In this paper, we consider recent progress in estimating the average treatment effect when extreme inverse probability weights are present and focus on methods that account for a possible violation of the positivity assumption. These methods aim at estimating the treatment effect on the subpopulation of patients for whom there is a clinical equipoise. We propose a systematic approach to determine their related causal estimands and develop new insights into the properties of the weights targeting such a subpopulation. Then, we examine the roles of overlap weights, matching weights, Shannon's entropy weights, and beta weights. This helps us characterize and compare their underlying estimators, analytically and via simulations, in terms of the accuracy, precision, and root mean squared error. Moreover, we study the asymptotic behaviors of their augmented estimators (that mimic doubly robust estimators), which lead to improved estimations when either the propensity or the regression models are correctly specified. Based on the analytical and simulation results, we conclude that overall overlap weights are preferable to matching weights, especially when there is moderate or extreme violations of the positivity assumption. Finally, we illustrate the methods using a real data example marked by extreme inverse probability weights.
Most causal inference studies rely on the assumption of overlap to estimate population or sample average causal effects. When data exhibit non-overlap, estimation of these estimands requires reliance on model specifications, due to poor data support. All existing methods to address non-overlap, such as trimming or down-weighting data in regions of poor support, change the estimand. In environmental health research, where study results are often intended to influence policy, changes in the estimand can diminish the study's impact, because estimates may not be representative of effects in the po…
Estimating causal effects with propensity scores relies upon the availability of treated and untreated units observed at each value of the estimated propensity score. In settings with strong confounding, limited so-called "overlap" in propensity score distributions can undermine the empirical basis for estimating causal effects and yield erratic finite-sample performance of existing estimators. We propose a Bayesian procedure designed to estimate causal effects in settings where there is limited overlap in propensity score distributions. Our method relies on the posterior predictive treatment …
In most nonrandomized observational studies, differences between treatment groups may arise not only due to the treatment but also because of the effect of confounders. Therefore, causal inference regarding the treatment effect is not as straightforward as in a randomized trial. To adjust for confounding due to measured covariates, a variety of methods based on the potential outcomes framework are used to estimate average treatment effects. One of the key assumptions is treatment positivity, which states that the probability of treatment is bounded away from zero and one for any possible combi…
Causal or unconfounded descriptive comparisons between multiple groups are common in observational studies. Motivated from a racial disparity study in health services research, we propose a unified propensity score weighting framework, the balancing weights, for estimating causal effects with multiple treatments. These weights incorporate the generalized propensity scores to balance the weighted covariate distribution of each treatment group, all weighted toward a common pre-specified target population. The class of balancing weights include several existing approaches such as the inverse prob…
A key condition for obtaining reliable estimates of the causal effect of a treatment is overlap (a.k.a. positivity): the distributions of the features used to perform causal adjustment cannot be too different in the treated and control groups. In cases where overlap is poor, causal effect estimators can become brittle, especially when they incorporate weighting. To address this problem, a number of proposals (including confounder selection or dimension reduction methods) incorporate feature representations to induce better overlap between the treated and control groups. A key concern in these …
Deconfounding Scores and Representation Learning for Causal Effect Estimation with Weak Overlap
University of Oxford（牛津大学）；Google DeepMind（谷歌DeepMind）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Stanford University（斯坦福大学）；Ellison Institute of Technology（埃里森技术研究所）；University of California, Berkeley（加州大学伯克利分校）
In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects, i.e., the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate sh…
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, and therefore both practical and theoretical researchers suggest dropping units with extreme estimated propensity scores. However, existing trimming methods ignore the uncertainty in this design stage and restrict inference only to the trimmed sample, due to the non-smoothness of the trimming. We propose a smooth weighting, which approximate…
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian ran…
A common goal in comparative effectiveness research is to estimate treatment effects on pre-specified subpopulations of patients. Though widely used in medical research, causal inference methods for such subgroup analysis remain underdeveloped, particularly in observational studies. In this article, we develop a suite of analytical methods and visualization tools for causal subgroup analysis. First, we introduce the estimand of subgroup weighted average treatment effect and provide the corresponding propensity score weighting estimator. We show that balancing covariates within a subgroup bound…
Inverse probability weights are commonly used in epidemiology to estimate causal effects in observational studies. Researchers can typically focus on either the average treatment effect or the average treatment effect on the treated with inverse probability weighting estimators. However, when overlap between the treated and control groups is poor, this can produce extreme weights that can result in biased estimates and large variances. One alternative to inverse probability weights are overlap weights, which target the population with the most overlap on observed characteristics. While estimat…
Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest themselves in extremes. This work aims to connect the two fields of causal inference and extreme value theory. We define the causal tail coefficient that captures asymmetries in the extremal dependence of two random variables. In the population case, the causal tail coefficient is shown to reveal the causal structure if the distribution follows a linear structura…
Babylon Health（巴比伦健康）；University College London（伦敦大学学院）
Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based on the assumption that all variables have been jointly measured in a single dataset. In many cases this assumption fails. Previous approaches to overcoming this shortcoming devised algorithms that returned all joint causal structures consistent with the conditional independence information contained in each individual dataset. But, as conditional independen…
The University of Chicago（芝加哥大学）；Google Research（谷歌研究院）
Consider the problem of estimating the causal effect of some attribute of a text document; for example: what effect does writing a polite vs. rude email have on response time? To estimate a causal effect from observational data, we need to adjust for confounding aspects of the text that affect both the treatment and outcome -- e.g., the topic or writing level of the text. These confounding aspects are unknown a priori, so it seems natural to adjust for the entirety of the text (e.g., using a transformer). However, causal identification and estimation procedures rely on the assumption of overla…
The Graduate University for Advanced Studies（综合研究大学院大学）；The Institute of Statistical Mathematics（统计数学研究所）
As an important problem in causal inference, we discuss the identification and estimation of treatment effects (TEs) under limited overlap; that is, when subjects with certain features belong to a single treatment group. We use a latent variable to model a prognostic score which is widely used in biostatistics and sufficient for TEs; i.e., we build a generative prognostic model. We prove that the latent variable recovers a prognostic score, and the model identifies individualized treatment effects. The model is then learned as β-Intact-VAE--a new type of variational autoencoder (VAE). We deriv…
Causal Inference for Heterogeneous Extreme Quantiles with Heavy-Tailed Outcomes
Nanjing University of Information Science and Technology（南京信息工程大学）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Rice University（莱斯大学）；Beijing Normal-Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院）；School of Statistics, East China Normal University（华东师范大学统计学院）
The inverse probability weighting approach is popular for evaluating treatment effects in observational studies, but extreme propensity scores could bias the estimator and induce excessive variance. Recently, the overlap weighting approach has been proposed to alleviate this problem, which smoothly down-weighs the subjects with extreme propensity scores. Although advantages of overlap weighting have been extensively demonstrated in literature with continuous and binary outcomes, research on its performance with time-to-event or survival outcomes is limited. In this article, we propose two weig…
Extreme hydrological events in the Danube river basin may severely impact human populations, aquatic organisms, and economic activity. One often characterizes the joint structure of the extreme events using the theory of multivariate and spatial extremes and its asymptotically justified models. There is interest however in cascading extreme events and whether one event causes another. In this paper, we argue that an improved understanding of the mechanism underlying severe events is achieved by combining extreme value modelling and causal discovery. We construct a causal inference method relyi…
Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new, efficient learning algorithms with leading performance on benchmark datasets in extreme value statistics. We give intuition, backed by performances on benchmark datasets, for why and when causal inference for extremes should be employed over classical methods. Finally, we list some open problems at the intersection of causal inference, tropical geometry and de…
In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness) in the empirically relevant context of limited overlap. I develop a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which relies on strong overlap. I show that IPW (or its augmented version), when valid, is a special case of the more general SPW…
The methodological development of this paper is motivated by the need to address the following scientific question: does the issuance of heat alerts prevent adverse health effects? Our goal is to address this question within a causal inference framework in the context of time series data. A key challenge is that causal inference methods require the overlap assumption to hold: each unit (i.e., a day) must have a positive probability of receiving the treatment (i.e., issuing a heat alert on that day). In our motivating example, the overlap assumption is often violated: the probability of issuing…
Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets
Leibniz Institute for Prevention Research and Epidemiology – BIPS（莱布尼茨预防研究与流行病学研究所（BIPS））；Faculty of Mathematics and Computer Science, University of Bremen（不来梅大学数学与计算机科学学院）
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…
Causal evidence is needed to act and it is often enough for the evidence to point towards a direction of the effect of an action. For example, policymakers might be interested in estimating the effect of slightly increasing taxes on private spending across the whole population. We study identifiability and estimation of causal effects, where a continuous treatment is slightly shifted across the whole population (termed average partial effect or incremental causal effect). We show that incremental effects are identified under local ignorability and local overlap assumptions, where exchangeabili…
Methods for inferring average causal effects have traditionally relied on two key assumptions: (i) the intervention received by one unit cannot causally influence the outcome of another; and (ii) units can be organized into non-overlapping groups such that outcomes of units in separate groups are independent. In this paper, we develop new statistical methods for causal inference based on a single realization of a network of connected units for which neither assumption (i) nor (ii) holds. The proposed approach allows both for arbitrary forms of interference, whereby the outcome of a unit may de…
Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict…
