Consider a situation with two treatments, the first of which is randomized but the second is not, and the multifactor version of this. Interest is in treatment effects, defined using standard factorial notation. We define estimators for the treatment effects and explore their properties when there is information about the nonrandomized treatment assignment and when there is no information on the assignment of the nonrandomized treatment. We show when and how hidden treatments can bias estimators and inflate their sampling variances.
An important step for any causal inference study design is understanding the distribution of the treated and control subjects in terms of measured baseline covariates. However, not all baseline variation is equally important. In the observational context, balancing on baseline variation summarized in a propensity score can help reduce bias due to self-selection. In both observational and experimental studies, controlling baseline variation associated with the expected outcomes can help increase the precision of causal effect estimates. We propose a set of visualizations which decompose the spa…
Posterior Predictive Treatment Assignment for Estimating Causal Effects with Limited Overlap
使用倾向得分估计因果效应依赖于在估计的每个倾向得分值下观察到的经处理和未经处理单位的可用性。在强混杂的环境中，倾向得分分布中有限的所谓“重叠”可能会破坏估计因果效应的经验基础，并产生现有估计量的不稳定的有限样本性能。我们提出了一个贝叶斯过程，旨在估计因果效应的设置有有限的重叠倾向得分分布。我们的方法依赖于后验预测治疗分配（PPTA），这是一个来自倾向得分的量，但在估计因果关系中起着不同的作用。我们使用PPTA来估计因果效应，通过边缘化每个观察是否是未知子集的成员的不确定性，可以假设治疗分配无混淆。由此产生的后验分布取决于估计每个观察结果的因果效应的经验基础，并且与Li et al.（2016）最近提出的“重叠权重”具有共性。我们发现，PPTA方法可以被解释为现有的ad-hoc方法，如修剪的基础上的倾向得分或截断的治疗权重的逆概率的随机版本，并突出几个实际的优势，包括不确定性量化和改进的有限样本性能。我们说明了在美国的发电厂减少有害污染排放的技术的有效性评估的方法。
This paper provides a link between causal inference and machine learning techniques - specifically, Classification and Regression Trees (CART) - in observational studies where the receipt of the treatment is not randomized, but the assignment to the treatment can be assumed to be randomized (irregular assignment mechanism). The paper contributes to the growing applied machine learning literature on causal inference, by proposing a modified version of the Causal Tree (CT) algorithm to draw causal inference from an irregular assignment mechanism. The proposed method is developed by merging the C…
Clinical studies sometimes encounter truncation by death, rendering outcomes undefined. Statistical analysis based solely on observed survivors may give biased results because the characteristics of survivors differ between treatment groups. By principal stratification, the survivor average causal effect was proposed as a causal estimand defined in always-survivors. However, this estimand is not identifiable when there is unmeasured confounding between the treatment assignment and survival or outcome process. In this paper, we consider the comparison between an aggressive treatment and a conse…
We consider the problem of estimating causal DAG models from a mix of observational and interventional data, when the intervention targets are partially or completely unknown. This problem is highly relevant for example in genomics, since gene knockout technologies are known to have off-target effects. We characterize the interventional Markov equivalence class of DAGs that can be identified from interventional data with unknown intervention targets. In addition, we propose a provably consistent algorithm for learning the interventional Markov equivalence class from such data. The proposed alg…
Unquantified sources of uncertainty in observational causal analyses can break the integrity of the results. One would never want another analyst to repeat a calculation with the same dataset, using a seemingly identical procedure, only to find a different conclusion. However, as we show in this work, there is a typical source of uncertainty that is essentially never considered in observational causal studies: the choice of match assignment for matched groups, that is, which unit is matched to which other unit before a hypothesis test is conducted. The choice of match assignment is anything bu…
Marginal structural models (MSM) with inverse probability weighting (IPW) are used to estimate causal effects of time-varying treatments, but can result in erratic finite-sample performance when there is low overlap in covariate distributions across different treatment patterns. Modifications to IPW which target the average treatment effect (ATE) estimand either introduce bias or rely on unverifiable parametric assumptions and extrapolation. This paper extends an alternate estimand, the average treatment effect on the overlap population (ATO) which is estimated on a sub-population with a reaso…
Regression discontinuity designs (RDDs) are a common quasi-experiment in economics and statistics. The most popular methodologies for analyzing RDDs utilize continuity-based assumptions and local polynomial regression, but recent works have developed alternative assumptions based on local randomization. The local randomization framework avoids modeling assumptions by instead placing assumptions on the assignment mechanism near the cutoff. However, most works have focused on completely randomized assignment mechanisms, which posit that propensity scores are equal for all units near the cutoff. …
Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes and treatment assignment mechanisms are unknown in observational studies, an individual's treatment efficacy is a counterfactual, and the existence of selection bias is often unavoidable. We propose a Bayesian framework for identifying subgroup counterfactual benefits of dynamic treatment regimes by adapting Bayesian g-computation algorithm (J. Robins, 1986; …
Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects when all potential confounders are observed, but thecontrol variables are unknown. When the data-generating process belongs to the class of acyclical linear structural causal models, we prove that themethod yields asymptotically valid confidence intervals. Our results build upon a smooth characterization of linear directed acyclic graphs. We verify the capabi…
With multiple potential mediators on the causal pathway from a treatment to an outcome, we consider the problem of decomposing the effects along multiple possible causal path(s) through each distinct mediator. Under Pearl's path-specific effects framework (Pearl, 2001; Avin et al., 2005), such fine-grained decompositions necessitate stringent assumptions, such as correctly specifying the causal structure among the mediators, and there being no unobserved confounding among the mediators. In contrast, interventional direct and indirect effects for multiple mediators (Vansteelandt and Daniel, 201…
The development of high-throughput sequencing and targeted therapies has led to the emergence of personalized medicine: a patient's molecular profile or the presence of a specific biomarker of drug response will correspond to a treatment recommendation made either by a physician or by a treatment assignment algorithm. The growing number of such algorithms raises the question of how to quantify their clinical impact knowing that a personalized medicine strategy will inherently include different versions of treatment. We thus specify an appropriate causal framework with multiple versions of trea…
A common assumption in causal inference is that random treatment assignment ensures that potential outcomes are independent of treatment, or in one word, unconfoundedness. This paper highlights that randomization and unconfoundedness are separate properties, and neither implies the other. A study with random treatment assignment does not have to be unconfounded, and a study with deterministic assignment can still be unconfounded. A corollary is that a propensity score is not the same thing as a treatment assignment probability. These facts should not be taken as arguments against randomization…
ETH Zürich（苏黎世联邦理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；IBM Research Zürich（苏黎世IBM研究院）
Inferring causal structures from experimentation is a central task in many domains. For example, in biology, recent advances allow us to obtain single-cell expression data under multiple interventions such as drugs or gene knockouts. However, the targets of the interventions are often uncertain or unknown and the number of observations limited. As a result, standard causal discovery methods can no longer be reliably used. To fill this gap, we propose a Bayesian framework (BaCaDI) for discovering and reasoning about the causal structure that underlies data generated under various unknown experi…
Describing the causal relations governing a system is a fundamental task in many scientific fields, ideally addressed by experimental studies. However, obtaining data under intervention scenarios may not always be feasible, while discovering causal relations from purely observational data is notoriously challenging. In certain settings, such as genomics, we may have data from heterogeneous study conditions, with soft (partial) interventions only pertaining to a subset of the study variables, whose effects and targets are possibly unknown. Combining data from experimental and observational stud…
Scientific researchers utilize randomized experiments to draw casual statements. Most early studies as well as current work on experiments with sequential intervention decisions has been focusing on estimating the causal effects among sequential treatments, ignoring the non-compliance issues that experimental units might not be compliant with the treatment assignments that they were originally allocated. A series of methodologies have been developed to address the non-compliance issues in randomized experiments with time-fixed treatment. However, to our best knowledge, there is little literatu…
Increasingly, there is a marked interest in estimating causal effects under network interference due to the fact that interference manifests naturally in networked experiments. However, network information generally is available only up to some level of error. We study the propagation of such errors to estimators of average causal effects under network interference. Specifically, assuming a four-level exposure model and Bernoulli random assignment of treatment, we characterize the impact of network noise on the bias and variance of standard estimators in homogeneous and inhomogeneous networks.…
Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes of the same units under different treatment conditions. Because for each unit at most one of the potential outcomes is observed and the rest are missing, causal inference is inherently a missing data problem. Indeed, there is a close analogy in the terminology and the inferential framework between causal inference and missing data. Despite the intrinsic con…
In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable $Y$ when the causal variable $X$ is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In …
This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of causal effects, and sensitivity analysis. We highlight issues that are unique to Bayesian causal inference, including the role of the propensity score, definition of identifiability, the choice of priors in both low and high dimensional regimes. We point out the central role of covariate overlap and more generally the design stage in Bayesian causal inference. W…
Pragmatic randomized trials are designed to provide evidence for clinical decision-making rather than regulatory approval. Common features of these trials include the inclusion of heterogeneous or diverse patient populations in a wide range of care settings, the use of active treatment strategies as comparators, unblinded treatment assignment, and the study of long-term, clinically relevant outcomes. These features can greatly increase the usefulness of the trial results for patients, clinicians, and other stakeholders. However, these features also introduce an increased risk of non-adherence,…
We develop methodology for causal inference in observational studies when using propensity score subclassification on data constructed with probabilistic record linkage techniques. We focus on scenarios where covariates and binary treatment assignments are in one file and outcomes are in another file, and the goal is to estimate an additive treatment effect by merging the files. We assume that the files can be linked using variables common to both files, e.g., names or birth dates, but that links are subject to errors, e.g., due to reporting errors in the linking variables. We develop methodol…
Interference exists when a unit's outcome depends on another unit's treatment assignment. For example, intensive policing on one street could have a spillover effect on neighboring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a given null hypothesis is sharp. Finding these subsets is challenging, however, and existing methods are limited to special cases or …
Arizona State University（亚利桑那州立大学）；University of Virginia（弗吉尼亚大学）
Counterfactual evaluation of novel treatment assignment functions (e.g., advertising algorithms and recommender systems) is one of the most crucial causal inference problems for practitioners. Traditionally, randomized controlled trials (A/B tests) are performed to evaluate treatment assignment functions. However, such trials can be time-consuming, expensive, and even unethical in some cases. Therefore, offline counterfactual evaluation of treatment assignment functions becomes a pressing issue because a massive amount of observational data is available in today's big data era. Counterfactual …
Hong Kong University of Science and Technology（香港科技大学）；New York University（纽约大学）；Spotify
This study presents a systematic comparison of methods for individual treatment assignment, a general problem that arises in many applications and has received significant attention from economists, computer scientists, and social scientists. We group the various methods proposed in the literature into three general classes of algorithms (or metalearners): learning models to predict outcomes (the O-learner), learning models to predict causal effects (the E-learner), and learning models to predict optimal treatment assignments (the A-learner). We compare the metalearners in terms of (1) their l…
It is often of interest in observational studies to measure the causal effect of a treatment on time-to-event outcomes. In a medical setting, observational studies commonly involve patients who initiate medication therapy and others who do not, and the goal is to infer the effect of medication therapy on time until recovery, a pre-defined level of improvement, or some other time-to-event outcome. A difficulty with such studies is that the notion of a medication initiation time does not exist in the control group. We propose an approach to infer causal effects of an intervention in longitudinal…
This paper presents a randomization-based framework for estimating causal effects under interference between units, motivated by challenges that arise in analyzing experiments on social networks. The framework integrates three components: (i) an experimental design that defines the probability distribution of treatment assignments, (ii) a mapping that relates experimental treatment assignments to exposures received by units in the experiment, and (iii) estimands that make use of the experiment to answer questions of substantive interest. We develop the case of estimating average unit-level cau…
