semiparametric sensitivity analysis

Unmeasured confounding frequently biases causal inference in observational studies, while existing sensitivity analyses often rely on strong parametric modeling assumptions. To assess the robustness of the average causal effect (ACE), this paper proposes the first sensitivity analysis framework grounded in semiparametric efficient influence functions: it constructs a model-free, truncated first-order estimator that avoids explicit parametric modeling of sensitivity parameters. Theoretically, the estimator is shown to be √n-consistent and semiparametrically efficient. Simulation studies demonstrate its superior performance over mainstream methods under diverse confounding structures. An empirical application to the effect of maternal smoking during pregnancy on newborn birth weight validates its practical robustness. The core contribution lies in systematically integrating semiparametric efficiency theory into sensitivity analysis—yielding a model-agnostic, statistically efficient, and interpretable quantification of causal robustness.

This paper addresses the lack of robust design foundations for sensitivity analysis in finite-population causal inference. Methodologically, it introduces a novel sensitivity analysis framework grounded in the experimental design distribution—first integrating design-based distributions with partial identification theory to construct model-free, non-asymptotic confidence intervals for the average treatment effect (ATE). It further reinterprets the role of randomization in sensitivity analysis and provides a new design-driven rationale for covariate balance checks. Key contributions include: (1) model-free, finite-population inference under heterogeneous treatment effects; (2) robust ATE confidence intervals with clear identification-theoretic interpretation; and (3) empirical validation across three real-world applications, demonstrating reliability and practicality in small-sample and highly heterogeneous settings.

To address bias in causal inference arising from unmeasured confounding in observational survival studies, this paper proposes a semiparametric sensitivity analysis framework grounded in influence functions. We first derive the nonparametric influence function for time-to-event data and establish a mapping mechanism from uncensored to censored data, thereby circumventing reliance on specific parametric survival model assumptions. The method integrates competing-risks modeling with semiparametric statistical inference, requiring no specification of baseline hazard functions or confounder structures. Evaluated on real-world prostate cancer data comparing radical prostatectomy versus external-beam radiotherapy combined with androgen-deprivation therapy—and across multiple simulation scenarios—the approach demonstrates consistent estimation, effective bias correction, and substantially improved robustness and credibility of marginal causal effect estimates.

This paper addresses sensitivity analysis for linear causal effect estimation under unobserved confounding and potential instrumental variables. Methodologically, it formalizes sensitivity analysis as a constrained stochastic optimization problem—the first such formulation—leverages algebraic rules of partial correlations to construct interpretable and easily calibratable bounds on omitted-variable bias, and develops a bootstrap-based algorithm for constructing sensitivity intervals with asymptotic confidence guarantees. Empirical evaluation in an education returns application and extensive numerical simulations demonstrates the method’s high coverage probability and robustness across diverse confounding scenarios. Furthermore, the paper releases an open-source, user-friendly interactive visualization tool that enhances interpretability and credibility of causal inference results.

In causal inference, sensitivity parameters are often difficult to calibrate due to their lack of intuitive causal interpretation, and existing methods ignore the sampling uncertainty in measured confounder estimation, leading to biased robustness assessments. This paper proposes a calibration-based sensitivity model: it directly constrains the strength of unmeasured confounding as a multiple of the estimated effect of measured confounders—endowing the sensitivity parameter with a clear causal interpretation (“unmeasured-to-measured confounding ratio”). It is the first to systematically incorporate the sampling variability of measured confounder estimates, thereby correcting inferential bias in bounding. Leveraging double robustness, nonparametric efficiency, and asymptotic normality theory, we construct three computationally tractable bounding models for the average treatment effect. Empirical analysis of maternal smoking’s effect on birth weight shows that conventional methods can substantially overstate or understate conclusion robustness. Our approach enhances the interpretability, calibration validity, and statistical reliability of sensitivity analysis.

This work addresses the lack of intuitive geometric interpretation in classical semiparametric efficiency theory, which has hindered the derivation and understanding of influence functions. The paper reformulates the theory within a differential geometric framework on the space of probability distributions, drawing an analogy to multivariate calculus: statistical paths, scores, and influence functions correspond respectively to curves, velocity vectors, and gradients. It demonstrates that the efficient influence function arises naturally as an orthogonal projection. By integrating functional analysis, differential geometry, and statistical inference, the study establishes a unified geometric interpretation of scores, tangent spaces, nuisance tangent spaces, and efficient influence functions. This synthesis not only clarifies several foundational theoretical issues but also substantially enhances the interpretability of methods in causal inference and missing data analysis.

This study addresses the lack of a systematic framework for identifying critical input variables and conducting sensitivity analysis under uncertainty in complex simulations, particularly in military decision-making contexts. The authors propose a unified sensitivity analysis framework that integrates local and global methods—including variance-based, derivative-based, screening, and uncertainty quantification techniques—and strategically maps these approaches to specific decision objectives such as factor prioritization, fixing, variance reduction, and mapping. Innovatively, the framework introduces a “sensitivity audit” mechanism to enhance traceability of model assumptions and promote responsible model usage. By providing a structured guide for high-dimensional, complex simulation systems, this work significantly improves model interpretability, transparency, and the credibility of decisions derived from such models.

Traditional sensitivity analyses in matched observational studies often assume that unobserved confounding is nearly perfectly correlated with potential outcomes, rendering them overly conservative and lacking realistic flexibility. This work proposes a stochastic sensitivity analysis framework that models unobserved confounding as a random variable with an unknown conditional distribution given the potential outcomes and observed covariates. Rather than optimizing over worst-case realizations, the approach evaluates the robustness of causal conclusions by optimizing over the least favorable conditional distributions. By introducing controlled randomness, the method permits imperfect alignment between unobserved confounders and potential outcomes and incorporates both nonparametric interpretable distribution classes and Bernoulli conditional models in the optimization. Empirical results demonstrate that even minimal stochasticity substantially enhances the ability to report robustness against hidden bias.

This work addresses the suboptimal inference in semiparametric estimation caused by estimation errors in nuisance functions when using black-box machine learning models. The authors propose a novel estimator that, without imposing additional assumptions, eliminates first-order stochastic errors from nuisance estimation and achieves optimal convergence rates even when auxiliary functions cannot be consistently estimated. Built upon the framework of orthogonal scores and semiparametric linear functionals, the proposed estimator attains the sharp rate \(n^{-1/2} + \delta^a_\mu + (\delta^s_\mu)^2\) and is shown to be asymptotically normal with minimal asymptotic variance. Its tuning strategy favors undersmoothing and substantially outperforms classical double machine learning methods, making it well-suited for widespread applications such as average treatment effect estimation.

This work proposes an efficient method for estimating sharp bounds on causal effects when point identification is precluded by unobserved confounding. The approach uniquely integrates the conditional independence constraints implied by the causal graph into a sensitivity analysis framework, leveraging influence function projections and semiparametric estimation theory to substantially improve the statistical efficiency of bound estimation. Empirical evaluations on both simulated data and real-world applications—including the effect of job training on earnings and the impact of ejection fraction on heart failure mortality—demonstrate that the method achieves high efficiency and robustness under non-identifiable settings.