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Causal Estimation with Functional Confounders

函数型混杂变量下的因果估计

Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting, ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions…

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Constructing valid instrumental variables in generalized linear causal models from directed acyclic graphs

从有向无环图构造广义线性因果模型的有效工具变量

Unlike other techniques of causality inference, the use of valid instrumental variables can deal with unobserved sources of both variable errors, variable omissions, and sampling bias, and still arrive at consistent estimates of average treatment effects. The only problem is to find the valid instruments. Using the definition of Pearl (2009) of valid instrumental variables, a formal condition for validity can be stated for variables in generalized linear causal models. The…

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Confidence Intervals for Policy Evaluation in Adaptive Experiments

自适应实验中政策评估的置信区间

Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials. Inferential challenges are exacerbated when our parameter of interest differs from the parameter the trial was designed to target, such as when we are interested in estimating the value of a sub-optimal treatment after running a trial to determine…

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Linear programming approach to nonparametric inference under shape restrictions: with an application to regression kink designs

形状约束下非参数推断的线性规划方法:回归折点设计应用

We develop a novel method of constructing confidence bands for nonparametric regression functions under shape constraints. This method can be implemented via a linear programming, and it is thus computationally appealing. We illustrate a usage of our proposed method with an application to the regression kink design (RKD). Econometric analyses based on the RKD often suffer from wide confidence intervals due to slow convergence rates of nonparametric derivative estimators. We…

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Sensitivity Analysis for Unmeasured Confounding via Effect Extrapolation

通过效应外推分析未测量混杂的敏感性

Inferring the causal effect of a non-randomly assigned exposure on an outcome requires adjusting for common causes of the exposure and outcome to avoid biased conclusions. Notwithstanding the efforts investigators routinely make to measure and adjust for such common causes (or confounders), some confounders typically remain unmeasured, raising the prospect of biased inference in observational studies. Therefore, it is crucial that investigators can practically assess their…

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Nonparametric Analysis of Delayed Treatment Effects using Single-Crossing Constraints

利用单交叉约束非参数分析延迟治疗效应

Clinical trials involving novel immuno-oncology (IO) therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two…

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Local Regression Distribution Estimators

局部回归分布估计量

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance…

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The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy

越早越好:意大利疫情封锁挽救生命的估计

This paper estimates the effects of non-pharmaceutical interventions - mainly, the lockdown - on the COVID-19 mortality rate for the case of Italy, the first Western country to impose a national shelter-in-place order. We use a new estimator, the Augmented Synthetic Control Method (ASCM), that overcomes some limits of the standard Synthetic Control Method (SCM). The results are twofold. From a methodological point of view, the ASCM outperforms the SCM in that the latter…

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Semi-parametric estimation of biomarker age trends with endogenous medication use in longitudinal data

内生用药下纵向生物标志物年龄趋势的半参数估计

In cohort studies, non-random medication use can pose barriers to estimation of the natural history trend in a mean biomarker value (namely, the association between a predictor of interest and a biomarker outcome that would be observed in the absence of biomarker-specific treatment). Common causes of treatment and outcomes are often unmeasured, obscuring our ability to easily account for medication use with commonly invoked assumptions such as ignorability. Further, absent…

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When the ends don't justify the means: Learning a treatment strategy to prevent harmful indirect effects

当结果不足以证明手段合理:学习避免有害间接效应的治疗策略

There is a growing literature on finding so-called optimal treatment rules, which are rules by which to assign treatment to individuals based on an individual's characteristics, such that a desired outcome is maximized. A related goal entails identifying individuals who are predicted to have a harmful indirect effect (the effect of treatment on an outcome through mediators) even in the presence of an overall beneficial effect of the treatment on the outcome. In some cases,…

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Sequential causal inference in a single world of connected units

关联个体单一世界中的序贯因果推断

We consider adaptive designs for a trial involving N individuals that we follow along T time steps. We allow for the variables of one individual to depend on its past and on the past of other individuals. Our goal is to learn a mean outcome, averaged across the N individuals, that we would observe, if we started from some given initial state, and we carried out a given sequence of counterfactual interventions for $τ$ time steps. We show how to identify a statistical…

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Modeling Treatment Effect Modification in Multidrug-Resistant Tuberculosis in an Individual Patient Data Meta-Analysis

耐多药结核病个体患者数据元分析中的治疗效应修饰建模

Effect modification occurs while the effect of the treatment is not homogeneous across the different strata of patient characteristics. When the effect of treatment may vary from individual to individual, precision medicine can be improved by identifying patient covariates to estimate the size and direction of the effect at the individual level. However, this task is statistically challenging and typically requires large amounts of data. Investigators may be interested in…

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Causal Gradient Boosting: Boosted Instrumental Variable Regression

因果梯度提升:提升式工具变量回归

Recent advances in the literature have demonstrated that standard supervised learning algorithms are ill-suited for problems with endogenous explanatory variables. To correct for the endogeneity bias, many variants of nonparameteric instrumental variable regression methods have been developed. In this paper, we propose an alternative algorithm called boostIV that builds on the traditional gradient boosting algorithm and corrects for the endogeneity bias. The algorithm is…

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Weighted Approach for Estimating Effects in Principal Strata with Missing Data for a Categorical Post-Baseline Variable in Randomized Controlled Trials

随机试验中分类基线后变量缺失时主分层效应的加权估计

This research was motivated by studying anti-drug antibody (ADA) formation and its potential impact on long-term benefit of a biologic treatment in a randomized controlled trial, in which ADA status was not only unobserved in the control arm but also in a subset of patients from the experimental treatment arm. Recent literature considers the principal stratum estimand strategy to estimate treatment effect in groups of patients defined by an intercurrent status, i.e. in…

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Kernel-Distance-Based Covariate Balancing

基于核距离的协变量平衡

A common concern in observational studies focuses on properly evaluating the causal effect, which usually refers to the average treatment effect or the average treatment effect on the treated. In this paper, we propose a data preprocessing method, the Kernel-distance-based covariate balancing, for observational studies with binary treatments. This proposed method yields a set of unit weights for the treatment and control groups, respectively, such that the reweighted…

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Regression Discontinuity Design with Many Thresholds

具有多个阈值的断点回归设计

Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of individuals local to existing cutoffs. However, researchers often want to make inferences on more meaningful ATEs, computed over general counterfactual distributions of individuals,…

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COVID-19 spreading in financial networks: A semiparametric matrix regression model

COVID-19 在金融网络中的传播:半参数矩阵回归模型

Network models represent a useful tool to describe the complex set of financial relationships among heterogeneous firms in the system. In this paper, we propose a new semiparametric model for temporal multilayer causal networks with both intra- and inter-layer connectivity. A Bayesian model with a hierarchical mixture prior distribution is assumed to capture heterogeneity in the response of the network edges to a set of risk factors including the European COVID-19 cases. We…

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Quasi-Experimental Shift-Share Research Designs

准实验性 Shift-share 研究设计

Many studies use shift-share (or ``Bartik'') instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be…

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Difference-in-Differences with Multiple Time Periods

多时期双重差分

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create…

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Augmented Minimax Linear Estimation

增广极小极大线性估计

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by…

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Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects

异质处理效应下事件研究动态处理效应的估计

To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and…

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Local Linear Forests

局部线性森林

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local linear regression adjustment to better capture smoothness. The resulting procedure, local linear forests, enables us to improve on asymptotic rates of…

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Policy Learning with Observational Data

利用观测数据学习处理分配政策

In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient…

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The role of parallel trends in event study settings: An application to environmental economics

事件研究中平行趋势的作用:环境经济学应用

Difference-in-Differences (DID) research designs usually rely on variation of treatment timing such that, after making an appropriate parallel trends assumption, one can identify, estimate, and make inference about causal effects. In practice, however, different DID procedures rely on different parallel trends assumptions (PTA), and recover different causal parameters. In this paper, we focus on staggered DID (also referred as event-studies) and discuss the role played by…

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