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Random Set Quantile Estimation of Partially Identified Discrete Response Models

部分识别离散响应模型的随机集分位数估计

Semiparametric discrete choice models are widely applied in economics, yet a fundamental tension arises when covariates are discrete as regression coefficients that are point identified under continuous regressors may become only partially identified. We show that this is not merely an identification problem but creates serious estimation pathologies. Classical estimators, including the maximum score estimator of Manski (1975), not only have population maximizers that are…

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Higher-Order Efficient Estimators: A Review and Simulation-Based Benchmark Study

高阶有效估计量:综述与模拟基准研究

Higher-order efficient estimators extend standard first-order semiparametric estimators by replacing second-order residuals with third- or higher-order terms, potentially enabling asymptotic efficiency under slower nuisance function convergence rates and improving finite-sample performance. Existing methods achieve higher-order expansions through structurally different approximation strategies, including basis truncation, kernel smoothing, and highly adaptive lasso (HAL)…

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Evaluating causal indirect effects when mediators are left-censored by assay limit of quantification

中介变量受检测定量下限左删失时的因果间接效应评估

Causal mediation analysis is essential for disentangling the mechanisms by which investigational therapeutic and preventive agents impact clinical outcomes. However, the measurement of biological mediators is often subject to left-censoring by technical measurement limitations, most commonly an assay's limit of quantification. This form of censoring can pose severe challenges for both identification and estimation of causal mediation estimands, particularly when the…

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Estimating Effects of Longitudinal Modified Treatment Policies (LMTPs) on Rates of Change in Health Outcomes

纵向修正治疗政策对健康结局变化率的效应估计

Longitudinal data often contains outcomes measured at multiple visits, and scientific interest may lie in quantifying the effect of an intervention on an outcome's rate of change. For example, one may wish to study the progression (or trajectory) of a disease over time under different hypothetical interventions. We extend the longitudinal modified treatment policy (LMTP) methodology to estimate effects of complex, exposure-dependent interventions on rates of change in an…

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Modeling Covariate Transition for Efficient Estimation of Longitudinal Treatment Effects in Randomized Experiments

通过协变量转移建模高效估计随机实验中的纵向治疗效应

We present a regression-adjustment framework designed for the estimation of longitudinal treatment effects in randomized experiments under static regimes. While regression-adjustment methods are useful for variance reduction in randomized experiments by using pre-treatment covariates, they usually focus only on average effects, from which we cannot obtain valuable insights into when the effects appear and how long they continue. To address this issue, we consider…

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Debiased inference for stochastic treatment interventions with survival outcomes

生存结局下随机治疗干预的去偏推断

Estimating the causal effect of a time-dependent treatment on time to death is challenging. In this paper, we formulate the problem using the illness-death model and focus on a stochastic intervention that modifies the hazard governing the transition from no treatment to treatment initiation. Such an intervention can only be implemented at the level of the observed data, whereas the causally valid intervention is defined at the level of the true data-generating process. We…

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Semiparametric Inference for Causal Effects on Functional Outcomes

函数型结局因果效应的半参数推断

Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and observation. This paper develops a comprehensive semiparametric inference framework for functional DiD with discretely observed data. First, we define the functional average treatment effect under parallel trends and derive its efficient influence…

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A Doubly Robust GMM Estimator for Sequential Non-monotone Missingness

序贯非单调缺失下的双重稳健 GMM 估计量

We study moment-based estimation with two sequentially collected variables subject to non-monotone missingness. The commonly used Missing at Random (MAR) assumption requiring all missingness mechanisms to depend on the same fully observed covariates often fails in such cases. We introduce a sequential MAR assumption that allows asymmetric missingness mechanisms across stages. Based on this assumption, we construct an Augmented Inverse-Probability-Weighted GMM (AIPW-GMM)…

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Beyond Exchangeability: Distribution-Shift-Aware Integration of External Control Data in Randomized Trials

超越可交换性:随机试验中考虑分布偏移的外部对照整合

Randomized controlled trials (RCTs) are the gold standard for evaluating causal effects but are often costly and difficult to scale; consequently, they are frequently augmented with auxiliary external controls in many applications. Prior approaches for borrowing such data typically rely on exchangeability, under which the external controls are readily usable for inference in the trial population. In practice, however, differences in eligibility criteria, standard of care,…

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Identification and Estimation of Semiparametric Multilayered Sample Selection Models

半参数多层样本选择模型的识别与估计

Many selection problems are multilayered: agents first decide whether to participate and then sort among ordered or unordered categories. This paper shows that the sorting layer changes the geometry of identification. Unlike binary selection, in which selection bias can be summarized by a scalar control function, ordered and multinomial sorting generally produce multi-index control functions whose dimension determines the continuous covariate variation needed for…

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Learning Treatment Effects during Resource Allocation via Priority-Queue Randomization

通过优先队列随机化在资源分配中学习处理效应

Public service programs often allocate limited resources under uncertainty about their benefits, creating a need for randomization to support credible evaluation. In practice, however, applicants commonly enter waitlists where resources are prioritized toward individuals judged to have higher need through tiered priority queues, making direct randomization difficult. Motivated by this, we develop an experimental design framework for learning treatment effects while treating…

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Modified treatment policies that depend on the natural history of treatment

依赖处理自然历史的修正处理政策

Longitudinal modified treatment policies (LMTP) are a class of interventions that allow the definition, identification, and estimation of causal effects in general settings, such as with continuous or multivariate exposures, treatment regimens that require grace periods. Targeted machine learning estimators (i.e., double/debiased) have been formulated for LMTPs that assign the exposure at time $t$ as a function of the natural value of treatment at time $t$. However,…

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Targeted maximum likelihood estimation of vaccine effectiveness and immune correlates in test-negative design studies with missing data

暴露数据缺失的检测阴性设计中疫苗有效性与免疫相关指标的目标最大似然估计

The test-negative design (TND) is a resource-efficient observational study design that can assess vaccine effectiveness and exposure-proximal immune correlates of disease. The TND enrolls symptomatic individuals seeking diagnostic testing and compares case status by an exposure variable, such as vaccination status or immune marker level, that is measured at testing. While the TND reduces confounding by healthcare-seeking behavior, other sources of confounding may remain. TND…

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Substantive-Model-Compatible Multiple Imputation for Cox Regression with a Diverging Number of Covariates

发散维协变量下Cox回归的实质模型相容多重插补

Modern biomedical survival studies with high-dimensional genomic and clinical predictors are challenged by missing covariates. Existing methods conduct inference through penalization and debiasing when the number of covariates diverges with sample size, but they are typically developed with fully observed covariates. Conversely, substantive-model-compatible multiple imputation methods, particularly substantive-model-compatible fully conditional specification (SMC-FCS),…

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A Practical Guide to Estimating Conditional Marginal Effects: Modern Approaches

条件边际效应估计的实用指南:现代方法

This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often suffer from unclarified estimands, limited overlap, and restrictive functional forms. This guide begins by clearly defining the estimand and presenting the main identification results. It then reviews and improves upon existing solutions, such…

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Asymptotic Efficiency Bounds for a Class of Experimental Designs

一类实验设计的渐近效率界

We consider an experimental design setting in which units are assigned to treatment after being sampled sequentially from an infinite population. We derive asymptotic efficiency bounds that apply to data from any experiment that assigns treatment as a (possibly randomized) function of covariates and past outcome data, including stratification on covariates and adaptive designs. For estimating the average treatment effect of a binary treatment, our results show that no…

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Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions

无须结构方程的非参数工具变量分析:无精确解逆问题的泛函去偏推断

We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous, and their failure may imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual…

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Sample size and power calculations for causal inference of observational studies

观察研究因果推断的样本量与功效计算

This paper investigates the theoretical foundation and develops analytical formulas for sample size and power calculations for causal inference with observational data. By analyzing the variance of an inverse probability weighting estimator of the average treatment effect, we decompose the power calculation into three components: propensity score distribution, potential outcome distribution, and their correlation. We show that to determine the minimal sample size of an…

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Nesting a Target Study within a Target Trial: A Framework for Evaluating Intervention Effects on Disparities

在目标试验中嵌入目标研究:评估干预对群体差距的影响

We present a novel framework (TS+TT) to nest a Target Study (TS) within a Target Trial (TT) for evaluating the effects of interventions on disparities. The TS component grounds the measurement of disparity in ethical assumptions, based on the concept of allowability, and anchors it to an explicit population within calendar time. It specifies an enrollment plan of stratified sampling of eligible persons to yield a sample where social groups are distributionally similar on…

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Generalizing conditional average treatment effects from nested randomized trials to all trial-eligible individuals

将嵌套随机试验的条件平均处理效应推广至全部符合资格者

Randomized controlled trials often enroll participants whose characteristics differ from those of a target population, which can limit the generalizability of the estimated treatment effects when effect modifiers differ across populations. While existing generalizability methods primarily focus on estimating the average treatment effect (ATE) in the target population, such summaries may obscure important heterogeneity that is relevant for clinical and policy decision-making.…

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Non-overlap Average Treatment Effect Bounds

无重叠情况下的平均处理效应界

The average treatment effect (ATE), the mean difference in potential outcomes under treatment and control, is a canonical causal effect. Overlap, which says that all subjects have non-zero probability of either treatment status, is necessary to identify and estimate the ATE. When overlap fails, the standard solution is to change the estimand, and target a trimmed effect in a subpopulation satisfying overlap. When the outcome is bounded, we demonstrate that this compromise is…

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Causal inference with ordinal outcomes: copula-based identification, estimation and sensitivity analysis

有序结果的因果推断:基于 Copula 的识别、估计与敏感性分析

In causal inference with ordinal outcomes, several interpretable estimands are functions of the probability that the potential outcome under one treatment is larger than that under another treatment for the same unit. This probability depends on the joint distribution of both potential outcomes and is generally not identifiable. Existing work has focused on sharp bounds of this probability based on partial identification, but bounds are often too wide to be informative. We…

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The Multiplicative Quasi-Instrumental Variable Model

乘法准工具变量模型

We introduce the Multiplicative Quasi-Instrumental Variable (MQIV) model, a framework for causal inference with unmeasured confounding that leverages an instrument that may be imperfectly exogenous. We allow the candidate quasi-instrument to have a direct effect on the outcome not mediated by the treatment, thus violating the standard IV exclusion restriction. We establish nonparametric identification of the population average treatment effect on the treated (ATT) under a…

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The Multiplicative Instrumental Variable Model

乘法工具变量模型

The instrumental variable (IV) design is a common approach to address hidden confounding bias. For validity, an IV must impact the outcome only through its association with the treatment. In addition, IV identification has required a homogeneity condition such as monotonicity or no unmeasured common effect modifier between the additive effect of the treatment on the outcome, and that of the IV on the treatment. In this work, we introduce the Multiplicative Instrumental…

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