasserman’s counterexample. Our results extend IPW robustness to Bayesian evidence estimation and average treatment effect evaluation, offering a novel paradigm for weighted inference in high-dimensional, sparse, or non-regular settings.

In pharmacoepidemiology, electronic health records frequently exhibit high missingness (>50%) in critical confounders and rare outcomes, leading to substantial bias in causal effect estimation. This study is the first to systematically compare doubly robust estimators—generalized raking and inverse-probability-weighted targeted maximum likelihood estimation (IPW-TMLE)—against conventional approaches—multiple imputation and inverse-probability weighting—within a plasmode simulation framework that preserves real-world data structure. Results demonstrate that both doubly robust estimators markedly reduce bias and mean squared error; IPW-TMLE consistently achieves superior performance across most scenarios. Furthermore, the study proposes a practical, bias–variance trade-off–informed guideline for selecting analytical methods. This work establishes an empirical benchmark and provides actionable recommendations for confounding control in observational studies characterized by high missingness and low event rates.

This study addresses the instability of conventional causal estimation methods—such as augmented inverse probability weighting (AIPW) and targeted maximum likelihood estimation (TMLE)—under high-dimensional confounding and violations of the positivity assumption. The authors propose a residual-on-residual regression strategy: after separately fitting exposure and outcome models adjusted for confounders, they regress the resulting residuals using ordinary least squares to obtain a robust estimate of the causal effect in a partially linear model. This approach is computationally straightforward, highly interpretable, and maintains unbiasedness with well-calibrated confidence interval coverage even when positivity is violated. In simulations, it substantially outperforms existing methods and was successfully applied to the nuMoM2b dataset, revealing a modest negative association between higher vegetable intake density and preeclampsia risk.

This study addresses the bias in causal effect estimation arising from misspecification of the propensity score model in inverse probability weighting (IPW). To mitigate this issue, the authors propose two clustering-informed strategies: a cluster-augmented IPW approach and a global propensity score model incorporating cluster membership indicators. The robustness of these methods is systematically evaluated through Monte Carlo simulations and an empirical analysis of breast cancer data across varying sample sizes and model specifications. Results demonstrate that the proposed clustering-aware methods substantially reduce both estimation bias and mean squared error, particularly when latent subgroup structures are present. Furthermore, they enable subgroup-specific causal effect estimation and significantly enhance robustness against propensity score model misspecification.

This study addresses the challenge of accurate parameter estimation in Bayesian inference when selection bias and systematic bias are present. The authors propose a generalized Bayesian approach that, for the first time, integrates inverse probability weighting (IPW) into the Bayesian framework. By interpreting IPW as a reweighting of the Kullback–Leibler divergence between the model and the true data-generating mechanism, they construct a posterior distribution that simultaneously inherits the bias-correction properties of frequentist IPW and maintains Bayesian coherence. Theoretical analysis establishes favorable asymptotic convergence properties of the proposed posterior. Empirical validation on both simulated data and a large-scale prostate cancer registry dataset—used to predict mortality based on PSA levels—demonstrates the method’s effectiveness, substantially extending the applicability of Bayesian inference to settings with biased observations.

In observational studies with limited covariate overlap, conventional inverse probability weighting (IPW) estimators of the average treatment effect (ATE) often exhibit substantial bias and unreliable confidence intervals due to violations of the strong overlap assumption. This work proposes a robust IPW approach based on polynomial extrapolation: by constructing a sequence of surrogate estimators indexed by a tuning parameter, it fits a polynomial function to these estimates and extrapolates to the target ATE, thereby substantially reducing reliance on strong overlap while preserving the original ATE definition. Theoretical analysis establishes that the proposed estimator remains consistent and asymptotically normal under weaker overlap conditions. Simulation studies demonstrate that it achieves markedly improved estimation accuracy and confidence interval coverage compared to standard IPW.

This study addresses the challenge of analyzing clinical outcomes with natural prioritization when censoring renders pairwise comparisons unobservable. The authors propose a win ratio regression framework that innovatively incorporates Future Score Correction (FC), substituting missing scores at censoring times with their conditional expectations. By integrating inverse probability weighting and baseline outcome augmentation, the method yields an estimator doubly robust to both treatment assignment and censoring mechanisms. Theoretical justification is grounded in U-statistics theory. Simulations demonstrate a relative efficiency of 1.50 under 65% censoring, with confidence interval coverage closely matching nominal levels. Application to OneFlorida electronic health records successfully analyzes a composite outcome where death is prioritized over hospitalization, confirming the approach’s practical utility and statistical efficiency.