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Journal of Causal Inference

ISSN: 2193-3685

Edited by: Kosuke Imai, Judea Pearl, Maya Liv Petersen, Mark J. van der Laan

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About this journal

Journal of Causal Inference is a fully peer-reviewed, open access, electronic journal that provides readers with free, instant, and permanent access to all content worldwide.

Aims and Scope

Journal of Causal Inference publishes papers on theoretical and applied causal research across the range of academic disciplines that use quantitative tools to study causality.

The past two decades have seen causal inference emerge as a unified field with a solid theoretical foundation, useful in many of the empirical and behavioral sciences. Journal of Causal Inference aims to provide a common venue for researchers working on causal inference in biostatistics and epidemiology, economics, political science and public policy, cognitive science and formal logic, and any field that aims to understand causality. The journal serves as a forum for this growing community to develop a shared language and study the commonalities and distinct strengths of their various disciplines' methods for causal analysis.

Existing discipline-specific journals tend to bury causal analysis in the language and methods of traditional statistical methodologies, creating the inaccurate impression that causal questions can be handled by routine methods of regression or simultaneous equations, glossing over the special precautions demanded by causal analysis. In contrast, JCI highlights both the uniqueness and interdisciplinary nature of causal research.

Topics

Any field aiming at understanding causality, especially

Biostatistics and epidemiology

Computer Science

Economics

Machine Learning

Political science

Public policy

Cognitive science

Formal logic

Causal inference:

Research design

Causal model and target parameter specification

Identifiability

Statistical estimation

Sensitivity analysis/interpretation.

Quantitative statistics’ elaboration of causal methods in applied data analyses

Cross-disciplinary methodological research

History of the causal inference field and its philosophical underpinnings

Journal of Causal Inference accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published, or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before submission.

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language polishing services upon acceptance for authors from non-English speaking regions

no limitations on colour figures and word count in published articles

all articles are freely available to the academic community worldwide without any restrictions

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distribution to open access directories (such as DOAJ) and thousands of libraries worldwide

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In order to sustain the publishing process, each article accepted for publication in Journal of Causal Inference is subject to an Article Processing Charge of €1000. This fee is used to cover the costs of the peer-review process, professional typesetting and copyediting, as well as online hosting, long-term preservation, and extensive promotion to potential readers. There is no submission fee. Information regarding payment of the charge will be provided following acceptance for publication. For more information please go to Article Processing Charges .

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Detailed information on Editorial Policy, Publication Ethics, Instructions for Authors etc. can be found in the Supplementary Materials section.

For more information on De Gruyter Publishing Ethics, please see the De Gruyter Guidelines online here.

Special Issues

Neyman (1923) and its influences on causal inference
COORDINATING EDITOR: Peng Ding (University of California, USA)
Deadline for submissions: October 30, 2023

Journal of Causal Inference will publish a Special Issue in cooperation with the 2023 Interactive Causal Learning Conference.

More information soon!

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Volume 11 Issue 1

January 2023

Research Articles

Open Access February 8, 2023

Adaptive normalization for IPW estimation

Samir Khan, Johan Ugander

Article number: 20220019

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Abstract

Inverse probability weighting (IPW) is a general tool in survey sampling and causal inference, used in both Horvitz–Thompson estimators, which normalize by the sample size, and Hájek/self-normalized estimators, which normalize by the sum of the inverse probability weights. In this work, we study a family of IPW estimators, first proposed by Trotter and Tukey in the context of Monte Carlo problems, that are normalized by an affine combination of the sample size and a sum of inverse weights. We show how selecting an estimator from this family in a data-dependent way to minimize asymptotic variance leads to an iterative procedure that converges to an estimator with connections to regression control methods. We refer to such estimators as adaptively normalized estimators. For mean estimation in survey sampling, the adaptively normalized estimator has asymptotic variance that is never worse than the Horvitz–Thompson and Hájek estimators. Going further, we show that adaptive normalization can be used to propose improvements of the augmented IPW (AIPW) estimator, average treatment effect (ATE) estimators, and policy learning objectives. Appealingly, these proposals preserve both the asymptotic efficiency of AIPW and the regret bounds for policy learning with IPW objectives, and deliver consistent finite sample improvements in simulations for all three of mean estimation, ATE estimation, and policy learning.

Open Access February 15, 2023

Matched design for marginal causal effect on restricted mean survival time in observational studies

Zihan Lin, Ai Ni, Bo Lu

Article number: 20220035

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Abstract

Investigating the causal relationship between exposure and time-to-event outcome is an important topic in biomedical research. Previous literature has discussed the potential issues of using hazard ratio (HR) as the marginal causal effect measure due to noncollapsibility. In this article, we advocate using restricted mean survival time (RMST) difference as a 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 matched design with sensitivity analysis is proposed. Matching is used to pair similar treated and untreated subjects together, which is generally more robust than outcome modeling due to potential misspecifications. Our propensity score matched RMST difference estimator is shown to be asymptotically unbiased, and the corresponding variance estimator is calculated by accounting for the correlation due to matching. Simulation studies also demonstrate that our method has adequate empirical performance and outperforms several competing methods used in practice. To assess the impact of unmeasured confounding, we develop a sensitivity analysis strategy by adapting the E -value approach to matched data. We apply the proposed method to the Atherosclerosis Risk in Communities Study (ARIC) to examine the causal effect of smoking on stroke-free survival.

Open Access February 20, 2023

Robust inference for matching under rolling enrollment

Amanda K. Glazer, Samuel D. Pimentel

Article number: 20220055

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Abstract

Matching in observational studies faces complications when units enroll in treatment on a rolling basis. While each treated unit has a specific time of entry into the study, control units each have many possible comparison, or “pseudo-treatment,” times. Valid inference must account for correlations between repeated measures for a single unit, and researchers must decide how flexibly to match across time and units. We provide three important innovations. First, we introduce a new matched design, GroupMatch with instance replacement, allowing maximum flexibility in control selection. This new design searches over all possible comparison times for each treated-control pairing and is more amenable to analysis than past methods. Second, we propose a block bootstrap approach for inference in matched designs with rolling enrollment and demonstrate that it accounts properly for complex correlations across matched sets in our new design and several other contexts. Third, we develop a falsification test to detect violations of the timepoint agnosticism assumption, which is needed to permit flexible matching across time. We demonstrate the practical value of these tools via simulations and a case study of the impact of short-term injuries on batting performance in major league baseball.

Open Access February 24, 2023

Attributable fraction and related measures: Conceptual relations in the counterfactual framework

Etsuji Suzuki, Eiji Yamamoto

Article number: 20210068

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Abstract

The attributable fraction (population) has attracted much attention from a theoretical perspective and has been used extensively to assess the impact of potential health interventions. However, despite its extensive use, there is much confusion about its concept and calculation methods. In this article, we discuss the concepts of and calculation methods for the attributable fraction and related measures in the counterfactual framework, both with and without stratification by covariates. Generally, the attributable fraction is useful when the exposure of interest has a causal effect on the outcome. However, it is important to understand that this statement applies to the exposed group. Although the target population of the attributable fraction (population) is the total population, the causal effect should be present not in the total population but in the exposed group. As related measures, we discuss the preventable fraction and prevented fraction, which are generally useful when the exposure of interest has a preventive effect on the outcome, and we further propose a new measure called the attributed fraction. We also discuss the causal and preventive excess fractions, and provide notes on vaccine efficacy. Finally, we discuss the relations between the aforementioned six measures and six possible patterns using a conceptual schema.

Open Access March 7, 2023

Causality and independence in perfectly adapted dynamical systems

Tineke Blom, Joris M. Mooij

Article number: 20210005

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Abstract

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. With the help of the causal ordering algorithm, one can construct graphical representations of dynamical systems that represent the causal relations between the variables and the conditional independences in the equilibrium distribution. We apply these tools to formulate sufficient graphical conditions for identifying perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply this method to a simple model for a protein signalling pathway and test its predictions in both simulations and using real-world protein expression data. We demonstrate that perfect adaptation can lead to misleading orientation of edges in the output of causal discovery algorithms.

Open Access March 23, 2023

Sensitivity analysis for causal decomposition analysis: Assessing robustness toward omitted variable bias

Soojin Park, Suyeon Kang, Chioun Lee, Shujie Ma

Article number: 20220031

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Abstract

A key objective of decomposition analysis is to identify a factor (the “mediator”) contributing to disparities in an outcome between social groups. In decomposition analysis, a scholarly interest often centers on estimating how much the disparity (e.g., health disparities between Black women and White men) would be reduced/remain if we set the mediator (e.g., education) distribution of one social group equal to another. However, causally identifying disparity reduction and remaining depends on the no omitted mediator–outcome confounding assumption, which is not empirically testable. Therefore, we propose a set of sensitivity analyses to assess the robustness of disparity reduction to possible unobserved confounding. We derived general bias formulas for disparity reduction, which can be used beyond a particular statistical model and do not require any functional assumptions. Moreover, the same bias formulas apply with unobserved confounding measured before and after the group status. On the basis of the formulas, we provide sensitivity analysis techniques based on regression coefficients and R 2 {R}^{2} values by extending the existing approaches. The R 2 {R}^{2} -based sensitivity analysis offers a straightforward interpretation of sensitivity parameters and a standard way to report the robustness of research findings. Although we introduce sensitivity analysis techniques in the context of decomposition analysis, they can be utilized in any mediation setting based on interventional indirect effects when the exposure is randomized (or conditionally ignorable given covariates).

Open Access April 4, 2023

Instrumental variable regression via kernel maximum moment loss

Rui Zhang, Masaaki Imaizumi, Bernhard Schölkopf, Krikamol Muandet

Article number: 20220073

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Abstract

We investigate a simple objective for nonlinear instrumental variable (IV) regression based on a kernelized conditional moment restriction known as a maximum moment restriction (MMR). The MMR objective is formulated by maximizing the interaction between the residual and the instruments belonging to a unit ball in a reproducing kernel Hilbert space. First, it allows us to simplify the IV regression as an empirical risk minimization problem, where the risk function depends on the reproducing kernel on the instrument and can be estimated by a U -statistic or V -statistic. Second, on the basis this simplification, we are able to provide consistency and asymptotic normality results in both parametric and nonparametric settings. Finally, we provide easy-to-use IV regression algorithms with an efficient hyperparameter selection procedure. We demonstrate the effectiveness of our algorithms using experiments on both synthetic and real-world data.

Open Access April 26, 2023

Randomization-based, Bayesian inference of causal effects

Thomas Leavitt

Article number: 20220025

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Abstract

Bayesian causal inference in randomized experiments usually imposes model-based structure on potential outcomes. Yet causal inferences from randomized experiments are especially credible because they depend on a known assignment process, not a probability model of potential outcomes. In this article, I derive a randomization-based procedure for Bayesian inference of causal effects in a finite population setting. I formally show that this procedure satisfies Bayesian analogues of unbiasedness and consistency under weak conditions on a prior distribution. Unlike existing model-based methods of Bayesian causal inference, my procedure supposes neither probability models that generate potential outcomes nor independent and identically distributed random sampling. Unlike existing randomization-based methods of Bayesian causal inference, my procedure does not suppose that potential outcomes are discrete and bounded. Consequently, researchers can reap the benefits of Bayesian inference without sacrificing the properties that make inferences from randomized experiments especially credible in the first place.

Open Access May 11, 2023

On the pitfalls of Gaussian likelihood scoring for causal discovery

Christoph Schultheiss, Peter Bühlmann

Article number: 20220068

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Abstract

We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We present a surprising negative result for Gaussian likelihood scoring in combination with nonparametric regression methods.

Open Access May 23, 2023

Double machine learning and automated confounder selection: A cautionary tale

Paul Hünermund, Beyers Louw, Itamar Caspi

Article number: 20220078

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Abstract

Double machine learning (DML) has become an increasingly popular tool for automated variable selection in high-dimensional settings. Even though the ability to deal with a large number of potential covariates can render selection-on-observables assumptions more plausible, there is at the same time a growing risk that endogenous variables are included, which would lead to the violation of conditional independence. This article demonstrates that DML is very sensitive to the inclusion of only a few “bad controls” in the covariate space. The resulting bias varies with the nature of the theoretical causal model, which raises concerns about the feasibility of selecting control variables in a data-driven way.

Open Access May 25, 2023

Randomized graph cluster randomization

Johan Ugander, Hao Yin

Article number: 20220014

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Abstract

The global average treatment effect (GATE) is a primary quantity of interest in the study of causal inference under network interference. With a correctly specified exposure model of the interference, the Horvitz–Thompson (HT) and Hájek estimators of the GATE are unbiased and consistent, respectively, yet known to exhibit extreme variance under many designs and in many settings of interest. With a fixed clustering of the interference graph, graph cluster randomization (GCR) designs have been shown to greatly reduce variance compared to node-level random assignment, but even so the variance is still often prohibitively large. In this work, we propose a randomized version of the GCR design, descriptively named randomized graph cluster randomization (RGCR), which uses a random clustering rather than a single fixed clustering. By considering an ensemble of many different clustering assignments, this design avoids a key problem with GCR where the network exposure probability of a given node can be exponentially small in a single clustering. We propose two inherently randomized graph decomposition algorithms for use with RGCR designs, randomized 3-net and 1-hop-max , adapted from the prior work on multiway graph cut problems and the probabilistic approximation of (graph) metrics. We also propose weighted extensions of these two algorithms with slight additional advantages. All these algorithms result in network exposure probabilities that can be estimated efficiently. We derive structure-dependent upper bounds on the variance of the HT estimator of the GATE, depending on the metric structure of the graph driving the interference. Where the best-known such upper bound for the HT estimator under a GCR design is exponential in the parameters of the metric structure, we give a comparable upper bound under RGCR that is instead polynomial in the same parameters. We provide extensive simulations comparing RGCR and GCR designs, observing substantial improvements in GATE estimation in a variety of settings.

Open Access July 5, 2023

Efficient and flexible mediation analysis with time-varying mediators, treatments, and confounders

Iván Díaz, Nicholas Williams, Kara E. Rudolph

Article number: 20220077

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Abstract

Understanding the mechanisms of action of interventions is a major general goal of scientific inquiry. The collection of statistical methods that use data to achieve this goal is referred to as mediation analysis . Natural direct and indirect effects provide a definition of mediation that matches scientific intuition, but they are not identified in the presence of time-varying confounding. Interventional effects have been proposed as a solution to this problem, but existing estimation methods are limited to assuming simple (e.g., linear) and unrealistic relations between the mediators, treatments, and confounders. 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, and mediator-outcome relationships. Identification is achieved under the standard no-unmeasured-confounders and positivity assumptions. In this article, we study semi-parametric efficiency theory for the functional identifying the mediation parameter, including the non-parametric efficiency bound, and was used to propose non-parametrically efficient estimators. Implementation of our estimators only relies on the availability of regression algorithms, and the estimators in a general framework that allows the analyst to use arbitrary regression machinery were developed. The estimators are doubly robust, n \sqrt{n} -consistent, asymptotically Gaussian, under slow convergence rates for the regression algorithms used. This allows the use of flexible machine learning for regression while permitting uncertainty quantification through confidence intervals and p p -values. A free and open-source R package implementing the methods is available on GitHub. The proposed estimator to a motivating example from a trial of two medications for opioid-use disorder was applied, where we estimate the extent to which differences between the two treatments on risk of opioid use are mediated by craving symptoms.

Open Access July 14, 2023

Minimally capturing heterogeneous complier effect of endogenous treatment for any outcome variable

Goeun Lee, Jin-young Choi, Myoung-jae Lee

Article number: 20220036

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Abstract

When a binary treatment D D is possibly endogenous, a binary instrument δ \delta is often used to identify the “effect on compliers.” If covariates X X affect both D D and an outcome Y Y , X X should be controlled to identify the “ X X -conditional complier effect.” However, its nonparametric estimation leads to the well-known dimension problem. To avoid this problem while capturing the effect heterogeneity, we identify the complier effect heterogeneous with respect to only the one-dimensional “instrument score” E ( δ ∣ X ) E\left(\delta | X) for non-randomized δ \delta . This effect heterogeneity is minimal, in the sense that any other “balancing score” is finer than the instrument score. We establish two critical “reduced-form models” that are linear in D D or δ \delta , even though no parametric assumption is imposed. The models hold for any form of Y Y (continuous, binary, count, …). The desired effect is then estimated using either single index model estimators or an instrumental variable estimator after applying a power approximation to the effect. Simulation and empirical studies are performed to illustrate the proposed approaches.

Open Access July 15, 2023

Quantitative probing: Validating causal models with quantitative domain knowledge

Daniel Grünbaum, Maike L. Stern, Elmar W. Lang

Article number: 20220060

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Abstract

We propose quantitative probing as a model-agnostic framework for validating causal models in the presence of quantitative domain knowledge. The method is constructed in analogy to the train/test split in correlation-based machine learning. It is consistent with the logic of scientific discovery and enhances current causal validation strategies. The effectiveness of the method is illustrated using Pearl’s sprinkler example, before a thorough simulation-based investigation is conducted. Limits of the technique are identified by studying exemplary failing scenarios, which are furthermore used to propose a list of topics for future research and improvements of the presented version of quantitative probing. A guide for practitioners is included to facilitate the incorporation of quantitative probing in causal modelling applications. The code for integrating quantitative probing into causal analysis, as well as the code for the presented simulation-based studies of the effectiveness of quantitative probing are provided in two separate open-source Python packages.

Open Access July 28, 2023

On the dimensional indeterminacy of one-wave factor analysis under causal effects

Tyler J. VanderWeele, Charles J. K. Batty

Article number: 20220074

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Abstract

It is shown, with two sets of indicators that separately load on two distinct factors, independent of one another conditional on the past, that if it is the case that at least one of the factors causally affects the other, then, in many settings, the process will converge to a factor model in which a single factor will suffice to capture the covariance structure among the indicators. Factor analysis with one wave of data then cannot distinguish between factor models with a single factor vs those with two factors that are causally related. Therefore, unless causal relations between factors can be ruled out a priori, alleged empirical evidence from one-wave factor analysis for a single factor still leaves open the possibilities of a single factor or of two factors that causally affect one another. The implications for interpreting the factor structure of psychological scales, such as self-report scales for anxiety and depression, or for happiness and purpose, are discussed. The results are further illustrated through simulations to gain insight into the practical implications of the results in more realistic settings prior to the convergence of the processes. Some further generalizations to an arbitrary number of underlying factors are noted. Factor analyses with one wave of data should themselves be interpreted as characterizing associations among indicators that may be present either due to conceptual relations or due to causal relations concerning the underlying construct phenomena.

Open Access July 29, 2023

Heterogeneous interventional effects with multiple mediators: Semiparametric and nonparametric approaches

Max Rubinstein, Zach Branson, Edward H. Kennedy

Article number: 20220070

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Abstract

We propose semiparametric and nonparametric methods to estimate conditional interventional indirect effects in the setting of two discrete mediators whose causal ordering is unknown. Average interventional indirect effects have been shown to decompose an average treatment effect into a direct effect and interventional indirect effects that quantify effects of hypothetical interventions on mediator distributions. Yet these effects may be heterogeneous across the covariate distribution. We consider the problem of estimating these effects at particular points. We propose an influence function-based estimator of the projection of the conditional effects onto a working model, and show under some conditions that we can achieve root-n consistent and asymptotically normal estimates. Second, we propose a fully nonparametric approach to estimation and show the conditions where this approach can achieve oracle rates of convergence. Finally, we propose a sensitivity analysis that identifies bounds on both the average and conditional effects in the presence of mediator-outcome confounding. We show that the same methods easily extend to allow estimation of these bounds. We conclude by examining heterogeneous effects with respect to the effect of COVID-19 vaccinations on depression during February 2021.

Open Access August 3, 2023

Exploiting neighborhood interference with low-order interactions under unit randomized design

Mayleen Cortez-Rodriguez, Matthew Eichhorn, Christina Lee Yu

Article number: 20220051

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Abstract

Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we provide an unbiased estimator for the TTE when network interference effects are constrained to low-order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. We derive a bound on the variance of our estimator and show in simulated experiments that it performs well compared with standard estimators for the TTE. We also derive a minimax lower bound on the mean squared error of our estimator, which suggests that the difficulty of estimation can be characterized by the degree of interactions in the potential outcomes model. We also prove that our estimator is asymptotically normal under boundedness conditions on the network degree and potential outcomes model. Central to our contribution is a new framework for balancing model flexibility and statistical complexity as captured by this low-order interactions structure.

Open Access August 11, 2023

Robust variance estimation and inference for causal effect estimation

Linh Tran, Maya Petersen, Joshua Schwab, Mark J. van der Laan

Article number: 20210067

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Abstract

We present two novel approaches to variance estimation of semi-parametric efficient point estimators of the treatment-specific mean: (i) a robust approach that directly targets the variance of the influence function (IF) as a counterfactual mean outcome and (ii) a modified non-parametric bootstrap-based approach. The performance of these approaches to variance estimation is compared to variance estimation based on the sample variance of the empirical IF in simulations across different levels of positivity violations and treatment effect sizes. In this article, we focus on estimation of the nuisance parameters using correctly specified parametric models for the treatment mechanism in order to highlight the challenges posed by violation of positivity assumptions (distinct from the challenges posed by non-parametric estimation of the nuisance parameters). Results demonstrate that (1) variance estimation based on the empirical IF may provide highly anti-conservative confidence interval coverage (as reported previously), (2) the proposed robust approach to variance estimation in this setting provides conservative coverage, and (3) the proposed modified bootstrap maintains close to nominal coverage and improves power. In the appendix, we (a) generalize the robust approach of estimating variance to marginal structural working models and (b) provide a proof of the consistency of the targeted minimum loss-based estimation bootstrap.

Open Access August 23, 2023

Bounding the probabilities of benefit and harm through sensitivity parameters and proxies

Jose M. Peña

Article number: 20230012

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Abstract

We present two methods for bounding the probabilities of benefit (a.k.a. the probability of necessity and sufficiency, i.e., the desired effect occurs if and only if exposed) and harm (i.e., the undesired effect occurs if and only if exposed) under unmeasured confounding. The first method computes the upper or lower bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters, which can then be presented to the analyst as a 2-D plot to assist in decision-making. The second method assumes the existence of a measured nondifferential proxy for the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.

Open Access October 25, 2023

Potential outcome and decision theoretic foundations for statistical causality

Thomas S. Richardson, James M. Robins

Article number: 20220012

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Abstract

In a recent work published in this journal, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In this way, a correspondence is established between Dawid's approach and those based on potential outcomes such as Robins’ finest fully randomized causally interpreted structured tree graphs. In more detail, a reformulation of Dawid s theory is given that is essentially equivalent to his proposal and isomorphic to SWIGs.

Open Access October 26, 2023

2D score-based estimation of heterogeneous treatment effects

Steven Siwei Ye, Yanzhen Chen, Oscar Hernan Madrid Padilla

Article number: 20220016

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Abstract

Statisticians show growing interest in estimating and analyzing heterogeneity in causal effects in observational studies. However, there usually exists a trade-off between accuracy and interpretability for developing a desirable estimator for treatment effects, especially in the case when there are a large number of features in estimation. To make efforts to address the issue, we propose a score-based framework for estimating the conditional average treatment effect (CATE) function in this article. The framework integrates two components: (i) leverage the joint use of propensity and prognostic scores in a matching algorithm to obtain a proxy of the heterogeneous treatment effects for each observation and (ii) utilize nonparametric regression trees to construct an estimator for the CATE function conditioning on the two scores. The method naturally stratifies treatment effects into subgroups over a 2d grid whose axis are the propensity and prognostic scores. We conduct benchmark experiments on multiple simulated data and demonstrate clear advantages of the proposed estimator over state-of-the-art methods. We also evaluate empirical performance in real-life settings, using two observational data from a clinical trial and a complex social survey, and interpret policy implications following the numerical results.

Open Access November 6, 2023

Identification of in-sample positivity violations using regression trees: The PoRT algorithm

Gabriel Danelian, Yohann Foucher, Maxime Léger, Florent Le Borgne, Arthur Chatton

Article number: 20220032

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Abstract

Background The positivity assumption is crucial when drawing causal inferences from observational studies, but it is often overlooked in practice. A violation of positivity occurs when the sample contains a subgroup of individuals with an extreme relative frequency of experiencing one of the levels of exposure. To correctly estimate the causal effect, we must identify such individuals. For this purpose, we suggest a regression tree-based algorithm. Development Based on a succession of regression trees, the algorithm searches for combinations of covariate levels that result in subgroups of individuals with a low (un)exposed relative frequency. Application We applied the algorithm by reanalyzing four recently published medical studies. We identified the two violations of the positivity reported by the authors. In addition, we identified ten subgroups with a suspicion of violation. Conclusions The PoRT algorithm helps to detect in-sample positivity violations in causal studies. We implemented the algorithm in the R package RISCA to facilitate its use.

Open Access November 7, 2023

Model-based regression adjustment with model-free covariates for network interference

Kevin Han, Johan Ugander

Article number: 20230005

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Abstract

When estimating a global average treatment effect (GATE) under network interference, units can have widely different relationships to the treatment depending on a combination of the structure of their network neighborhood, the structure of the interference mechanism, and how the treatment was distributed in their neighborhood. In this work, we introduce a sequential procedure to generate and select graph- and treatment-based covariates for GATE estimation under regression adjustment. We show that it is possible to simultaneously achieve low bias and considerably reduce variance with such a procedure. To tackle inferential complications caused by our feature generation and selection process, we introduce a way to construct confidence intervals based on a block bootstrap. We illustrate that our selection procedure and subsequent estimator can achieve good performance in terms of root-mean-square error in several semi-synthetic experiments with Bernoulli designs, comparing favorably to an oracle estimator that takes advantage of regression adjustments for the known underlying interference structure. We apply our method to a real-world experimental dataset with strong evidence of interference and demonstrate that it can estimate the GATE reasonably well without knowing the interference process a priori .

Special Issue on Integration of observational studies with randomized trials - Part II

Open Access April 19, 2023

Personalized decision making – A conceptual introduction

Scott Mueller, Judea Pearl

Article number: 20220050

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Abstract

Personalized decision making targets the behavior of a specific individual, while population-based decision making concerns a subpopulation resembling that individual. This article clarifies the distinction between the two and explains why the former leads to more informed decisions. We further show that by combining experimental and observational studies, we can obtain valuable information about individual behavior and, consequently, improve decisions over those obtained from experimental studies alone. In particular, we show examples where such a combination discriminates between individuals who can benefit from a treatment and those who cannot – information that would not be revealed by experimental studies alone. We outline areas where this method could be of benefit to both policy makers and individuals involved.

Open Access August 23, 2023

Precise unbiased estimation in randomized experiments using auxiliary observational data

Johann A. Gagnon-Bartsch, Adam C. Sales, Edward Wu, Anthony F. Botelho, John A. Erickson, Luke W. Miratrix, Neil T. Heffernan

Article number: 20220011

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Abstract

Randomized controlled trials (RCTs) admit unconfounded design-based inference – randomization largely justifies the assumptions underlying statistical effect estimates – but often have limited sample sizes. However, researchers may have access to big observational data on covariates and outcomes from RCT nonparticipants. For example, data from A/B tests conducted within an educational technology platform exist alongside historical observational data drawn from student logs. We outline a design-based approach to using such observational data for variance reduction in RCTs. First, we use the observational data to train a machine learning algorithm predicting potential outcomes using covariates and then use that algorithm to generate predictions for RCT participants. Then, we use those predictions, perhaps alongside other covariates, to adjust causal effect estimates with a flexible, design-based covariate-adjustment routine. In this way, there is no danger of biases from the observational data leaking into the experimental estimates, which are guaranteed to be exactly unbiased regardless of whether the machine learning models are “correct” in any sense or whether the observational samples closely resemble RCT samples. We demonstrate the method in analyzing 33 randomized A/B tests and show that it decreases standard errors relative to other estimators, sometimes substantially.

Open Access August 29, 2023

Conditional average treatment effect estimation with marginally constrained models

Wouter A. C. van Amsterdam, Rajesh Ranganath

Article number: 20220027

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Abstract

Treatment effect estimates are often available from randomized controlled trials as a single average treatment effect for a certain patient population. Estimates of the conditional average treatment effect (CATE) are more useful for individualized treatment decision-making, but randomized trials are often too small to estimate the CATE. Examples in medical literature make use of the relative treatment effect (e.g. an odds ratio) reported by randomized trials to estimate the CATE using large observational datasets. One approach to estimating these CATE models is by using the relative treatment effect as an offset , while estimating the covariate-specific untreated risk. We observe that the odds ratios reported in randomized controlled trials are not the odds ratios that are needed in offset models because trials often report the marginal odds ratio. We introduce a constraint or a regularizer to better use marginal odds ratios from randomized controlled trials and find that under the standard observational causal inference assumptions, this approach provides a consistent estimate of the CATE. Next, we show that the offset approach is not valid for CATE estimation in the presence of unobserved confounding. We study if the offset assumption and the marginal constraint lead to better approximations of the CATE relative to the alternative of using the average treatment effect estimate from the randomized trial. We empirically show that when the underlying CATE has sufficient variation, the constraint and offset approaches lead to closer approximations to the CATE.

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Editorial

Editors
Kosuke Imai, Harvard University, USA
Judea Pearl, University of California, Los Angeles, USA
Maya Petersen, University of California, Berkeley School of Public Health, USA
Mark van der Laan, University of California, Berkeley School of Public Health, USA

Editorial Board
Alberto Abadie, Massachusetts Institute of Technology, USA
Laura Balzer, University of Massachusetts, Amherst, USA
Elias Bareinboim, Columbia University, USA
David Benkeser, Emory University, USA
Marco Carone, University of Washington, USA
Matias Cattaneo, Princeton University, USA
Antoine Chambaz, Université Paris Ouest Nanterre, France
Carlos Cinelli, University of Washington, USA
Rhian Daniel, Cardiff University, UK
Philip Dawid, University of Cambridge, UK
Ivan Diaz, Weill Cornell Medicine, USA
Peng Ding, University of California, Berkeley, USA
Felix Elwert, University of Wisconsin-Madison, USA
Avi Feller, University of California, Berkeley, USA
Maria Glymour, University of California, San Francisco, USA
Joseph Halpern, Cornell University, USA
Larry Han, Harvard T.H. Chan School of Public Health, USA
Nima Hejazi, Harvard T.H. Chan School of Public Health, USA
Jennifer Hill, New York University, USA
Christopher Hitchcock, California Institute of Technology, USA
Paul Hünermund, Copenhagen Business School, Denmark
Cheng Ju, University of California Berkeley, USA
Luke Keele, Georgetown University, USA
Manabu Kuroki, The Institute of Statistical Mathematics, Tokyo, Japan
Karthika Mohan, Oregon State University, USA
Joris Mooij, University of Amsterdam, Netherlands
Romain Neugebauer, Kaiser Permanente, USA
Jonas Peters, University of Copenhagen, Denmark
Sam Pimentel, University of California, Berkeley, USA
Michael Rosenblum, Johns Hopkins University, USA
Helene Rytgaard, University of Copenhagen, Denmark
Ilya Shpitser, Johns Hopkins University, USA
Ricardo Silva, University College London, UK
Elizabeth Stuart, Johns Hopkins University, USA
Jin Tian, Iowa State University, USA
Tyler VanderWeele, Harvard University, USA
Teppei Yamamoto, Massachusetts Institute of Technology, USA

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Type: Journal
Language: English
Publisher: De Gruyter
First published: June 1, 2013
Publication Frequency: 1 Issue per Year
Audience: All those interested in the causal inference, especially researchers