In observational clinic registries, time to treatment is often of interest, but treatment can be given at any time during follow-up and there is no structure or intervention to ensure regular clinic visits for data collection. To address these challenges, we introduce the time-dependent propensity process as a generalization of the propensity score. We show that the propensity process balances the entire time-varying covariate history which cannot be achieved by existing propensity score methods and that treatment assignment is strongly ignorable conditional on the propensity process. We develop methods for estimating the propensity process using observed data and for matching based on the propensity process. We illustrate the propensity process method using the Emory Amyotrophic Lateral Sclerosis (ALS) Registry data.
We investigate the estimation of subgroup treatment effects with observational data. Existing propensity score matching and weighting methods are mostly developed for estimating overall treatment effect. Although the true propensity score should balance covariates for the subgroup populations, the estimated propensity score may not balance covariates for the subgroup samples. We propose the subgroup balancing propensity score (SBPS) method, which selects, for each subgroup, to use either the overall sample or the subgroup sample to estimate propensity scores for units within that subgroup, in …
The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss two broad approaches to estimating these weights: the more traditional one, which fits a propensity score model and then uses the reciprocal of the estimated propensity score to construct weights, and the balancing approach, which estimates the inverse propensity weights essentially by the method of moments, finding weights that achieve balance in the sample.…
In observational studies, propensity scores are commonly estimated by maxi- mum likelihood but may fail to balance high-dimensional pre-treatment covariates even after specification search. We introduce a general framework that unifies and generalizes several recent proposals to improve covariate balance when designing an observational study. In- stead of the likelihood function, we propose to optimize special loss functions---covariate balancing scoring rules (CBSR)---to estimate the propensity score. A CBSR is uniquely determined by the link function in the GLM and the estimand (a weighted a…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases…
In this paper, we propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. We first use a class of penalized M-estimators for the propensity score and outcome models. We then calibrate the initial estimate of the propensity score by balancing a carefully selected subset of covariates that are predictive of the outcome. Finally, the estimated propensity score is used to construct the inverse probability weighting estimator. We prove that the proposed estimator, which has the…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The effect of a functional variable on an outcome is an essential theme in functional data analysis, but a majority of related studies are restricted to correlational effects rather than causal effects. This paper makes the first attempt to study the causal effect of a functional variable as a treatment in observational studies. Despite the lack of a probability dens…
About forty years ago, in a now--seminal contribution, Rosenbaum & Rubin (1983) introduced a critical characterization of the propensity score as a central quantity for drawing causal inferences in observational study settings. In the decades since, much progress has been made across several research fronts in causal inference, notably including the re-weighting and matching paradigms. Focusing on the former and specifically on its intersection with machine learning and semiparametric efficiency theory, we re-examine the role of the propensity score in modern methodological developments. As Ro…
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…
Propensity score matching (PSM) is the de-facto standard for estimating causal effects in observational studies. We show that PSM and its implementations are susceptible to several major drawbacks and illustrate these findings using a case study with $17,427$ patients. We derive four formal properties an optimal statistical matching algorithm should meet, and propose Deterministic Balancing Score exact Matching (DBSeM) which meets the aforementioned properties for an exact matching. Furthermore, we investigate one of the main problems of PSM, that is that common PSM results in one valid set of…
Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pre-treatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asympto…
Weighting methods are used in observational studies to adjust for covariate imbalances between treatment and control groups. Entropy balancing (EB) is an alternative to inverse probability weighting with an estimated propensity score. The EB weights are constructed to satisfy balance constraints and optimized towards stability. We describe large sample properties of EB estimators of the average causal treatment effect, based on the Kullback-Leibler and quadratic Rényi relative entropies. Additionally, we propose estimators of their asymptotic variances. Even though the objective of EB is to re…
Covariate Balancing Value Estimation for Optimal Individualized Treatment Rules
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；School of Mathematics and Statistics, Beijing Technology and Business University（北京工商大学数学与统计学院）
A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have desirable asymptotic properties, but they often fail to adequately balance covariate data in finite samples. Empirical covariate balancing methods pose as an appealing alternative by exactly balancing the sample moments of the covariate distribution.…
Propensity score weighting is widely used to improve the representativeness and correct the selection bias in the voluntary sample. The propensity score is often developed using a model for the sampling probability, which can be subject to model misspecification. In this paper, we consider an alternative approach of estimating the inverse of the propensity scores using the density ratio function satisfying the self-efficiency condition. The smoothed density ratio function is obtained by the solution to the information projection onto the space satisfying the moment conditions on the balancing …
In a pilot program during the 2016-17 admissions cycle, the University of California, Berkeley invited many applicants for freshman admission to submit letters of recommendation. We use this pilot as the basis for an observational study of the impact of submitting letters of recommendation on subsequent admission, with the goal of estimating how impacts vary across pre-defined subgroups. Understanding this variation is challenging in observational studies, however, because estimated impacts reflect both actual treatment effect variation and differences in covariate balance across groups. To ad…
Propensity score weighting is an important tool for comparative effectiveness research.Besides the inverse probability of treatment weights (IPW), recent development has introduced a general class of balancing weights, corresponding to alternative target populations and estimands. In particular, the overlap weights (OW) lead to optimal covariate balance and estimation efficiency, and a target population of scientific and policy interest. We develop the R package PSweight to provide a comprehensive design and analysis platform for causal inference based on propensity score weighting. PSweight s…
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…
The Consent-to-Contact (C2C) registry at the University of California, Irvine collects data from community participants to aid in the recruitment to clinical research studies. Self-selection into the C2C likely leads to bias due in part to enrollees having more years of education relative to the US general population. Salazar et al. (2020) recently used the C2C to examine associations of race/ethnicity with participant willingness to be contacted about research studies. To address questions about generalizability of estimated associations we estimate propensity for self-selection into the conv…
Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a recently proposed entropy maximization method called Entropy Balancing (EB), which exactly matches the covariate moments for the different experimental groups in its optimization problem. We show EB is doubly robust with respect to linear outcome regression and logistic propensity score regression, and it reaches the asymptotic semiparametric variance bound when…
Propensity score analysis with latent covariates: Measurement error bias correction using the covariate's posterior mean, aka the inclusive factor score
Johns Hopkins Bloomberg School of Public Health（约翰斯·霍普金斯大学彭博公共卫生学院）
Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic s…
In observational study, the propensity score has the central role to estimate causal effects. Since the propensity score is usually unknown, estimating by appropriate procedures is an indispensable step. A point to note that a causal effect estimator might have some bias if a propensity score model was misspecified; valid model construction is important. To overcome the problem, a variety of interesting methods has been proposed. In this paper, we review four methods: using ordinary logistic regression approach; CBPS proposed by Imai and Ratkovic; boosted CART proposed by McCaffrey and colleag…
Survival outcomes are common in comparative effectiveness studies and require unique handling because they are usually incompletely observed due to right-censoring. A ``once for all'' approach for causal inference with survival outcomes constructs pseudo-observations and allows standard methods such as propensity score weighting to proceed as if the outcomes are completely observed. For a general class of model-free causal estimands with survival outcomes on user-specified target populations, we develop corresponding propensity score weighting estimators based on the pseudo-observations and es…
Self Balancing Neural Network: A Novel Method to Estimate Average Treatment Effect
KLATASDS-MOE, School of Statistics, East China Normal University（KLATASDS-MOE统计学院，华东师范大学）；Department of Statistics, College of Natural and Computational Sciences, Addis Ababa University（统计系，自然与计算科学学院，亚的斯亚贝巴大学）
We expand upon the simulation study of Setodji et al. (2017) which compared three promising balancing methods when assessing the average treatment effect on the treated for binary treatments: generalized boosted models (GBM), covariate-balancing propensity scores (CBPS), and entropy balance (EB). The study showed that GBM can outperform CBPS and EB when there are likely to be non-linear associations in both the treatment assignment and outcome models and CBPS and EB are fine-tuned to obtain balance only on first order moments. We explore the potential benefit of using higher-order moments in t…
Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weig…
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…
We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching/balancing fail in such settings due to miscalibrated propensity nets and inappropriate covariate representations, respectively. We propose a new method based on adversarial training of a weighting and a discriminator network that effectively addresses this methodological gap. This is demonstrated through new theoretical characterizations of the method as w…
Propensity score plays a central role in causal inference, but its use is not limited to causal comparisons. As a covariate balancing tool, propensity score can be used for controlled descriptive comparisons between groups whose memberships are not manipulable. A prominent example is racial disparities in health care. However, conceptual confusion and hesitation persists for using propensity score in racial disparities studies. In this commentary, we argue that propensity score, possibly combined with other methods, is an effective tool for racial disparities analysis. We describe relevant est…
In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate balancing weights, a generalization of inverse propensity score weights that solve a convex optimization problem to find a set of weights that directly minimize a measure of covariate imbalance, subject to an additional penalty on the variance of the weights. We tailor the approximate balancing weights optimization problem to both adjustment sets by deriving an u…
We study nonparametric estimation for the partially conditional average treatment effect, defined as the treatment effect function over an interested subset of confounders. We propose a hybrid kernel weighting estimator where the weights aim to control the balancing error of any function of the confounders from a reproducing kernel Hilbert space after kernel smoothing over the subset of interested variables. In addition, we present an augmented version of our estimator which can incorporate estimations of outcome mean functions. Based on the representer theorem, gradient-based algorithms can b…
This paper introduces entropy balancing for continuous treatments (EBCT) by extending the original entropy balancing methodology of Hainmüller (2012). In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem. EBCT weights reliably eradicate Pearson correlations between covariates and the continuous treatment variable. This is the case even when other methods based on the generalized propensity score tend to yield insufficient balance due to strong selection into different treatment intensities. Moreover, the optimization procedure …
Bias in causal comparisons has a direct correspondence with distributional imbalance of covariates between treatment groups. Weighting strategies such as inverse propensity score weighting attempt to mitigate bias by either modeling the treatment assignment mechanism or balancing specified covariate moments. This paper introduces a new weighting method, called energy balancing, which instead aims to balance weighted covariate distributions. By directly targeting distributional imbalance, the proposed weighting strategy can be flexibly utilized in a wide variety of causal analyses, including th…
Propensity score weighting is a tool for causal inference to adjust for measured confounders in observational studies. In practice, data often present complex structures, such as clustering, which make propensity score modeling and estimation challenging. In addition, for clustered data, there may be unmeasured cluster-specific variables that are related to both the treatment assignment and the outcome. When such unmeasured cluster-specific confounders exist and are omitted in the propensity score model, the subsequent propensity score adjustment may be biased. In this article, we propose a ca…
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…
Amazon.com, Inc.（亚马逊公司）；Wharton School of the University of Pennsylvania（宾夕法尼亚大学沃顿商学院）
We study the problem of observational causal inference with continuous treatments in the framework of inverse propensity-score weighting. To obtain stable weights, we design a new algorithm based on entropy balancing that learns weights to directly maximize causal inference accuracy using end-to-end optimization. In the process of optimization, these weights are automatically tuned to the specific dataset and causal inference algorithm being used. We provide a theoretical analysis demonstrating consistency of our approach. Using synthetic and real-world data, we show that our algorithm estimat…
Analyses of environmental phenomena often are concerned with understanding unlikely events such as floods, heatwaves, droughts or high concentrations of pollutants. Yet the majority of the causal inference literature has focused on modelling means, rather than (possibly high) quantiles. We define a general estimator of the population quantile treatment (or exposure) effects (QTE) -- the weighted QTE (WQTE) -- of which the population QTE is a special case, along with a general class of balancing weights incorporating the propensity score. Asymptotic properties of the proposed WQTE estimators ar…
In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are based on modelling of the treatment assignment mechanism and their doubly robust extensions have been difficult to motivate using formal Bayesian arguments, in principle, for likelihood-based inferences, the treatment assignment model can play no part in inferences concerning the expected outcomes if the models are assumed to be correctly specified. On the other…
Continuous treatments have posed a significant challenge for causal inference, both in the formulation and identification of scientifically meaningful effects and in their robust estimation. Traditionally, focus has been placed on techniques applicable to binary or categorical treatments with few levels, allowing for the application of propensity score-based methodology with relative ease. Efforts to accommodate continuous treatments introduced the generalized propensity score, yet estimators of this nuisance parameter commonly utilize parametric regression strategies that sharply limit the ro…
