在许多临床情境中，估计时间到事件数据中治疗的效应变得复杂，不仅因为混杂、删失和异质性，还因为存在一个治愈亚群，其中感兴趣的事件 never 发生。在这种情况下，治疗可能对（1）被治愈的概率和（2）非治愈个体的事件时间有不同影响。标准的生存分析和因果推断方法通常不区分治愈和非治愈个体，模糊了治疗对治愈概率和事件时间的机制差异。为了解决这些挑战，我们提出了一种基于匹配的框架，构建不同的匹配组以分别估计异质治疗效应（HTE）在治愈概率和事件时间上的影响。我们使用混合治愈模型来识别两个估计量的特征重要性，这反过来又指导了在高维空间中匹配的加权距离度量。在匹配组内，Kaplan-Meier估计器提供治愈概率和预期事件时间的估计，从而推导出个体层面的治疗效应。我们提供了估计器一致性和距离度量最优性的理论保证，在等规模约束下。我们进一步将估计误差分解为删失、模型拟合和不可约噪声的贡献。模拟和真实世界数据分析表明，我们的方法在时间到事件设置中提供了可解释和稳健的HTE估计。
英文摘要：
In many clinical contexts, estimating effects of treatment in time-to-event data is complicated not only by confounding, censoring, and heterogeneity, but also by the presence of a cured subpopulation in which the event of interest never occurs. In such settings, treatment may have distinct effects on (1) the probability of being cured and (2) the event timing among non-cured individuals. Standard survival analysis and causal inference methods typically do not separate cured from non-cured individuals, obscuring distinct treatment mechanisms on cure probability and event timing. To address these challenges, we propose a matching-based framework that constructs distinct match groups to estimate heterogeneous treatment effects (HTE) on cure probability and event timing, respectively. We use mixture cure models to identify feature importance for both estimands, which in turn informs weighted distance metrics for matching in high-dimensional spaces. Within matched groups, Kaplan-Meier estimators provide estimates of cure probability and expected time to event, from which individual-level treatment effects are derived. We provide theoretical guarantees for estimator consistency and distance metric optimality under an equal-scale constraint. We further decompose estimation error into contributions from censoring, model fitting, and irreducible noise. Simulations and real-world data analyses demonstrate that our approach delivers interpretable and robust HTE estimates in time-to-event settings.
Randomized clinical trials (RCTs) are ideal for estimating causal effects, because the distributions of background covariates are similar in expectation across treatment groups. When estimating causal effects using observational data, matching is a commonly used method to replicate the covariate balance achieved in a RCT. Matching algorithms have a rich history dating back to the mid-1900s, but have been used mostly to estimate causal effects between two treatment groups. When there are more than two treatments, estimating causal effects requires additional assumptions and techniques. We propo…
We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be expressed as optimal in this framework, including nearest-neighbor matching, coarsened exact matching, and mean-matched sampling. This reveals their motivation and aptness as structural priors formulated by embedding the effect in a particular functional space. This also gives rise to a range of new, kernel-based matching estimators that arise when one embe…
We compare the performance of standard nearest-neighbor propensity score matching with that of an analogous Bayesian propensity score matching procedure. We show that the Bayesian approach makes better use of available information, as it makes less arbitrary decisions about which observations to drop and which ones to keep in the matched sample. We conduct a simulation study to evaluate the performance of standard and Bayesian nearest-neighbor matching when matching is done with and without replacement. We then use both methods to replicate a recent study about the impact of land reform on gue…
Matching estimators for average treatment effects are widely used in the binary treatment setting, in which missing potential outcomes are imputed as the average of observed outcomes of all matches for each unit. With more than two treatment groups, however, estimation using matching requires additional techniques. In this paper, we propose a nearest-neighbors matching estimator for use with multiple, nominal treatments, and use simulations to show that this method is precise and has coverage levels that are close to nominal. In addition, we implement the proposed inference methods to examine …
To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for matching in the literature, the reduced covariates are estimable nonparametrically under a mild assumption on the original covariates, and are sufficient and effective in imputing the missing potential outcomes. Under the ignorability assumption, the consistency of the proposed approach requires a weaker common support condition. In addition, the researcher…
Propensity score matching has been a long-standing tradition for handling confounding in causal inference, however requiring stringent model assumptions. In this article, we propose double score matching(DSM) for general causal estimands utilizing two balancing scores including the propensity score and prognostic score. To gain the protection of possible model misspecification, we posit multiple candidate models for each score. We show that the de-biasing DSM estimator achieves the multiple robustness property in that it is consistent for the true causal estimand if any model of the propensity…
We introduce profile matching, a multivariate matching method for randomized experiments and observational studies that finds the largest possible unweighted samples across multiple treatment groups that are balanced relative to a covariate profile. This covariate profile can represent a specific population or a target individual, facilitating the generalization and personalization of causal inferences. For generalization, because the profile often amounts to summary statistics for a target population, profile matching does not always require accessing individual-level data, which may be unava…
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…
Marine conservation preserves fish biodiversity, protects marine and coastal ecosystems, and supports climate resilience and adaptation. Despite the importance of establishing marine protected areas (MPAs), research on the effectiveness of MPAs with different conservation policies is limited due to the lack of quantitative MPA information. In this paper, leveraging a global MPA database, we investigate the causal impact of MPA policies on fish biodiversity. To address challenges posed by this clustered and confounded observational study, we construct a matching estimator of the average treatme…
The propensity score is a common tool for estimating the causal effect of a binary treatment in observational data. In this setting, matching, subclassification, imputation, or inverse probability weighting on the propensity score can reduce the initial covariate bias between the treatment and control groups. With more than two treatment options, however, estimation of causal effects requires additional assumptions and techniques, the implementations of which have varied across disciplines. This paper reviews current methods, and it identifies and contrasts the treatment effects that each one …
The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal inference studies may require unobserved high-level information which needs to be inferred from other observed attributes. In such cases, inaccuracies of the applied inference methods will result in noisy outputs. In this study, we propose a novel approach for causal inference when one or more key variables are noisy. Our method utilizes the knowledge about th…
This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.
Assumption violations in causal discovery and the robustness of score matching
Università di Genova（热那亚大学）；AWS（亚马逊云科技）；German Cancer Research Center (DKFZ)（德国癌症研究中心）；MIT（麻省理工学院）；CBMM（计算生物学与机器学习中心）；Istituto Italiano di Tecnologia（意大利技术研究院）；University of Chicago（芝加哥大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）
In this note we explore a fully unsupervised deep-learning framework for simulating non-linear structural equation models from observational training data. The main contribution of this note is an architecture for applying moment-matching loss functions to the edges of a causal Bayesian graph, resulting in a generative conditional-moment-matching graph-neural-network. This framework thus enables automated sampling of latent space conditional probability distributions for various graphical interventions, and is capable of generating out-of-sample interventional probabilities that are often fait…
Matching on covariates is a well-established framework for estimating causal effects in observational studies. The principal challenge stems from the often high-dimensional structure of the problem. Many methods have been introduced to address this, with different advantages and drawbacks in computational and statistical performance as well as interpretability. This article introduces a natural optimal matching method based on multimarginal unbalanced optimal transport that possesses many useful properties in this regard. It provides interpretable weights based on the distance of matched indiv…
We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new functional-analytical formulation of optimal matching, giving rise to the class of GOM methods, for which we provide a single unified theory to analyze tractability, consistency, and efficiency. Many commonly used existing methods are included in GOM and, using their GOM interpretation, can be extended to optimally and automatically trade off balance for variance and…
Investigating the causal relationship between exposure and the time-to-event outcome is an important topic in biomedical research. Previous literature has discussed the potential issues of using the hazard ratio as a marginal causal effect measure due to its noncollapsibility property. In this paper, we advocate using the restricted mean survival time (RMST) difference as the marginal causal effect measure, which is collapsible and has a simple interpretation as the difference of area under survival curves over a certain time horizon. To address both measured and unmeasured confounding, a matc…
In the context of a binary treatment, matching is a well-established approach in causal inference. However, in the context of a continuous treatment or exposure, matching is still underdeveloped. We propose an innovative matching approach to estimate an average causal exposure-response function under the setting of continuous exposures that relies on the generalized propensity score (GPS). Our approach maintains the following attractive features of matching: a) clear separation between the design and the analysis; b) robustness to model misspecification or to the presence of extreme values of …
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching methods do not pass basic sanity checks: they fail when irrelevant variables are introduced, and tend to be either computationally slow or produce low-quality matches. The method proposed in this work aims to match units on a weighted Hamming distance, taking into account the relative importance of the covariates; the algorithm aims to match units on as many …
The timing of antiretroviral therapy (ART) initiation for HIV and tuberculosis (TB) co-infected patients needs to be considered carefully. CD4 cell count can be used to guide decision making about when to initiate ART. Evidence from recent randomized trials and observational studies generally supports early initiation but does not provide information about effects of initiation time on a continuous scale. In this paper, we develop and apply a highly flexible structural proportional hazards model for characterizing the effect of treatment initiation time on a survival distribution. The model ca…
Case-control designs are an important tool in contrasting the effects of well-defined treatments. In this paper, we reconsider classical concepts, assumptions and principles and explore when the results of case-control studies can be endowed a causal interpretation. Our focus is on identification of target causal quantities, or estimands. We cover various estimands relating to intention-to-treat or per-protocol effects for popular sampling schemes (case-base, survivor, and risk-set sampling), each with and without matching. Our approach may inform future research on different estimands, other …
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a finite sample concentration inequality. We apply this framework to coarsened exact matching as well as matching using the propensity score and suggest how to apply it to other algorithms. Simulation studies are used to evaluate the procedures.
Matching is an important tool in causal inference. The method provides a conceptually straightforward way to make groups of units comparable on observed characteristics. The use of the method is, however, limited to situations where the study design is fairly simple and the sample is moderately sized. We illustrate the issue by revisiting a large-scale voter mobilization experiment that took place in Michigan for the 2006 election. We ask what the causal effects would have been if the treatments in the experiment were scaled up to the full population. Matching could help us answer this questio…
In studies of discrimination, researchers often seek to estimate a causal effect of race or gender on outcomes. For example, in the criminal justice context, one might ask whether arrested individuals would have been subsequently charged or convicted had they been a different race. It has long been known that such counterfactual questions face measurement challenges related to omitted-variable bias, and conceptual challenges related to the definition of causal estimands for largely immutable characteristics. Another concern, which has been the subject of recent debates, is post-treatment bias:…
In observational causal inference, exact covariate matching plays two statistical roles: (i) it effectively controls for bias due to measured confounding; (ii) it justifies assumption-free inference based on randomization tests. This paper shows that inexact covariate matching does not always play these same roles. We find that inexact matching often leaves behind statistically meaningful bias and that this bias renders standard randomization tests asymptotically invalid. We therefore recommend additional model-based covariate adjustment after inexact matching. In the framework of local misspe…
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 en…
When investigators seek to estimate causal effects, they often assume that selection into treatment is based only on observed covariates. Under this identification strategy, analysts must adjust for observed confounders. While basic regression models have long been the dominant method of statistical adjustment, more robust methods based on matching or weighting have become more common. Of late, even more flexible methods based on machine learning methods have been developed for statistical adjustment. These machine learning methods are designed to be black box methods with little input from th…
A classical problem in causal inference is that of matching, where treatment units need to be matched to control units based on covariate information. In this work, we propose a method that computes high quality almost-exact matches for high-dimensional categorical datasets. This method, called FLAME (Fast Large-scale Almost Matching Exactly), learns a distance metric for matching using a hold-out training data set. In order to perform matching efficiently for large datasets, FLAME leverages techniques that are natural for query processing in the area of database management, and two implementa…
Propensity score matching (PSM) is a pseudo-experimental method that uses statistical techniques to construct an artificial control group by matching each treated unit with one or more untreated units of similar characteristics. To date, the problem of determining the optimal number of matches per unit, which plays an important role in PSM, has not been adequately addressed. We propose a tuning-parameter-free PSM method based on the nonparametric maximum-likelihood estimation of the propensity score under the monotonicity constraint. The estimated propensity score is piecewise constant, and th…
Representation Learning Preserving Ignorability and Covariate Matching for Treatment Effects
Indian Institute of Science Education and Research, Bhopal（印度科学教育与研究学院，布巴兰普尔）；Indian Institute of Science, Bangalore（印度科学研究院，班加罗尔）；Indraprastha Institute of Information Technology, Delhi（印度理工信息学院，德里）；Google Deepmind, Bangalore（谷歌DeepMind，班加罗尔）
Stanford University Graduate School of Business（斯坦福大学商学院）
In this paper, we propose deep learning techniques for econometrics, specifically for causal inference and for estimating individual as well as average treatment effects. The contribution of this paper is twofold: 1. For generalized neighbor matching to estimate individual and average treatment effects, we analyze the use of autoencoders for dimensionality reduction while maintaining the local neighborhood structure among the data points in the embedding space. This deep learning based technique is shown to perform better than simple k nearest neighbor matching for estimating treatment effects…
Causal inference methods are widely applied in the fields of medicine, policy, and economics. Central to these applications is the estimation of treatment effects to make decisions. Current methods make binary yes-or-no decisions based on the treatment effect of a single outcome dimension. These methods are unable to capture continuous space treatment policies with a measure of intensity. They also lack the capacity to consider the complexity of treatment such as matching candidate treatments with the subject. We propose to formulate the effectiveness of treatment as a parametrizable model, ex…
