ipw pseudo-observations

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.

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.

This study addresses causal effect estimation with count-valued exposure variables under missing data, systematically evaluating five inverse probability of treatment weighting (IPTW) approaches—multinomial binning, covariate balancing propensity score (CBPS and its nonparametric extension npCBPS), generalized boosted models (GBM), and energy balancing weights—combined with multiple imputation and Rubin’s rules. Results show that all IPTW methods perform well under complete data and missing completely at random (MCAR) scenarios. However, under missing at random (MAR) conditions, substantial bias emerges, primarily due to limitations in the imputation models’ ability to adequately capture the right-truncated, overdispersed nature of count data, rather than inherent flaws in the IPTW estimators themselves. The findings offer practical guidance on weighting strategies and method selection for causal inference with high-dimensional count exposures.

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.

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 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 work addresses the challenge of off-policy evaluation under right-censored survival outcomes, where existing methods are prone to systematic bias and yield inaccurate policy value estimates. To mitigate this issue, the study introduces inverse probability of censoring weighting (IPCW) into off-policy evaluation for the first time, proposing two novel estimators—IPCW-IPS and IPCW-DR—that are both unbiased and doubly robust, effectively correcting for censoring-induced bias. Furthermore, the proposed framework naturally extends to policy optimization under budget constraints. Experimental results on both synthetic and real-world datasets demonstrate that the method substantially improves the accuracy of policy evaluation and enhances learning performance in censored environments.

This study addresses the challenge of efficiently and robustly estimating the difference in restricted mean survival time (RMST) under right-censored time-to-event data commonly encountered in clinical trials. The authors propose a novel framework that integrates targeted minimum loss-based estimation (TMLE) with pseudo-observations, marking the first application of this combination for RMST difference estimation. Additionally, they introduce an innovative replication reference approach to facilitate sensitivity analysis under right censoring. Empirical evaluation on real clinical trial data demonstrates that the proposed method substantially improves estimation efficiency while maintaining robustness, offering a theoretically sound and practically valuable tool for RMST-based comparative analyses in survival settings.

This study addresses the instability of policy value estimation in causal inference under practical positivity violations (limited overlap). The authors propose an Adaptive Targeted Maximum Likelihood Estimation (A-TMLE) framework that constructs a projected policy value parameter using a data-driven conditional average treatment effect (CATE) model and incorporates regularized TMLE to avoid direct reliance on inverse probability weighting. By integrating adaptive function approximation, projection techniques, and influence function theory, A-TMLE substantially enhances estimation robustness under limited overlap. Empirical evaluations on both simulated data and real-world right heart catheterization data demonstrate that A-TMLE achieves lower mean squared error, higher confidence interval coverage, and more compact and stable inference compared to standard IPW, AIPW, and conventional TMLE approaches.

This paper addresses the bias in variance estimation for the inverse probability weighted Kaplan–Meier (IPTW-KM) estimator in observational survival analysis. We show that the classical “XL” method neglects variability induced by propensity score estimation, leading to upwardly biased variance estimates. To resolve this, we establish the first rigorous asymptotic theory for the IPTW-KM estimator under data-driven propensity score estimation—revealing that propensity score estimation actually reduces the asymptotic variance. Building on this insight, we propose a consistent plug-in variance estimator that explicitly accounts for uncertainty from propensity score estimation. Through theoretical derivation and extensive simulation studies, our method achieves substantially improved variance estimation accuracy, eliminates upward bias, and enhances the reliability of causal effect inference in survival analysis.