现代纵向研究在许多时间点收集特征数据,通常是相同的样本大小顺序。这些研究通常受到{辍学}和积极违规的影响。我们通过概括近期增量干预的效果(转换倾向分数而不是设置治疗价值)来解决这些问题,以适应多种结果和主题辍学。当条件忽略(不需要治疗阳性)时,我们给出了识别表达式的增量干预效果,并导出估计这些效果的非参数效率。然后我们提出了高效的非参数估计器,表明它们以快速参数速率收敛并产生均匀的推理保证,即使在较慢的速率下灵活估计滋扰函数。我们还研究了新型无限时间范围设置中的更传统的确定性效果的增量干预效应的方差比,其中时间点的数量可以随着样本大小而生长,并显示增量干预效果在统计精度下产生近乎指数的收益这个设置。最后,我们通过模拟得出结论,并在研究低剂量阿司匹林对妊娠结果的研究中进行了方法。
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历史上用于结果很少或数据收集昂贵的设置,与结果相关的采样与许多现代环境有关,在许多现代设置中,数据可用于偏见的目标人群(例如公共行政数据)。在依赖结果的采样下,未确定诸如平均风险差异和平均风险比率之类的常见效应措施,但条件上的优势比为。条件优势比的聚合具有挑战性,因为通常未确定汇总措施。此外,边际优势比可以大于所有条件优势比。如果我们使用标准算术平均值的替代聚合,则可以避免这种所谓的优势比的非碰撞能力。我们提供了一种对可折叠性的新定义,该定义使这种聚合方法的选择显式,并证明了几何汇总的优势比是可折叠的。我们描述了如何部分识别,估计和推断在结果依赖性抽样下的几何比值比。我们提出的估计器基于有效的影响函数,因此具有双重稳健风格的性能。
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有许多可用于选择优先考虑治疗的可用方法,包括基于治疗效果估计,风险评分和手工制作规则的遵循申请。我们将秩加权平均治疗效应(RATY)指标作为一种简单常见的指标系列,用于比较水平竞争范围的治疗优先级规则。对于如何获得优先级规则,率是不可知的,并且仅根据他们在识别受益于治疗中受益的单位的方式进行评估。我们定义了一系列速率估算器,并证明了一个中央限位定理,可以在各种随机和观测研究环境中实现渐近精确的推断。我们为使用自主置信区间的使用提供了理由,以及用于测试关于治疗效果中的异质性的假设的框架,与优先级规则相关。我们对速率的定义嵌套了许多现有度量,包括QINI系数,以及我们的分析直接产生了这些指标的推论方法。我们展示了我们从个性化医学和营销的示例中的方法。在医疗环境中,使用来自Sprint和Accor-BP随机对照试验的数据,我们发现没有明显的证据证明异质治疗效果。另一方面,在大量的营销审判中,我们在一些数字广告活动的治疗效果中发现了具有的强大证据,并证明了如何使用率如何比较优先考虑估计风险的目标规则与估计治疗效益优先考虑的目标规则。
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In many investigations, the primary outcome of interest is difficult or expensive to collect. Examples include long-term health effects of medical interventions, measurements requiring expensive testing or follow-up, and outcomes only measurable on small panels as in marketing. This reduces effective sample sizes for estimating the average treatment effect (ATE). However, there is often an abundance of observations on surrogate outcomes not of primary interest, such as short-term health effects or online-ad click-through. We study the role of such surrogate observations in the efficient estimation of treatment effects. To quantify their value, we derive the semiparametric efficiency bounds on ATE estimation with and without the presence of surrogates and several intermediary settings. The difference between these characterizes the efficiency gains from optimally leveraging surrogates. We study two regimes: when the number of surrogate observations is comparable to primary-outcome observations and when the former dominates the latter. We take an agnostic missing-data approach circumventing strong surrogate conditions previously assumed. To leverage surrogates' efficiency gains, we develop efficient ATE estimation and inference based on flexible machine-learning estimates of nuisance functions appearing in the influence functions we derive. We empirically demonstrate the gains by studying the long-term earnings effect of job training.
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预测一组结果 - 而不是独特的结果 - 是统计学习中不确定性定量的有前途的解决方案。尽管有关于构建具有统计保证的预测集的丰富文献,但适应未知的协变量转变(实践中普遍存在的问题)还是一个严重的未解决的挑战。在本文中,我们表明具有有限样本覆盖范围保证的预测集是非信息性的,并提出了一种新型的无灵活分配方法PredSet-1Step,以有效地构建了在未知协方差转移下具有渐近覆盖范围保证的预测集。我们正式表明我们的方法是\ textIt {渐近上可能是近似正确},对大型样本的置信度有很好的覆盖误差。我们说明,在南非队列研究中,它在许多实验和有关HIV风险预测的数据集中实现了名义覆盖范围。我们的理论取决于基于一般渐近线性估计器的WALD置信区间覆盖范围的融合率的新结合。
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在TAN(2006)边缘敏感模型下,在不观察到的混淆存在下构建平均处理效应的界限问题。结合涉及对冲倾向分数的现有表征具有对问题的新的分布稳健特征,我们提出了我们称之为“双重有效/双重尖锐”(DVD)估计的这些界限的新颖估算器。双重清晰度对应于DVD估计始终估计灵敏度模型所暗示的最有可能(即,夏普)的界限,即使当所有滋扰参数都适当一致时,即使在两个滋扰参数中的一个被击败并实现半污染参数之一。双倍有效性是部分识别的全新财产:DVD估计仍然提供有效,但即使在大多数滋扰参数都被遗漏时,仍然没有锐利。实际上,即使在DVDS点估计无法渐近正常的情况下,标准沃尔德置信区间也可能保持有效。在二进制结果的情况下,DVD估计是特别方便的并且在结果回归和倾向评分方面具有闭合形式的表达。我们展示了模拟研究中的DVD估计,以及对右心导管插入的案例研究。
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Statistical risk assessments inform consequential decisions such as pretrial release in criminal justice, and loan approvals in consumer finance. Such risk assessments make counterfactual predictions, predicting the likelihood of an outcome under a proposed decision (e.g., what would happen if we approved this loan?). A central challenge, however, is that there may have been unmeasured confounders that jointly affected past decisions and outcomes in the historical data. This paper proposes a tractable mean outcome sensitivity model that bounds the extent to which unmeasured confounders could affect outcomes on average. The mean outcome sensitivity model partially identifies the conditional likelihood of the outcome under the proposed decision, popular predictive performance metrics (e.g., accuracy, calibration, TPR, FPR), and commonly-used predictive disparities. We derive their sharp identified sets, and we then solve three tasks that are essential to deploying statistical risk assessments in high-stakes settings. First, we propose a doubly-robust learning procedure for the bounds on the conditional likelihood of the outcome under the proposed decision. Second, we translate our estimated bounds on the conditional likelihood of the outcome under the proposed decision into a robust, plug-in decision-making policy. Third, we develop doubly-robust estimators of the bounds on the predictive performance of an existing risk assessment.
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我们提出了用于中介分析和动态治疗效果的内核脊回归估计。我们允许治疗,协变量和介质是离散或连续的,低,高或无限的尺寸。我们在内核矩阵操作方面提出了具有封闭式解决方案的依据,增量和分布的估算者。对于连续治疗案例,我们证明了具有有限样本速率的均匀一致性。对于离散处理案例,我们证明了根 - N一致性,高斯近似和半占用效率。我们进行仿真,然后估计美国职务团计划的介导和动态治疗效果,弱势青少年。
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在制定政策指南时,随机对照试验(RCT)代表了黄金标准。但是,RCT通常是狭窄的,并且缺乏更广泛的感兴趣人群的数据。这些人群中的因果效应通常是使用观察数据集估算的,这可能会遭受未观察到的混杂和选择偏见。考虑到一组观察估计(例如,来自多项研究),我们提出了一个试图拒绝偏见的观察性估计值的元偏值。我们使用验证效应,可以从RCT和观察数据中推断出的因果效应。在拒绝未通过此测试的估计器之后,我们对RCT中未观察到的亚组的外推性效应产生了保守的置信区间。假设至少一个观察估计量在验证和外推效果方面是渐近正常且一致的,我们为我们算法输出的间隔的覆盖率概率提供了保证。为了促进在跨数据集的因果效应运输的设置中,我们给出的条件下,即使使用灵活的机器学习方法用于估计滋扰参数,群体平均治疗效应的双重稳定估计值也是渐近的正常。我们说明了方法在半合成和现实世界数据集上的特性,并表明它与标准的荟萃分析技术相比。
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In various fields of data science, researchers are often interested in estimating the ratio of conditional expectation functions (CEFR). Specifically in causal inference problems, it is sometimes natural to consider ratio-based treatment effects, such as odds ratios and hazard ratios, and even difference-based treatment effects are identified as CEFR in some empirically relevant settings. This chapter develops the general framework for estimation and inference on CEFR, which allows the use of flexible machine learning for infinite-dimensional nuisance parameters. In the first stage of the framework, the orthogonal signals are constructed using debiased machine learning techniques to mitigate the negative impacts of the regularization bias in the nuisance estimates on the target estimates. The signals are then combined with a novel series estimator tailored for CEFR. We derive the pointwise and uniform asymptotic results for estimation and inference on CEFR, including the validity of the Gaussian bootstrap, and provide low-level sufficient conditions to apply the proposed framework to some specific examples. We demonstrate the finite-sample performance of the series estimator constructed under the proposed framework by numerical simulations. Finally, we apply the proposed method to estimate the causal effect of the 401(k) program on household assets.
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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 treatment effect, and have an asymptotically Gaussian and centered sampling distribution. We also discuss a practical method for constructing asymptotic confidence intervals for the true treatment effect that are centered at the causal forest estimates. Our theoretical results rely on a generic Gaussian theory for a large family of random forest algorithms. To our knowledge, this is the first set of results that allows any type of random forest, including classification and regression forests, to be used for provably valid statistical inference. In experiments, we find causal forests to be substantially more powerful than classical methods based on nearest-neighbor matching, especially in the presence of irrelevant covariates.
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在本文中,我们提出了一种非参数估计的方法,并推断了一般样本选择模型中因果效应参数的异质界限,初始治疗可能会影响干预后结果是否观察到。可观察到的协变量可能会混淆治疗选择,而观察结果和不可观察的结果可能会混淆。该方法提供条件效应界限作为策略相关的预处理变量的功能。它允许对身份不明的条件效应曲线进行有效的统计推断。我们使用灵活的半参数脱偏机学习方法,该方法可以适应柔性功能形式和治疗,选择和结果过程之间的高维混杂变量。还提供了易于验证的高级条件,以进行估计和错误指定的鲁棒推理保证。
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基于中央限制定理(CLT)的置信区间是经典统计的基石。尽管仅渐近地有效,但它们是无处不在的,因为它们允许在非常弱的假设下进行统计推断,即使不可能进行非反应性推断,通常也可以应用于问题。本文引入了这种渐近置信区间的时间均匀类似物。为了详细说明,我们的方法采用置信序列(CS)的形式 - 随着时间的推移均匀有效的置信区间序列。 CSS在任意停止时间时提供有效的推断,与需要预先确定样本量的经典置信区间不同,因此没有受到“窥视”数据的惩罚。文献中现有的CSS是非肿瘤的,因此不享受上述渐近置信区间的广泛适用性。我们的工作通过给出“渐近CSS”的定义来弥合差距,并得出仅需要类似CLT的假设的通用渐近CS。虽然CLT在固定样本量下近似于高斯的样本平均值的分布,但我们使用强大的不变性原理(来自Komlos,Major和Tusnady的1970年代的开创性工作),按照整个样品平均过程均匀地近似于整个样品平均过程。隐性的高斯过程。我们通过在观察性研究中基于双重稳健的估计量来得出非参数渐近级别的CSS来证明它们的实用性,即使在固定的时间方案中,也可能不存在非催化方法(由于混淆偏见)。这些使双重强大的因果推断可以连续监测并自适应地停止。
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我们考虑在估计涉及依赖参数的高维滋扰的估计方程中估计一个低维参数。一个中心示例是因果推理中(局部)分位数处理效应((L)QTE)的有效估计方程,涉及在分位数以估计的分位数评估的协方差累积分布函数。借记机学习(DML)是一种使用灵活的机器学习方法估算高维滋扰的数据分解方法,但是将其应用于参数依赖性滋扰的问题是不切实际的。对于(L)QTE,DML要求我们学习整个协变量累积分布函数。相反,我们提出了局部偏见的机器学习(LDML),该学习避免了这一繁重的步骤,并且只需要对参数进行一次初始粗糙猜测而估算烦恼。对于(L)QTE,LDML仅涉及学习两个回归功能,这是机器学习方法的标准任务。我们证明,在松弛速率条件下,我们的估计量与使用未知的真实滋扰的不可行的估计器具有相同的有利渐近行为。因此,LDML值得注意的是,当我们必须控制许多协变量和/或灵活的关系时,如(l)QTES在((l)QTES)中,实际上可以有效地估算重要数量,例如(l)QTES。
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治疗效应估计的因果推理方法通常假设独立的实验单位。但是,由于实验单元可能会相互作用,因此这种假设通常值得怀疑。我们开发了增强的反可能性加权(AIPW),以估计和推断因果治疗对依赖观察数据的影响。我们的框架涵盖了网络中相互作用的单位引起的溢出效应的非常普遍的案例。我们使用插件机学习来估计无限维的滋扰成分,导致一致的治疗效应估计器以参数速率收敛,渐近地遵循高斯分布。
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我们推出了一般,但简单,尖锐的界限,用于广泛的因果参数的省略可变偏置,可以被识别为结果的条件期望函数的线性功能。这些功能包括许多传统的因果推断研究中的调查目标,例如(加权)平均潜在结果,平均治疗效果(包括亚组效应,例如对处理的效果),(加权)平均值来自协变态分布的转变的衍生品和政策影响 - 所有是一般的非参数因果模型。我们的建设依赖于目标功能的riesz-frechet表示。具体而言,我们展示了偏差的绑定如何仅取决于潜在变量在结果中创建的附加变型以及用于感兴趣的参数的RIESZ代表。此外,在许多重要病例中(例如,部分线性模型中的平均治疗效果,或在具有二元处理的不可分配模型中),所示的界定依赖于两个易于解释的数量:非参数部分$ r ^ 2 $(Pearson的相关性与治疗和结果的未观察变量的比例“。因此,对省略变量的最大解释力(在解释处理和结果变化时)的简单合理性判断足以将整体界限放置在偏置的尺寸上。最后,利用脱叠机器学习,我们提供灵活有效的统计推理方法,以估计从观察到的分布识别的界限的组件。
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在因果推理和强盗文献中,基于观察数据的线性功能估算线性功能的问题是规范的。我们分析了首先估计治疗效果函数的广泛的两阶段程序,然后使用该数量来估计线性功能。我们证明了此类过程的均方误差上的非反应性上限:这些边界表明,为了获得非反应性最佳程序,应在特定加权$ l^2 $中最大程度地估算治疗效果的误差。 -规范。我们根据该加权规范的约束回归分析了两阶段的程序,并通过匹配非轴突局部局部最小值下限,在有限样品中建立了实例依赖性最优性。这些结果表明,除了取决于渐近效率方差之外,最佳的非质子风险除了取决于样本量支持的最富有函数类别的真实结果函数与其近似类别之间的加权规范距离。
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Testing the significance of a variable or group of variables $X$ for predicting a response $Y$, given additional covariates $Z$, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for $X$ is non-zero. However, when the model is misspecified, the test may have poor power, for example when $X$ is involved in complex interactions, or lead to many false rejections. In this work we study the problem of testing the model-free null of conditional mean independence, i.e. that the conditional mean of $Y$ given $X$ and $Z$ does not depend on $X$. We propose a simple and general framework that can leverage flexible nonparametric or machine learning methods, such as additive models or random forests, to yield both robust error control and high power. The procedure involves using these methods to perform regressions, first to estimate a form of projection of $Y$ on $X$ and $Z$ using one half of the data, and then to estimate the expected conditional covariance between this projection and $Y$ on the remaining half of the data. While the approach is general, we show that a version of our procedure using spline regression achieves what we show is the minimax optimal rate in this nonparametric testing problem. Numerical experiments demonstrate the effectiveness of our approach both in terms of maintaining Type I error control, and power, compared to several existing approaches.
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Strategic test allocation plays a major role in the control of both emerging and existing pandemics (e.g., COVID-19, HIV). Widespread testing supports effective epidemic control by (1) reducing transmission via identifying cases, and (2) tracking outbreak dynamics to inform targeted interventions. However, infectious disease surveillance presents unique statistical challenges. For instance, the true outcome of interest - one's positive infectious status, is often a latent variable. In addition, presence of both network and temporal dependence reduces the data to a single observation. As testing entire populations regularly is neither efficient nor feasible, standard approaches to testing recommend simple rule-based testing strategies (e.g., symptom based, contact tracing), without taking into account individual risk. In this work, we study an adaptive sequential design involving n individuals over a period of {\tau} time-steps, which allows for unspecified dependence among individuals and across time. Our causal target parameter is the mean latent outcome we would have obtained after one time-step, if, starting at time t given the observed past, we had carried out a stochastic intervention that maximizes the outcome under a resource constraint. We propose an Online Super Learner for adaptive sequential surveillance that learns the optimal choice of tests strategies over time while adapting to the current state of the outbreak. Relying on a series of working models, the proposed method learns across samples, through time, or both: based on the underlying (unknown) structure in the data. We present an identification result for the latent outcome in terms of the observed data, and demonstrate the superior performance of the proposed strategy in a simulation modeling a residential university environment during the COVID-19 pandemic.
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估计平均因果效应的理想回归(如果有)是什么?我们在离散协变量的设置中研究了这个问题,从而得出了各种分层估计器的有限样本方差的表达式。这种方法阐明了许多广泛引用的结果的基本统计现象。我们的博览会结合了研究因果效应估计的三种不同的方法论传统的见解:潜在结果,因果图和具有加性误差的结构模型。
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