Estimating the individual treatment effect (ITE) from observational data is meaningful and practical in healthcare. Existing work mainly relies on the strong ignorability assumption that no hidden confounders exist, which may lead to bias in estimating causal effects. Some studies consider the hidden confounders are designed for static environment and not easily adaptable to a dynamic setting. In fact, most observational data (e.g., electronic medical records) is naturally dynamic and consists of sequential information. In this paper, we propose Deep Sequential Weighting (DSW) for estimating ITE with time-varying confounders. Specifically, DSW infers the hidden confounders by incorporating the current treatment assignments and historical information using a deep recurrent weighting neural network. The learned representations of hidden confounders combined with current observed data are leveraged for potential outcome and treatment predictions. We compute the time-varying inverse probabilities of treatment for re-weighting the population. We conduct comprehensive comparison experiments on fully-synthetic, semi-synthetic and real-world datasets to evaluate the performance of our model and baselines. Results demonstrate that our model can generate unbiased and accurate treatment effect by conditioning both time-varying observed and hidden confounders, paving the way for personalized medicine.
The fundamental problem in treatment effect estimation from observational data is confounder identification and balancing. Most of the previous methods realized confounder balancing by treating all observed pre-treatment variables as confounders, ignoring further identifying confounders and non-confounders. In general, not all the observed pre-treatment variables are confounders that refer to the common causes of the treatment and the outcome, some variables only contribute to the treatment and some only contribute to the outcome. Balancing those non-confounders, including instrumental variabl…
Causal mediation analysis is used to evaluate direct and indirect causal effects of a treatment on an outcome of interest through an intermediate variable or a mediator.It is difficult to identify the direct and indirect causal effects because the mediator cannot be randomly assigned in many real applications. In this article, we consider a causal model including latent confounders between the mediator and the outcome. We present sufficient conditions for identifying the direct and indirect effects and propose an approach for estimating them. The performance of the proposed approach is evaluat…
The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the fractional impu…
Estimating treatment effects plays a crucial role in causal inference, having many real-world applications like policy analysis and decision making. Nevertheless, estimating treatment effects in the longitudinal setting in the presence of hidden confounders remains an extremely challenging problem. Recently, there is a growing body of work attempting to obtain unbiased ITE estimates from time-dynamic observational data by ignoring the possible existence of hidden confounders. Additionally, many existing works handling hidden confounders are not applicable for continuous-time settings. In this …
Using observational data to estimate the effect of a treatment is a powerful tool for decision-making when randomized experiments are infeasible or costly. However, observational data often yields biased estimates of treatment effects, since treatment assignment can be confounded by unobserved variables. A remedy is offered by deconfounding methods that adjust for such unobserved confounders. In this paper, we develop the Sequential Deconfounder, a method that enables estimating individualized treatment effects over time in presence of unobserved confounders. This is the first deconfounding me…
University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）；UCLA（加州大学洛杉矶分校）；University of Cambridge（剑桥大学）
The estimation of treatment effects is a pervasive problem in medicine. Existing methods for estimating treatment effects from longitudinal observational data assume that there are no hidden confounders, an assumption that is not testable in practice and, if it does not hold, leads to biased estimates. In this paper, we develop the Time Series Deconfounder, a method that leverages the assignment of multiple treatments over time to enable the estimation of treatment effects in the presence of multi-cause hidden confounders. The Time Series Deconfounder uses a novel recurrent neural network arch…
Causal inference in observational studies can be challenging when confounders are subject to missingness. Generally, the identification of causal effects is not guaranteed even under restrictive parametric model assumptions when confounders are missing not at random. To address this, We propose a general framework to establish the identification of causal effects when confounders are subject to treatment-independent missingness, which means that the missing data mechanism is independent of the treatment, given the outcome and possibly missing confounders. We give special consideration to commo…
Inferring the causal effect of a treatment on an outcome in an observational study requires adjusting for observed baseline confounders to avoid bias. However, adjusting for all observed baseline covariates, when only a subset are confounders of the effect of interest, is known to yield potentially inefficient and unstable estimators of the treatment effect. Furthermore, it raises the risk of finite-sample bias and bias due to model misspecification. For these stated reasons, confounder (or covariate) selection is commonly used to determine a subset of the available covariates that is sufficie…
Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estima…
University of California, Los Angeles（加州大学洛杉矶分校）；University of Oxford（牛津大学）；University at Buffalo（布法罗大学）
Estimating the individual treatment effect (ITE) from observational data is essential in medicine. A central challenge in estimating the ITE is handling confounders, which are factors that affect both an intervention and its outcome. Most previous work relies on the unconfoundedness assumption, which posits that all the confounders are measured in the observational data. However, if there are unmeasurable (latent) confounders, then confounding bias is introduced. Fortunately, noisy proxies for the latent confounders are often available and can be used to make an unbiased estimate of the ITE. I…
Clinical trials traditionally employ blinding as a design mechanism to reduce the influence of placebo effects. In practice, however, it can be difficult or impossible to blind study participants and unblinded trials are common in medical research. Here we show how instrumental variables can be used to quantify and disentangle treatment and placebo effects in randomized clinical trials comparing control and active treatments in the presence of confounders. The key idea is to use randomization to separately manipulate treatment assignment and psychological encouragement messages that increase t…
Treatment-induced confounders complicate analyses of time-varying treatment effects and causal mediation. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. Although several methods for estimating marginal effects avoid these complications, including inverse-probability-of-treatment-weighted (IPTW) estimation of marginal structural models (MSMs) as well as g- and regression-with-residuals (RWR) estimation of highly constrained structural nested me…
Many scientific questions require estimating the effects of continuous treatments. Outcome modeling and weighted regression based on the generalized propensity score are the most commonly used methods to evaluate continuous effects. However, these techniques may be sensitive to model misspecification, extreme weights or both. In this paper, we propose Kernel Optimal Orthogonality Weighting (KOOW), a convex optimization-based method, for estimating the effects of continuous treatments. KOOW finds weights that minimize the worst-case penalized functional covariance between the continuous treatme…
In causal mediation studies that decompose an average treatment effect into a natural indirect effect (NIE) and a natural direct effect (NDE), examples of post-treatment confounding are abundant. Past research has generally considered it infeasible to adjust for a post-treatment confounder of the mediator-outcome relationship due to incomplete information: it is observed under the actual treatment condition while missing under the counterfactual treatment condition. This study proposes a new sensitivity analysis strategy for handling post-treatment confounding and incorporates it into weightin…
Omitted variable bias can affect treatment effect estimates obtained from observational data due to the lack of random assignment to treatment groups. Sensitivity analyses adjust these estimates to quantify the impact of potential omitted variables. This paper presents methods of sensitivity analysis to adjust interval estimates of treatment effect---both the point estimate and standard error---obtained using multiple linear regression. Central to our approach is what we term benchmarking, the use of data to establish reference points for speculation about omitted confounders. The method adapt…
Causal Effect Estimation using identifiable Variational AutoEncoder with Latent Confounders and Post-Treatment Variables
College of Informatics, Huazhong Agricultural University（华中农业大学信息学院）；Data 61, Commonwealth Scientific and Industrial Research Organisation (CSIRO)（联邦科学与工业研究组织数据61分部）；STEM, University of South Australia（南澳大学 STEM 学院）
Background/aims: While randomized controlled trials are the gold standard for measuring causal effects, robust conclusions about causal relationships can be obtained using data from observational studies if proper statistical techniques are used to account for the imbalance of pretreatment confounders across groups. Propensity score (PS) and balance weighting are useful techniques that aim to reduce the observed imbalances between treatment groups by weighting the groups to be as similar as possible with respect to observed confounders. Methods: We have created CoBWeb, a free and easy-to-use w…
Interventional effects have been proposed as a solution to the unidentifiability of natural (in)direct effects under mediator-outcome confounders affected by the exposure. Such confounders are an intrinsic characteristic of studies with time-varying exposures and mediators, yet the generalization of the interventional effect framework to the time-varying case has received little attention in the literature. We present an identification result for interventional effects in a general longitudinal data structure that allows flexibility in the specification of treatment-outcome, treatment-mediator…
New York University（纽约大学）；Columbia University（哥伦比亚大学）
Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treatments in the presence of unobserved confounding. We develop two assumptions based on shared confounding between treatments and independence of treatments given the confounder. Together, these assumptions lead to a confounder estimator regularized by mutual information. For this e…
The treatment effects of medications play a key role in guiding medical prescriptions. They are usually assessed with randomized controlled trials (RCTs), which are expensive. Recently, large-scale electronic health records (EHRs) have become available, opening up new opportunities for more cost-effective assessments. However, assessing a treatment effect from EHRs is challenging: it is biased by unobserved confounders, unmeasured variables that affect both patients' medical prescription and their outcome, e.g. the patients' social economic status. To adjust for unobserved confounders, we deve…
The Doubly Robust (DR) estimation of ATE can be carried out in 2 steps, where in the first step, the treatment and outcome are modeled, and in the second step the predictions are inserted into the DR estimator. The model misspecification in the first step has led researchers to utilize Machine Learning algorithms instead of parametric algorithms. However, existence of strong confounders and/or Instrumental Variables (IVs) can lead the complex ML algorithms to provide perfect predictions for the treatment model which can violate the positivity assumption and elevate the variance of DR estimator…
Estimating individualized treatment effects (ITEs) from observational data is crucial for decision-making. In order to obtain unbiased ITE estimates, a common assumption is that all confounders are observed. However, in practice, it is unlikely that we observe these confounders directly. Instead, we often observe noisy measurements of true confounders, which can serve as valid proxies. In this paper, we address the problem of estimating ITE in the longitudinal setting where we observe noisy proxies instead of true confounders. To this end, we develop the Deconfounding Temporal Autoencoder, a n…
No unmeasured confounding is often assumed in estimating treatment effects in observational data when using approaches such as propensity scores and inverse probability weighting. However, in many such studies due to the limitation of the databases, collected confounders are not exhaustive, and it is crucial to examine the extent to which the resulting estimate is sensitive to the unmeasured confounders. We consider this problem for survival and competing risks data. Due to the complexity of models for such data, we adapt the simulated potential confounders approach of Carnegie et al. (2016), …
Estimating causal effects of continuous-time dynamic treatments with unmeasured confounders
Key Laboratory of Advanced Theory and Application in Statistics and Data Science -MOE, School of Statistics, East China Normal University（华东师范大学统计学院统计学与数据科学前沿理论及应用教育部重点实验室）
When assessing the presence of an exposure causal effect on a given outcome, it is well known that classical measurement error of the exposure can reduce the power of a test of the null hypothesis in question, although its type I error rate will generally remain at the nominal level. In contrast, classical measurement error of a confounder can inflate the type I error rate of a test of treatment effect. In this paper, we develop a large class of semiparametric test statistics of an exposure causal effect, which are completely robust to classical measurement error of a subset of confounders. A …
Identifying causal treatment (or exposure) effects in observational studies requires the data to satisfy the unconfoundedness assumption which is not testable using the observed data. With sensitivity analysis, one can determine how the conclusions might change if assumptions are violated to a certain degree. In this paper, we propose a new technique for sensitivity analysis applicable to clusters observational data with a normally distributed or binary outcome. The proposed methods aim to assess the robustness of estimated treatment effects in a single study as well as in multiple studies, i.…
Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a nondifferential proxy of it is observed. We show that, under certain monotonicity assumption that is empirically verifiable, adjusting for the proxy produces a measure of the effect that is between the unadjusted and the true measures.
Marginal structural models (MSMs) estimate the causal effect of a time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting (IPTW) can lead to high-variance estimates due to extreme weights and be sensitive to model misspecification. Various methods have been proposed to partially address this, including truncation and stabilized-IPTW to temper extreme weights and covariate balancing propensity score (CBPS) to address treatment model misspecification. In this paper, we present Kernel O…
Conditioning on some set of confounders that causally affect both treatment and outcome variables can be sufficient for eliminating bias introduced by all such confounders when estimating causal effect of the treatment on the outcome from observational data. It is done by including them in propensity score model in so-called potential outcome framework for causal inference whereas in causal graphical modeling framework usual conditioning on them is done. However in the former framework, it is confusing when modeler finds a variable that is non-causally associated with both the treatment and th…
Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a non-differential binary proxy of it is observed. We identify conditions under which adjusting for the proxy comes closer to the incomputable true average causal effect than not adjusting at all. Unlike other works, we do not assume that the average causal effect of the confounder on the outcome is in the same direction among treated and untreated.
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 …
It is important to draw causal inference from observational studies, which, however, becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. We propose a novel framework to nonparametrically identify causal effects with confounders subject to an outcome-independent missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal…
Natural direct and indirect effects are mediational estimands that decompose the average treatment effect and describe how outcomes would be affected by contrasting levels of a treatment through changes induced in mediator values (in the case of the indirect effect) or not through induced changes in the mediator values (in the case of the direct effect). Natural direct and indirect effects are not generally point-identifiable in the presence of a treatment-induced confounder, however they may still be identified if one is willing to assume monotonicity between a treatment and the treatment-ind…
Participant noncompliance, in which participants do not follow their assigned treatment protocol, often obscures the causal relationship between treatment and treatment effect in randomized trials. In the longitudinal setting, the G-computation algorithm can adjust for confounding to estimate causal effects. Typically, G-computation assumes that both 1) compliance is observed; and 2) the densities of the confounders can be correctly specified. We aim to develop a G-computation estimator in the setting where both assumptions are violated. For 1), in place of unobserved compliance, we substitute…
Observational studies can play a useful role in assessing the comparative effectiveness of competing treatments. In a clinical trial the randomization of participants to treatment and control groups generally results in well-balanced groups with respect to possible confounders, which makes the analysis straightforward. However, when analysing observational data, the potential for unmeasured confounding makes comparing treatment effects much more challenging. Causal inference methods such as Instrumental Variable and Prior Even Rate Ratio approaches make it possible to circumvent the need to ad…
Arizona State University（亚利桑那州立大学）；City University of Hong Kong（香港城市大学）
An important problem in causal inference is to break down the total effect of a treatment on an outcome into different causal pathways and to quantify the causal effect in each pathway. For instance, in causal fairness, the total effect of being a male employee (i.e., treatment) constitutes its direct effect on annual income (i.e., outcome) and the indirect effect via the employee's occupation (i.e., mediator). Causal mediation analysis (CMA) is a formal statistical framework commonly used to reveal such underlying causal mechanisms. One major challenge of CMA in observational studies is handl…
Proximal Mediation Analysis with Unmeasured Treatment-Induced Confounding
Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学统计学院与应用统计中心）；Department of Biostatistics & Medical Informatics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校生物统计与医学信息学系）
