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Sharp Minimax Theory for Randomized Experiments

随机实验的锐极小极大理论

We study minimax-optimal designs and estimators for estimating the sample average treatment effect in finite population randomized experiments, where both design and estimator are unrestricted. For binary potential outcomes, we show this minimax risk is equivalent to the minimax risk $ρ_n^*$ of an estimation problem with $2$ unknown parameters. We leverage this reduction to establish a second-order risk expansion $ρ_n^* = n^{-1} - Cn^{-4/3} + o_n(n^{-4/3})$ for an explicit…

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Partial Identification of Causal Effects Using Proxy Variables

利用代理变量对因果效应进行部分识别

Proximal causal inference is a framework for evaluating the causal effects in the presence of unmeasured confounding. For point identification, it leverages a pair of proxy variables to identify a bridge function that matches the dependence of potential outcomes or treatment variables on the hidden factors to corresponding functions of observed proxies. Unique identification requires that proxies are sufficiently relevant for hidden factors, a requirement that has previously…

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Structural Nested Mean Models Under Parallel Trends Assumptions

平行趋势假设下的结构嵌套均值模型

We link and extend two approaches to estimating time-varying treatment effects on repeated continuous outcomes--time-varying Difference in Differences (DiD; see Roth et al. (2023) and Chaisemartin et al. (2023) for reviews) and Structural Nested Mean Models (SNMMs; see Vansteelandt and Joffe (2014) for a review). In particular, we show that SNMMs, previously known to be nonparametrically identified under a no unobserved confounding assumption, are also identified under a…

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Causal Inference with a Hidden Treatment

真实处理不可观测时的因果推断

In many causal inference settings, the treatment of interest is not directly observed; instead, one or more error-prone proxy measurements are available, creating a fundamental identification challenge. Building on identification methods for hidden treatments with proxies, we develop a general semiparametric framework for causal effect estimation that accommodates several common estimands. Hidden treatment models differ fundamentally from classical missing-data settings,…

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A Nonparametric Framework for Universal Difference-in-Differences

通用双重差分的非参数框架

Difference-in-differences (DiD) is a popular approach to evaluate treatment effects in settings where both pre- and post-treatment measurements of the outcome are available. Despite its popularity, existing methods face important limitations. Specifically, they either: (i) only apply to continuous outcomes and the average treatment effect on the treated; (ii) are sensitive to the transformation of the outcome; (iii) rely on a no unmeasured confounding assumption given…

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Proximal Causal Inference for Conditional Separable Effects

条件可分离效应的近端因果推断

Scientists regularly pose questions about treatment effects on outcomes conditional on a post-treatment event. However, causal inference in such settings requires care, even in perfectly executed randomized experiments. Recently, the conditional separable effect (CSE) was proposed as an interventionist estimand that corresponds to scientifically meaningful questions in these settings. However, existing results for the CSE require no unmeasured confounding between the outcome…

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Nonparametric Inference with an Instrumental Variable under a Separable Binary Treatment Choice Model

可分二元治疗选择模型下的工具变量非参数推断

Instrumental variable (IV) methods are widely used to infer treatment effects in the presence of unmeasured confounding. In this paper, we study nonparametric inference with an IV under a separable binary treatment choice model, which posits that the odds of the probability of taking the treatment, conditional on the instrument and the treatment-free potential outcome, factor into separable components for each variable. While nonparametric identification of smooth…

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Finding Distributions that Differ, with False Discovery Rate Control

在控制错误发现率下识别分布差异

We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that of the reference group. Viewing this as a multiple testing problem, we introduce a methodology that provides exact, distribution-free control of the false discovery rate. To do so, we introduce the concept of batch conformal p-values and…

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Combining Experimental and Observational Data for Identification and Estimation of Long-Term Causal Effects

结合实验与观察数据识别和估计长期因果效应

We study identifying and estimating the causal effect of a treatment variable on a long-term outcome using data from an observational and an experimental domain. The observational data are subject to unobserved confounding. Furthermore, subjects in the experiment are only followed for a short period; thus, long-term effects are unobserved, though short-term effects are available. Consequently, neither data source alone suffices for causal inference on the long-term outcome,…

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Quasi Instrumental Variable Methods for Stable Hidden Confounding and Binary Outcome

稳定隐性混杂与二元结果的准工具变量方法

Instrumental variable (IV) methods are central to causal inference from observational data, particularly when a randomized experiment is not feasible. However, of the three conventional core IV identification conditions, only one, IV relevance, is empirically verifiable; often one or both of the other conditions, exclusion restriction and IV independence from unmeasured confounders, are unmet in real-world applications. These challenges are compounded when the outcome is…

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Adaptive Proximal Causal Inference with Some Invalid Proxies

含部分无效代理变量的自适应近端因果推断

Proximal causal inference (PCI) is a recently proposed framework to identify and estimate the causal effect of an exposure on an outcome in the presence of hidden confounders, using observed proxies. Specifically, PCI relies on two types of proxies: a treatment-inducing confounding proxy, related to the outcome only through its association with unmeasured confounders (given treatment and covariates), and an outcome-inducing confounding proxy, related to the treatment only…

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Test-negative designs with various reasons for testing: statistical bias and solution

多种检测原因下的检测阴性设计:统计偏差与解决方法

Test-negative designs are widely used for post-market evaluation of vaccine effectiveness, particularly in cases when randomized trials are not feasible. Differing from classical test-negative designs where only healthcare-seekers with symptoms are included, recent test-negative designs have involved individuals with various reasons for testing, especially in an outbreak setting. While including these data can increase sample size and hence improve precision, concerns have…

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Single Proxy Synthetic Control

单代理合成控制

Synthetic control methods are widely used to estimate the treatment effect on a single treated unit in time-series settings. A common approach to estimate synthetic control weights is to regress the treated unit's pre-treatment outcome and covariates' time series measurements on those of untreated units via ordinary least squares. However, this approach can perform poorly if the pre-treatment fit is not near perfect, whether the weights are normalized or not. In this paper,…

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Doubly Robust Proximal Synthetic Controls

双重稳健的近端合成控制

To infer the treatment effect for a single treated unit using panel data, synthetic control methods construct a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and used to estimate the treatment effect. Existing synthetic control methods rely on correctly…

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Single Proxy Control

单代理混杂控制

Negative control variables are sometimes used in non-experimental studies to detect the presence of confounding by hidden factors. A negative control outcome (NCO) is an outcome that is influenced by unobserved confounders of the exposure effects on the outcome in view, but is not causally impacted by the exposure. Tchetgen Tchetgen (2013) introduced the Control Outcome Calibration Approach (COCA) as a formal NCO counterfactual method to detect and correct for residual…

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Forster-Warmuth Counterfactual Regression: A Unified Learning Approach

Forster–Warmuth 反事实回归:统一学习方法

Series or orthogonal basis regression is one of the most popular non-parametric regression techniques in practice, obtained by regressing the response on features generated by evaluating the basis functions at observed covariate values. The most routinely used series estimator is based on ordinary least squares fitting, which is known to be minimax rate optimal in various settings, albeit under stringent restrictions on the basis functions and the distribution of covariates.…

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GENIUS-MAWII: For Robust Mendelian Randomization with Many Weak Invalid Instruments

GENIUS-MAWII:应对大量弱且无效工具变量的稳健孟德尔随机化

Mendelian randomization (MR) has become a popular approach to study causal effects by using genetic variants as instrumental variables. We propose a new MR method, GENIUS-MAWII, which simultaneously addresses the two salient phenomena that adversely affect MR analyses: many weak instruments and widespread horizontal pleiotropy. Similar to MR GENIUS (Tchetgen Tchetgen et al., 2021), we achieve identification of the treatment effect by leveraging heteroscedasticity of the…

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Proximal Causal Inference without Uniqueness Assumptions

不要求解唯一性的近端因果推断

We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference (Miao et al. [2018], Tchetgen Tchetgen et al. [2020]). Proximal causal inference requires existence of solutions to at least one of two integral equations. We motivate the existence of solutions to the integral equations from proximal causal inference by demonstrating that, assuming the existence of a solution to one of…

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Universal Difference-in-Differences for Causal Inference in Epidemiology

流行病学因果推断中的通用双重差分

Difference-in-differences is undoubtedly one of the most widely used methods for evaluating the causal effect of an intervention in observational (i.e., nonrandomized) settings. The approach is typically used when pre- and post-exposure outcome measurements are available, and one can reasonably assume that the association of the unobserved confounder with the outcome has the same absolute magnitude in the two exposure arms, and is constant over time; a so-called parallel…

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Theory for identification and Inference with Synthetic Controls: A Proximal Causal Inference Framework

合成控制的识别与推断:近端因果推断框架

Synthetic control (SC) methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. An SC is a weighted average of control units built to match the treated unit, with weights typically estimated by regressing (summaries of) pre-treatment outcomes and measured covariates of the treated unit to those of the control units. However, it has been established that in the absence of a good fit, such regression estimator will generally…

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Causal Inference with Hidden Mediators

存在隐含中介变量时的因果推断

Proximal causal inference was recently proposed as a framework to identify causal effects from observational data in the presence of hidden confounders for which proxies are available. In this paper, we extend the proximal causal inference approach to settings where identification of causal effects hinges upon a set of mediators which are not observed, yet error prone proxies of the hidden mediators are measured. Specifically, (i) We establish causal hidden mediation…

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Doubly Robust Calibration of Prediction Sets under Covariate Shift

协变量漂移下预测集的双重稳健校准

Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more robust and efficient uncertainty quantification. In this paper, we consider the problem of obtaining distribution-free prediction regions accounting for a shift in the distribution of the covariates between the training and test data. Under…

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Rejoinder to discussions on "Instrumental variable estimation of the causal hazard ratio"

对《因果风险比的工具变量估计》讨论的答复

We respond to comments on our paper, titled "Instrumental variable estimation of the causal hazard ratio."

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Doubly Robust Proximal Causal Inference under Confounded Outcome-Dependent Sampling

混杂性结局依赖抽样下的双重稳健近端因果推断

Unmeasured confounding and selection bias are often of concern in observational studies and may invalidate a causal analysis if not appropriately accounted for. Under outcome-dependent sampling, a latent factor that has causal effects on the treatment, outcome, and sample selection process may cause both unmeasured confounding and selection bias, rendering standard causal parameters unidentifiable without additional assumptions. Under an odds ratio model for the treatment…

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