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The Bias-Variance Tradeoff of Doubly Robust Estimator with Targeted $L_1$ regularized Neural Networks Predictions

采用定向 L1 正则化神经网络预测的双重稳健估计偏差—方差权衡

The Doubly Robust (DR) estimation of ATE can be carried out in 2 steps, where in the first step, the treatment and outcome are modeled, and in the second step the predictions are inserted into the DR estimator. The model misspecification in the first step has led researchers to utilize Machine Learning algorithms instead of parametric algorithms. However, existence of strong confounders and/or Instrumental Variables (IVs) can lead the complex ML algorithms to provide perfect…

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Causal Inference in Educational Systems: A Graphical Modeling Approach

教育系统中的因果推断:图模型方法

Educational systems have traditionally been evaluated using cross-sectional studies, namely, examining a pretest, posttest, and single intervention. Although this is a popular approach, it does not model valuable information such as confounding variables, feedback to students, and other real-world deviations of studies from ideal conditions. Moreover, learning inherently is a sequential process and should involve a sequence of interventions. In this paper, we propose various…

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Implementing an Improved Test of Matrix Rank in Stata

在 Stata 中实现改进的矩阵秩检验

We develop a Stata command, bootranktest, for implementing the matrix rank test of Chen and Fang (2019) in linear instrumental variable regression models. Existing rank tests employ critical values that may be too small, and hence may not even be first order valid in the sense that they may fail to control the Type I error. By appealing to the bootstrap, they devise a test that overcomes the deficiency of existing tests. The command bootranktest implements the two-step…

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A Uniformly Consistent Estimator of non-Gaussian Causal Effects Under the k-Triangle-Faithfulness Assumption

k 三角忠实性假设下非高斯因果效应的统一一致估计

Kalisch and Bühlmann (2007) showed that for linear Gaussian models, under the Causal Markov Assumption, the Strong Causal Faithfulness Assumption, and the assumption of causal sufficiency, the PC algorithm is a uniformly consistent estimator of the Markov Equivalence Class of the true causal DAG for linear Gaussian models; it follows from this that for the identifiable causal effects in the Markov Equivalence Class, there are uniformly consistent estimators of causal effects…

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To adjust or not to adjust? Estimating the average treatment effect in randomized experiments with missing covariates

调整还是不调整:协变量缺失的随机实验中平均处理效应估计

Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an important question: should we adjust for covariates subject to missingness, and if so, how? The…

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Causal mediation analysis with mediator values below an assay limit

中介变量低于检测下限时的因果中介分析

Causal indirect and direct effects provide an interpretable method for decomposing the total effect of an exposure on an outcome into the effect through a mediator and the effect through all other pathways. When the mediator is a biomarker, values can be subject to an assay lower limit. The mediator is affected by the treatment and is a putative cause of the outcome, so the assay lower limit presents a compounded problem in mediation analysis. We propose three approaches to…

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The Influence Function of Semiparametric Estimators

半参数估计量的影响函数

Many useful parameters depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, constructing debiased machine learning estimators, in efficiency…

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Doing Great at Estimating CATE? On the Neglected Assumptions in Benchmark Comparisons of Treatment Effect Estimators

条件平均处理效应估计器基准比较中被忽视的假设

The machine learning toolbox for estimation of heterogeneous treatment effects from observational data is expanding rapidly, yet many of its algorithms have been evaluated only on a very limited set of semi-synthetic benchmark datasets. In this paper, we show that even in arguably the simplest setting -- estimation under ignorability assumptions -- the results of such empirical evaluations can be misleading if (i) the assumptions underlying the data-generating mechanisms in…

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Outcome-Adjusted Balance Measure for Generalized Propensity Score Model Selection

用于广义倾向得分模型选择的结局调整平衡指标

In this article, we propose the outcome-adjusted balance measure to perform model selection for the generalized propensity score (GPS), which serves as an essential component in estimation of the pairwise average treatment effects (ATEs) in observational studies with more than two treatment levels. The primary goal of the balance measure is to identify the GPS model specification such that the resulting ATE estimator is consistent and efficient. Following recent empirical…

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Post-Treatment Confounding in Causal Mediation Studies: A Cutting-Edge Problem and A Novel Solution via Sensitivity Analysis

因果中介研究中的处理后混杂与敏感性分析

In causal mediation studies that decompose an average treatment effect into a natural indirect effect (NIE) and a natural direct effect (NDE), examples of post-treatment confounding are abundant. Past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due to incomplete information: it is observed under the actual treatment condition while missing under the counterfactual treatment condition. This…

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Evaluating Effectiveness of Public Health Intervention Strategies for Mitigating COVID-19 Pandemic

评估缓解新冠疫情的公共卫生干预策略

Coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global public health challenge. In the United States (US), state governments have implemented various non-pharmaceutical interventions (NPIs), such as physical distance closure (lockdown), stay-at-home order, mandatory facial mask in public in response to the rapid spread of COVID-19. To evaluate the effectiveness of these NPIs, we propose a nested case-control design with propensity score weighting under the…

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How balance and sample size impact bias in the estimation of causal treatment effects: A simulation study

平衡性与样本量如何影响因果处理效应估计的偏差:一项模拟研究

Observational studies are often used to understand relationships between exposures and outcomes. They do not, however, allow conclusions about causal relationships to be drawn unless statistical techniques are used to account for the imbalance of confounders across exposure groups. Propensity score and balance weighting (PSBW) are useful techniques that aim to reduce the imbalances between exposure groups by weighting the groups to look alike on the observed confounders.…

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Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

贝叶斯分位数回归中收缩与变量选择的解耦

This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of the art continuous priors and in the second step, we sparsify the posterior through an efficient variant of the adaptive lasso, the signal adaptive variable selection (SAVS) algorithm. We propose a new variant of the SAVS which automates…

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Covariate adjustment in randomised trials: canonical link functions protect against model mis-specification

随机试验中的协变量调整:典范链接函数对模型误设的保护

Covariate adjustment has the potential to increase power in the analysis of randomised trials, but mis-specification of the adjustment model could cause error. We explore what error is possible when the adjustment model omits a covariate by randomised treatment interaction, in a setting where the covariate is perfectly balanced between randomised treatments. We use mathematical arguments and analyses of single hypothetical data sets. We show that analysis by a generalised…

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Method of Moments Confidence Intervals for a Semi-Supervised Two-Component Mixture Model

半监督双成分混合模型的矩估计置信区间

A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients…

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Assessment of Immune Correlates of Protection via Controlled Vaccine Efficacy and Controlled Risk

通过受控疫苗效力与受控风险评估免疫保护相关指标

Immune correlates of protection (CoPs) are immunologic biomarkers accepted as a surrogate for an infectious disease clinical endpoint and thus can be used for traditional or provisional vaccine approval. To study CoPs in randomized, placebo-controlled trials, correlates of risk (CoRs) are first assessed in vaccine recipients. This analysis does not assess causation, as a CoR may fail to be a CoP. We propose a causal CoP analysis that estimates the controlled vaccine efficacy…

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Machine Learning for Financial Forecasting, Planning and Analysis: Recent Developments and Pitfalls

财务预测、规划与分析中的机器学习:近期进展与陷阱

This article is an introduction to machine learning for financial forecasting, planning and analysis (FP\&A). Machine learning appears well suited to support FP\&A with the highly automated extraction of information from large amounts of data. However, because most traditional machine learning techniques focus on forecasting (prediction), we discuss the particular care that must be taken to avoid the pitfalls of using them for planning and resource allocation (causal…

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Algorithmic Causal Effect Identification with causaleffect

使用causaleffect进行算法化因果效应识别

Our evolution as a species made a huge step forward when we understood the relationships between causes and effects. These associations may be trivial for some events, but they are not in complex scenarios. To rigorously prove that some occurrences are caused by others, causal theory and causal inference were formalized, introducing the $do$-operator and its associated rules. The main goal of this report is to review and implement in Python some algorithms to compute…

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Adaptive normalization for IPW estimation

逆概率加权估计的自适应归一化

Inverse probability weighting (IPW) is a general tool in survey sampling and causal inference, used both in Horvitz-Thompson estimators, which normalize by the sample size, and Hájek/self-normalized estimators, which normalize by the sum of the inverse probability weights. In this work we study a family of IPW estimators, first proposed by Trotter and Tukey in the context of Monte Carlo problems, that are normalized by an affine combination of these two terms. We show how…

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Hypothetical estimands in clinical trials: a unification of causal inference and missing data methods

临床试验中的假想目标量:因果推断与缺失数据方法的统一

The ICH E9 addendum introduces the term intercurrent event to refer to events that happen after randomisation and that can either preclude observation of the outcome of interest or affect its interpretation. It proposes five strategies for handling intercurrent events to form an estimand but does not suggest statistical methods for estimation. In this paper we focus on the hypothetical strategy, where the treatment effect is defined under the hypothetical scenario in which…

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Synthetic Difference in Differences

合成双重差分

We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference in differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this "synthetic difference in differences" estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the…

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Designing efficient randomized trials: power and sample size calculation when using semiparametric efficient estimators

高效随机试验设计:使用半参数有效估计量时的功效与样本量计算

Trials enroll a large number of subjects in order to attain power, making them expensive and time-consuming. Sample size calculations are often performed with the assumption of an unadjusted analysis, even if the trial analysis plan specifies a more efficient estimator (e.g. ANCOVA). This leads to conservative estimates of required sample sizes and an opportunity for savings. Here we show that a relatively simple formula can be used to estimate the power of any two-arm,…

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Partial Identification and Inference in Duration Models with Endogenous Censoring

内生删失持续时间模型的部分识别与推断

This paper studies identification and inference in transformation models with endogenous censoring. Many kinds of duration models, such as the accelerated failure time model, proportional hazard model, and mixed proportional hazard model, can be viewed as transformation models. We allow the censoring of a duration outcome to be arbitrarily correlated with observed covariates and unobserved heterogeneity. We impose no parametric restrictions on either the transformation…

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Estimating Average Treatment Effects with Support Vector Machines

使用支持向量机估计平均处理效应

Support vector machine (SVM) is one of the most popular classification algorithms in the machine learning literature. We demonstrate that SVM can be used to balance covariates and estimate average causal effects under the unconfoundedness assumption. Specifically, we adapt the SVM classifier as a kernel-based weighting procedure that minimizes the maximum mean discrepancy between the treatment and control groups while simultaneously maximizing effective sample size. We also…

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