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Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions

近似残差平衡:高维平均处理效应的去偏推断

Summary There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on pretreatment variables. The unconfoundedness assumption is often more plausible if a large number of pretreatment variables are included in the analysis, but this can worsen the performance of standard approaches to treatment effect…

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A semi-nonparametric estimator of regression discontinuity design with discrete duration outcomes

离散持续时间结果的断点回归半非参数估计

We consider the regression discontinuity (RD) design with the duration outcome which has discrete support. The parameters of policy interest are treatment effects on unconditional (duration effect) and conditional (hazard effect) exiting probabilities for each discrete level. We propose a novel semi-nonparametric estimator which exploits a flexible separability structure of the underlying continuous-time duration process. Simultaneous inference over discrete levels is…

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Comparing distributions by multiple testing across quantiles or CDF values

通过跨分位数或累积分布函数值的多重检验比较分布

We first show that one-sample and two-sample Kolmogorov–Smirnov tests may be interpreted as multiple testing procedures, nonparametrically testing equality at each point in the distribution with strong control of the finite-sample familywise error rate. Second, we provide an alternative procedure that distributes power across the distribution more evenly than the Kolmogorov–Smirnov test, which suffers low sensitivity to tail deviations. Third, we provide a formula for…

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Bounds on treatment effects on transitions

条件转移概率处理效应的界限

This paper considers the identification of treatment effects on conditional transition probabilities. We show that even under random assignment only the instantaneous average treatment effect is point identified. Since treated and control units drop out at different rates, randomization only ensures the comparability of treatment and controls at the time of randomization, so that long-run average treatment effects are not point identified. Instead, we derive bounds on these…

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Robust and efficient estimation for the treatment effect in causal inference and missing data problems

因果推断与缺失数据问题中处理效应的稳健高效估计

The Mann–Whitney statistic based on complete data only might be invalid if the outcome variables are missing due to certain covariates. In this paper, we used the probabilistic index modelling (Thas et al., 2012) to obtain a new Mann–Whitney statistic when missingness occurs in the outcomes but multiple explanatory variables are observable. Our method combined the efficiency of the model-based approach and the robustness of the nonparametric approach. It requires few model…

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Front-Door Versus Back-Door Adjustment With Unmeasured Confounding: Bias Formulas for Front-Door and Hybrid Adjustments With Application to a Job Training Program

存在未测混杂时的前门与后门调整:前门及混合调整的偏差公式与职业培训应用

We demonstrate that the front-door adjustment can be a useful alternative to standard covariate adjustments (i.e., back-door adjustments), even when the assumptions required for the front-door approach do not hold. We do this by providing asymptotic bias formulas for the front-door approach that can be compared directly to bias formulas for the back-door approach. In some cases, this allows the tightening of bounds on treatment effects. We also show that under one-sided…

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A Bayesian Machine Learning Approach for Optimizing Dynamic Treatment Regimes

优化动态治疗方案的贝叶斯机器学习方法

Medical therapy often consists of multiple stages, with a treatment chosen by the physician at each stage based on the patient's history of treatments and clinical outcomes. These decisions can be formalized as a dynamic treatment regime. This paper describes a new approach for optimizing dynamic treatment regimes that bridges the gap between Bayesian inference and existing approaches, like Q-learning. The proposed approach fits a series of Bayesian regression models, one…

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Functional Feature Construction for Individualized Treatment Regimes

个体化治疗方案的函数型特征构造

Evidence-based personalized medicine formalizes treatment selection as an individualized treatment regime that maps up-to-date patient information into the space of possible treatments. Available patient information may include static features such race, gender, family history, genetic and genomic information, as well as longitudinal information including the emergence of comorbidities, waxing and waning of symptoms, side-effect burden, and adherence. Dynamic information…

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Assessing Time-Varying Causal Effect Moderation in Mobile Health

移动健康干预中的时变因果效应调节评估

In mobile health interventions aimed at behavior change and maintenance, treatments are provided in real time to manage current or impending high risk situations or promote healthy behaviors in near real time. Currently there is great scientific interest in developing data analysis approaches to guide the development of mobile interventions. In particular data from mobile health studies might be used to examine effect moderators-individual characteristics, time-varying…

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Cross-Screening in Observational Studies That Test Many Hypotheses

多假设观察性研究中的交叉筛选

We discuss observational studies that test many causal hypotheses, either hypotheses about many outcomes or many treatments. To be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment. In a sense that needs to be defined carefully, hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for…

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Optimal Probability Weights for Inference With Constrained Precision

精度约束下用于推断的最优概率权重

Probability weights are used in many areas of research including complex survey designs, missing data analysis, and adjustment for confounding factors. They are useful analytic tools but can lead to statistical inefficiencies when they contain outlying values. This issue is frequently tackled by replacing large weights with smaller ones or by normalizing them through smoothing functions. While these approaches are practical, they are also prone to yield biased inferences.…

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Quantile-Optimal Treatment Regimes

分位数最优治疗规则

Finding the optimal treatment regime (or a series of sequential treatment regimes) based on individual characteristics has important applications in areas such as precision medicine, government policies and active labor market interventions. In the current literature, the optimal treatment regime is usually defined as the one that maximizes the average benefit in the potential population. This paper studies a general framework for estimating the quantile-optimal treatment…

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Estimation and Inference of Heterogeneous Treatment Effects using Random Forests

利用随机森林估计异质性处理效应并进行统计推断

Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true…

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Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited

货币政策效应的半参数估计:重新审视“推绳子”理论

We develop flexible semiparametric time series methods for the estimation of the causal effect of monetary policy on macroeconomic aggregates. Our estimator captures the average causal response to discrete policy interventions in a macrodynamic setting, without the need for assumptions about the process generating macroeconomic outcomes. The proposed estimation strategy, based on propensity score weighting, easily accommodates asymmetric and nonlinear responses. Using this…

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A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

工具变量识别不同局部平均处理效应时的 2SLS 一致方差估计量

Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). With multiple instruments, two-stage least squares (2SLS) estimand is a weighted average of different LATEs. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroscedasticity-robust variance estimator would be…

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Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective

非参数加性工具变量估计:组收缩估计视角

In this article, we study a nonparametric approach regarding a general nonlinear reduced form equation to achieve a better approximation of the optimal instrument. Accordingly, we propose the nonparametric additive instrumental variable estimator (NAIVE) with the adaptive group Lasso. We theoretically demonstrate that the proposed estimator is root-n consistent and asymptotically normal. The adaptive group Lasso helps us select the valid instruments while the dimensionality…

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Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design

断点回归中的近似置换检验与诱导次序统计量

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing whether the means of baseline covariates do not change at the cut-off (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cut-off. We propose a permutation test based on…

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Misspecification of noncausal order in autoregressive processes

自回归过程中的非因果阶数误设

This paper examines noncausal order misspecification in noncausal and mixed processes. We consider the constrained maximum likelihood (ML) estimators of autoregressive parameters obtained when noncausal order s is fixed and potentially different from the true order s0. The effect of such noncausal order misspecification on the constrained ML estimators of the autoregressive parameters is examined by means of the binding function. We find that, surprisingly, the misspecified…

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Flexible prices and leverage

价格灵活性与企业杠杆

The frequency with which firms adjust output prices helps explain persistent differences in capital structure across firms. Unconditionally, the most flexible-price firms have a 19% higher long-term leverage ratio than the most sticky-price firms, controlling for known determinants of capital structure. Sticky-price firms increased leverage more than flexible-price firms following the staggered implementation of bank deregulation across states and over time, which we use in…

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Semiparametric regression analysis for composite endpoints subject to componentwise censoring

分量分别删失的复合终点半参数回归分析

Composite endpoints with censored data are commonly used as study outcomes in clinical trials. For example, progression-free survival is a widely used composite endpoint, with disease progression and death as the two components. Progression-free survival time is often defined as the time from randomization to the earlier occurrence of disease progression or death from any cause. The censoring times of the two components could be different for patients not experiencing the…

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Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores

按估计倾向得分修剪的观察性研究中因果效应的渐近推断

Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores close to |$0$| or |$1$|⁠, so both practical and theoretical researchers suggest dropping units with extreme estimated propensity scores. However, existing trimming methods often do not incorporate the uncertainty in this design stage and…

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Uniformly minimum variance conditionally unbiased estimation in multi-arm multi-stage clinical trials

多臂多阶段临床试验中的一致最小方差条件无偏估计

Multi-arm multi-stage clinical trials compare several experimental treatments with a control treatment, with poorly performing treatments dropped at interim analyses. This leads to inferential challenges, including the construction of unbiased treatment effect estimators. A number of estimators which are unbiased conditional on treatment selection have been proposed, but are specific to certain selection rules, may ignore the comparison to the control and are not all minimum…

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Bounded, Efficient and Multiply Robust Estimation of Average Treatment Effects Using Instrumental Variables

利用工具变量进行有界、高效且多重稳健的平均处理效应估计

Summary Instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard instrumental variable model, however, the average treatment effect is only partially identifiable. To address this, we propose novel assumptions that enable identification of the average treatment effect. Our identification assumptions are clearly separated from model assumptions that are needed for estimation, so researchers are not…

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High-dimensional $A$-learning for optimal dynamic treatment regimes

最优动态治疗方案的高维A-learning

Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of…

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