Causal Inference

Estimation and Inference of Heterogeneous Treatment Effects using Random Forests

Stefan Wager, Susan Athey · Journal of the American Statistical Association · 2017 · 2,737 citations

Many scientific and engineering challenges—ranging from personalized medicine to customized marketing recommendations—require an understanding of treatment effect heterogeneity. In this article, we develop a nonparametric causal forest for estimating heterogeneous treatment effects that extends Breiman’s widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true treatment effect and have an asymptotically Gaussian and centered sampling distribution. We also discuss a practical method for constructing asymptotic confidence intervals for the true treatment effect that are centered at the causal forest estimates. Our theoretical results rely on a generic Gaussian theory for a large family of random forest algorithms. To our knowledge, this is the first set of results that allows any type of random forest, including classification and regression forests, to be used for provably valid statistical inference. In experiments, we find causal forests to be substantially more powerful than classical methods based on nearest-neighbor matching, especially in the presence of irrelevant covariates.

Causal inference in statistics: An overview

Judea Pearl · Statistics Surveys · 2009 · 2,309 citations

This review presents empirical researchers with recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret,” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.

Towards Causal Representation Learning

Bernhard Scholkopf, Francesco Locatello, Stefan Bauer +4 more · Proceedings of the IEEE · 2021 · 1,404 citations

A field-defining overview connecting causal inference to representation learning, transfer, modularity, generalization, and discovery of high-level causal variables.

Elements of Causal Inference: Foundations and Learning Algorithms

Jonas Peters, Dominik Janzing, Bernhard Scholkopf · MIT Press · 2017

A machine-learning-facing treatment of structural causal models, causal discovery, invariance, and causal learning algorithms.

On Pearl's Hierarchy and the Foundations of Causal Inference

Elias Bareinboim, Juan D. Correa, Duligur Ibeling +1 more · Probabilistic and Causal Inference: The Works of Judea Pearl · 2022

An overview of the Pearl Causal Hierarchy and the formal distinctions between associational, interventional, and counterfactual queries.

Causal Inference: What If

Miguel A. Hernan, James M. Robins · Chapman & Hall/CRC · 2020

A book-length applied introduction to causal questions, target trials, time-varying treatment, confounding, selection, and potential-outcomes estimands.

On Causal Inference in the Presence of Interference

Eric J. Tchetgen Tchetgen, Tyler J. VanderWeele · Statistical Methods in Medical Research · 2012 · 500 citations

A compact overview of causal inference when one unit's treatment can affect another unit's outcome, including finite-sample inference, IPW estimators, and estimands.

Causal Machine Learning: A Survey and Open Problems

Jean Kaddour, Aengus Lynch, Qi Liu +2 more · arXiv · 2022

A broad survey of causal machine learning spanning supervised learning, generative modeling, explanations, fairness, reinforcement learning, and open problems.

A Survey on Causal Discovery: Theory and Practice

Alessio Zanga, Elif Ozkirimli, Fabio Stella · International Journal of Approximate Reasoning · 2023 · 136 citations

A recent survey of causal discovery algorithms, assumptions, evaluation data, metrics, software, applications, and practical tooling.

A Survey on Causal Discovery Methods for I.I.D. and Time Series Data

Uzma Hasan, Emam Hossain, Md Osman Gani · Transactions on Machine Learning Research · 2023

A survey of causal discovery methods for both independent tabular data and temporally dependent time-series settings.

Making Sense of Sensitivity: Extending Omitted Variable Bias

Carlos Cinelli, Chad Hazlett · Journal of the Royal Statistical Society: Series B · 2020 · 885 citations

A modern omitted-variable sensitivity framework for regression-style causal analysis, using partial R-squared calibration to assess robustness to unmeasured confounding.

Review of Causal Discovery Methods Based on Graphical Models

Clark Glymour, Kun Zhang, Peter Spirtes · Frontiers in Genetics · 2019 · 1,115 citations

A review of graphical-model causal discovery methods, including constraint-based, score-based, and functional causal model approaches.

Transportability of Causal Effects: Completeness Results

Elias Bareinboim, Judea Pearl · AAAI · 2012

A foundational paper on when causal effects learned in one domain can be transported to another and how to compute transport formulas.

A General Approach to Causal Mediation Analysis

Kosuke Imai, Luke Keele, Dustin Tingley · Psychological Methods · 2010 · 3,587 citations

A modern framework for causal mediation analysis with explicit direct and indirect effects and identification assumptions beyond linear structural equation models.

Sensitivity Analyses for Unmeasured Confounders

Lucy D'Agostino McGowan · Current Epidemiology Reports · 2022 · 33 citations

A practical review of sensitivity-analysis tools for unmeasured confounding, with guidance by scenario and implementation details.

Metalearners for Estimating Heterogeneous Treatment Effects using Machine Learning

Soren R. Kunzel, Jasjeet S. Sekhon, Peter J. Bickel +1 more · Proceedings of the National Academy of Sciences · 2019 · 1,243 citations

The standard S-learner, T-learner, and X-learner framing for estimating heterogeneous treatment effects with machine learning.

Heterogeneous Treatment Effects Analysis for Social Scientists: A Review

Anning Hu · Social Science Research · 2023 · 29 citations

An accessible review of heterogeneous treatment effect methods including interactions, GAMs, propensity scores, causal trees, causal forests, BART, and meta-learners.

Markov Decision Processes with Unobserved Confounders: A Causal Approach

Junzhe Zhang, Elias Bareinboim · CausalAI Lab Technical Report R-23 · 2016

Extends causal reasoning to MDPs where hidden variables may affect both actions and outcomes, motivating CRL methods that reason about confounding in sequential settings.

Bandits with Unobserved Confounders: A Causal Approach

Elias Bareinboim, Andrew Forney, Judea Pearl · NeurIPS · 2015

Introduces a causal treatment of bandit problems where observational feedback may be confounded, showing when causal structure can improve intervention selection.

Causal Imitation Learning with Unobserved Confounders

Junzhe Zhang, Daniel Kumor, Elias Bareinboim · NeurIPS · 2020

Formulates imitation learning when expert demonstrations are confounded and rewards may not be directly observed.

Structural Causal Bandits: Where to Intervene?

Sanghack Lee, Elias Bareinboim · NeurIPS · 2018

Introduces structural causal bandits, where the learner chooses interventions in a causal graph rather than arms with unrelated reward distributions.

Off-Policy Policy Evaluation for Sequential Decisions under Unobserved Confounding

Hongseok Namkoong, Ramtin Keramati, Steve Yadlowsky +1 more · arXiv · 2020

Studies off-policy evaluation for sequential decisions when hidden confounders may bias logged trajectories.

An Introduction to Causal Reinforcement Learning

Elias Bareinboim, Junzhe Zhang, Sanghack Lee · CausalAI Lab Technical Report R-65 · 2024

A tutorial survey that organizes causal reinforcement learning around offline-to-online learning, intervention choice, counterfactual decision-making, transportability, causal discovery, imitation, curriculum learning, reward shaping, and causal game theory.

Near-Optimal Reinforcement Learning in Dynamic Treatment Regimes

Junzhe Zhang, Elias Bareinboim · NeurIPS · 2019

Connects causal reinforcement learning with dynamic treatment regimes, focusing on near-optimal sequential treatment policies.

Confounding-Robust Policy Improvement

Nathan Kallus, Angela Zhou · NeurIPS · 2018

Develops policy improvement methods that account for possible unobserved confounding in observational decision data.

Estimation and Inference of Heterogeneous Treatment Effects using Random Forests

Stefan Wager, Susan Athey · 2015

Many scientific and engineering challenges -- ranging from personalized medicine to customized marketing recommendations -- require an understanding of treatment effect heterogeneity. In this paper, we develop a non-parametric causal forest for estimating heterogeneous treatment effects that extends Breiman's widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true treatment effect, and have an asymptotically Gaussian and centered sampling distribution. We also discuss a practical method for constructing asymptotic confidence intervals for the true treatment effect that are centered at the causal forest estimates. Our theoretical results rely on a generic Gaussian theory for a large family of random forest algorithms. To our knowledge, this is the first set of results that allows any type of random forest, including classification and regression forests, to be used for provably valid statistical inference. In experiments, we find causal forests to be substantially more powerful than classical methods based on nearest-neighbor matching, especially in the presence of irrelevant covariates.

Quasi-Oracle Estimation of Heterogeneous Treatment Effects

Xinkun Nie, Stefan Wager · 2017

Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges, such as personalized medicine and optimal resource allocation. In this paper, we develop a general class of two-step algorithms for heterogeneous treatment effect estimation in observational studies. We first estimate marginal effects and treatment propensities in order to form an objective function that isolates the causal component of the signal. Then, we optimize this data-adaptive objective function. Our approach has several advantages over existing methods. From a practical perspective, our method is flexible and easy to use: In both steps, we can use any loss-minimization method, e.g., penalized regression, deep neural networks, or boosting; moreover, these methods can be fine-tuned by cross validation. Meanwhile, in the case of penalized kernel regression, we show that our method has a quasi-oracle property: Even if the pilot estimates for marginal effects and treatment propensities are not particularly accurate, we achieve the same error bounds as an oracle who has a priori knowledge of these two nuisance components. We implement variants of our approach based on penalized regression, kernel ridge regression, and boosting in a variety of simulation setups, and find promising performance relative to existing baselines.

Budgeted Experiment Design for Causal Structure Learning

AmirEmad Ghassami, Saber Salehkaleybar, Negar Kiyavash +1 more · ICML · 2018

Addresses how to allocate a limited intervention budget to learn causal structure efficiently.

Sequential Causal Imitation Learning with Unobserved Confounders

Daniel Kumor, Junzhe Zhang, Elias Bareinboim · NeurIPS · 2021

Extends causal imitation learning to sequential settings where confounding can persist across time.

Experimental Design for Learning Causal Graphs with Latent Variables

Murat Kocaoglu, Karthikeyan Shanmugam, Elias Bareinboim · NeurIPS · 2017

Studies how to choose experiments for learning causal graphs when latent variables may be present.

Causally Aligned Curriculum Learning

Mengyue Li, Junzhe Zhang, Elias Bareinboim · ICLR · 2024

Studies curriculum learning through causal alignment between source subtasks and the target task.

Structural Causal Bandits with Non-Manipulable Variables

Sanghack Lee, Elias Bareinboim · AAAI · 2019

Extends structural causal bandits to settings where some variables can be observed but not directly manipulated.

Characterizing Optimal Mixed Policies: Where to Intervene, What to Observe

Sanghack Lee, Elias Bareinboim · NeurIPS · 2020

Characterizes policies that mix interventions and observations in causal decision problems.

Counterfactual Data-Fusion for Online Reinforcement Learners

Andrew Forney, Judea Pearl, Elias Bareinboim · ICML · 2017

Studies how online learners can combine heterogeneous observational and experimental data sources using counterfactual data-fusion principles.

Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression

Jack Bowden, George Davey Smith, Stephen Burgess · International Journal of Epidemiology · 2015 · 10,518 citations

BACKGROUND: The number of Mendelian randomization analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. However, some genetic variants may not be valid instrumental variables, in particular due to them having more than one proximal phenotypic correlate (pleiotropy). METHODS: We view Mendelian randomization with multiple instruments as a meta-analysis, and show that bias caused by pleiotropy can be regarded as analogous to small study bias. Causal estimates using each instrument can be displayed visually by a funnel plot to assess potential asymmetry. Egger regression, a tool to detect small study bias in meta-analysis, can be adapted to test for bias from pleiotropy, and the slope coefficient from Egger regression provides an estimate of the causal effect. Under the assumption that the association of each genetic variant with the exposure is independent of the pleiotropic effect of the variant (not via the exposure), Egger's test gives a valid test of the null causal hypothesis and a consistent causal effect estimate even when all the genetic variants are invalid instrumental variables. RESULTS: We illustrate the use of this approach by re-analysing two published Mendelian randomization studies of the causal effect of height on lung function, and the causal effect of blood pressure on coronary artery disease risk. The conservative nature of this approach is illustrated with these examples. CONCLUSIONS: An adaption of Egger regression (which we call MR-Egger) can detect some violations of the standard instrumental variable assumptions, and provide an effect estimate which is not subject to these violations. The approach provides a sensitivity analysis for the robustness of the findings from a Mendelian randomization investigation.

Combining information on multiple instrumental variables in Mendelian randomization: comparison of allele score and summarized data methods

Stephen Burgess, Frank Dudbridge, Simon G. Thompson · Statistics in Medicine · 2015 · 1,247 citations

Mendelian randomization is the use of genetic instrumental variables to obtain causal inferences from observational data. Two recent developments for combining information on multiple uncorrelated instrumental variables (IVs) into a single causal estimate are as follows: (i) allele scores, in which individual-level data on the IVs are aggregated into a univariate score, which is used as a single IV, and (ii) a summary statistic method, in which causal estimates calculated from each IV using summarized data are combined in an inverse-variance weighted meta-analysis. To avoid bias from weak instruments, unweighted and externally weighted allele scores have been recommended. Here, we propose equivalent approaches using summarized data and also provide extensions of the methods for use with correlated IVs. We investigate the impact of different choices of weights on the bias and precision of estimates in simulation studies. We show that allele score estimates can be reproduced using summarized data on genetic associations with the risk factor and the outcome. Estimates from the summary statistic method using external weights are biased towards the null when the weights are imprecisely estimated; in contrast, allele score estimates are unbiased. With equal or external weights, both methods provide appropriate tests of the null hypothesis of no causal effect even with large numbers of potentially weak instruments. We illustrate these methods using summarized data on the causal effect of low-density lipoprotein cholesterol on coronary heart disease risk. It is shown that a more precise causal estimate can be obtained using multiple genetic variants from a single gene region, even if the variants are correlated.

An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies

Peter C. Austin · Multivariate Behavioral Research · 2011 · 11,736 citations

The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects. I describe 4 different propensity score methods: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. I describe balance diagnostics for examining whether the propensity score model has been adequately specified. Furthermore, I discuss differences between regression-based methods and propensity score-based methods for the analysis of observational data. I describe different causal average treatment effects and their relationship with propensity score analyses.

A Survey on Causal Inference

Liuyi Yao, Zhixuan Chu, Sheng Li +3 more · ACM Transactions on Knowledge Discovery from Data · 2021 · 437 citations

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy, and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well-known causal inference frameworks. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine, and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption

Fernando Pires Hartwig, George Davey Smith, Jack Bowden · International Journal of Epidemiology · 2017 · 3,676 citations

Background: Mendelian randomization (MR) is being increasingly used to strengthen causal inference in observational studies. Availability of summary data of genetic associations for a variety of phenotypes from large genome-wide association studies (GWAS) allows straightforward application of MR using summary data methods, typically in a two-sample design. In addition to the conventional inverse variance weighting (IVW) method, recently developed summary data MR methods, such as the MR-Egger and weighted median approaches, allow a relaxation of the instrumental variable assumptions. Methods: Here, a new method - the mode-based estimate (MBE) - is proposed to obtain a single causal effect estimate from multiple genetic instruments. The MBE is consistent when the largest number of similar (identical in infinite samples) individual-instrument causal effect estimates comes from valid instruments, even if the majority of instruments are invalid. We evaluate the performance of the method in simulations designed to mimic the two-sample summary data setting, and demonstrate its use by investigating the causal effect of plasma lipid fractions and urate levels on coronary heart disease risk. Results: The MBE presented less bias and lower type-I error rates than other methods under the null in many situations. Its power to detect a causal effect was smaller compared with the IVW and weighted median methods, but was larger than that of MR-Egger regression, with sample size requirements typically smaller than those available from GWAS consortia. Conclusions: The MBE relaxes the instrumental variable assumptions, and should be used in combination with other approaches in sensitivity analyses.

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion)

P. Richard Hahn, Jared S. Murray, Carlos M. Carvalho · Bayesian Analysis · 2020 · 303 citations

This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding by observables. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively “shrink to homogeneity”. While we focus on observational data, our methods are equally useful for inferring heterogeneous treatment effects from randomized controlled experiments where careful regularization is somewhat less complicated but no less important. We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

The MR-Base platform supports systematic causal inference across the human phenome

Gibran Hemani, Jie Zheng, Benjamin Elsworth +17 more · eLife · 2018 · 8,325 citations

Results from genome-wide association studies (GWAS) can be used to infer causal relationships between phenotypes, using a strategy known as 2-sample Mendelian randomization (2SMR) and bypassing the need for individual-level data. However, 2SMR methods are evolving rapidly and GWAS results are often insufficiently curated, undermining efficient implementation of the approach. We therefore developed MR-Base (<ext-link ext-link-type="uri" xlink:href="http://www.mrbase.org">http://www.mrbase.org</ext-link>): a platform that integrates a curated database of complete GWAS results (no restrictions according to statistical significance) with an application programming interface, web app and R packages that automate 2SMR. The software includes several sensitivity analyses for assessing the impact of horizontal pleiotropy and other violations of assumptions. The database currently comprises 11 billion single nucleotide polymorphism-trait associations from 1673 GWAS and is updated on a regular basis. Integrating data with software ensures more rigorous application of hypothesis-driven analyses and allows millions of potential causal relationships to be efficiently evaluated in phenome-wide association studies.

Efficient and Robust Methods for Causally Interpretable Meta-Analysis: Transporting Inferences from Multiple Randomized Trials to a Target Population

Issa J Dahabreh, Sarah E. Robertson, Lucia C. Petito +2 more · Biometrics · 2022 · 47 citations

We present methods for causally interpretable meta-analyses that combine information from multiple randomized trials to draw causal inferences for a target population of substantive interest. We consider identifiability conditions, derive implications of the conditions for the law of the observed data, and obtain identification results for transporting causal inferences from a collection of independent randomized trials to a new target population in which experimental data may not be available. We propose an estimator for the potential outcome mean in the target population under each treatment studied in the trials. The estimator uses covariate, treatment, and outcome data from the collection of trials, but only covariate data from the target population sample. We show that it is doubly robust in the sense that it is consistent and asymptotically normal when at least one of the models it relies on is correctly specified. We study the finite sample properties of the estimator in simulation studies and demonstrate its implementation using data from a multicenter randomized trial.

A tutorial on propensity score estimation for multiple treatments using generalized boosted models

Daniel F. McCaffrey, Beth Ann Griffin, Daniel Almirall +3 more · Statistics in Medicine · 2013 · 1,479 citations

The use of propensity scores to control for pretreatment imbalances on observed variables in non-randomized or observational studies examining the causal effects of treatments or interventions has become widespread over the past decade. For settings with two conditions of interest such as a treatment and a control, inverse probability of treatment weighted estimation with propensity scores estimated via boosted models has been shown in simulation studies to yield causal effect estimates with desirable properties. There are tools (e.g., the twang package in R) and guidance for implementing this method with two treatments. However, there is not such guidance for analyses of three or more treatments. The goals of this paper are twofold: (1) to provide step-by-step guidance for researchers who want to implement propensity score weighting for multiple treatments and (2) to propose the use of generalized boosted models (GBM) for estimation of the necessary propensity score weights. We define the causal quantities that may be of interest to studies of multiple treatments and derive weighted estimators of those quantities. We present a detailed plan for using GBM to estimate propensity scores and using those scores to estimate weights and causal effects. We also provide tools for assessing balance and overlap of pretreatment variables among treatment groups in the context of multiple treatments. A case study examining the effects of three treatment programs for adolescent substance abuse demonstrates the methods.

Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator

Jack Bowden, George Davey Smith, Philip Haycock +1 more · Genetic Epidemiology · 2016 · 9,533 citations

Developments in genome-wide association studies and the increasing availability of summary genetic association data have made application of Mendelian randomization relatively straightforward. However, obtaining reliable results from a Mendelian randomization investigation remains problematic, as the conventional inverse-variance weighted method only gives consistent estimates if all of the genetic variants in the analysis are valid instrumental variables. We present a novel weighted median estimator for combining data on multiple genetic variants into a single causal estimate. This estimator is consistent even when up to 50% of the information comes from invalid instrumental variables. In a simulation analysis, it is shown to have better finite-sample Type 1 error rates than the inverse-variance weighted method, and is complementary to the recently proposed MR-Egger (Mendelian randomization-Egger) regression method. In analyses of the causal effects of low-density lipoprotein cholesterol and high-density lipoprotein cholesterol on coronary artery disease risk, the inverse-variance weighted method suggests a causal effect of both lipid fractions, whereas the weighted median and MR-Egger regression methods suggest a null effect of high-density lipoprotein cholesterol that corresponds with the experimental evidence. Both median-based and MR-Egger regression methods should be considered as sensitivity analyses for Mendelian randomization investigations with multiple genetic variants.

Functional mapping and annotation of genetic associations with FUMA

Kyoko Watanabe, Erdogan Taskesen, Arjen van Bochoven +1 more · Nature Communications · 2017 · 4,438 citations

A main challenge in genome-wide association studies (GWAS) is to pinpoint possible causal variants. Results from GWAS typically do not directly translate into causal variants because the majority of hits are in non-coding or intergenic regions, and the presence of linkage disequilibrium leads to effects being statistically spread out across multiple variants. Post-GWAS annotation facilitates the selection of most likely causal variant(s). Multiple resources are available for post-GWAS annotation, yet these can be time consuming and do not provide integrated visual aids for data interpretation. We, therefore, develop FUMA: an integrative web-based platform using information from multiple biological resources to facilitate functional annotation of GWAS results, gene prioritization and interactive visualization. FUMA accommodates positional, expression quantitative trait loci (eQTL) and chromatin interaction mappings, and provides gene-based, pathway and tissue enrichment results. FUMA results directly aid in generating hypotheses that are testable in functional experiments aimed at proving causal relations.

Recursive partitioning for heterogeneous causal effects

Susan Athey, Guido W. Imbens · Proceedings of the National Academy of Sciences · 2016 · 1,523 citations

In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population. We provide a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even with many covariates relative to the sample size, and without "sparsity" assumptions. We propose an "honest" approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation. We address the challenge that the "ground truth" for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that for our preferred method honest estimation results in nominal coverage for 90% confidence intervals, whereas coverage ranges between 74% and 84% for nonhonest approaches. Honest estimation requires estimating the model with a smaller sample size; the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7-22%.

Sensitivity Analyses for Robust Causal Inference from Mendelian Randomization Analyses with Multiple Genetic Variants

Stephen Burgess, Jack Bowden, Tove Fall +2 more · Epidemiology · 2016 · 2,128 citations

Mendelian randomization investigations are becoming more powerful and simpler to perform, due to the increasing size and coverage of genome-wide association studies and the increasing availability of summarized data on genetic associations with risk factors and disease outcomes. However, when using multiple genetic variants from different gene regions in a Mendelian randomization analysis, it is highly implausible that all the genetic variants satisfy the instrumental variable assumptions. This means that a simple instrumental variable analysis alone should not be relied on to give a causal conclusion. In this article, we discuss a range of sensitivity analyses that will either support or question the validity of causal inference from a Mendelian randomization analysis with multiple genetic variants. We focus on sensitivity analyses of greatest practical relevance for ensuring robust causal inferences, and those that can be undertaken using summarized data. Aside from cases in which the justification of the instrumental variable assumptions is supported by strong biological understanding, a Mendelian randomization analysis in which no assessment of the robustness of the findings to violations of the instrumental variable assumptions has been made should be viewed as speculative and incomplete. In particular, Mendelian randomization investigations with large numbers of genetic variants without such sensitivity analyses should be treated with skepticism.

Toward Causal Representation Learning

Bernhard Schölkopf, Francesco Locatello, Stefan Bauer +4 more · Proceedings of the IEEE · 2021 · 998 citations

The two fields of machine learning and graphical causality arose and are developed separately. However, there is, now, cross-pollination and increasing interest in both fields to benefit from the advances of the other. In this article, we review fundamental concepts of causal inference and relate them to crucial open problems of machine learning, including transfer and generalization, thereby assaying how causality can contribute to modern machine learning research. This also applies in the opposite direction: we note that most work in causality starts from the premise that the causal variables are given. A central problem for AI and causality is, thus, causal representation learning, that is, the discovery of high-level causal variables from low-level observations. Finally, we delineate some implications of causality for machine learning and propose key research areas at the intersection of both communities.

A More Credible Approach to Parallel Trends

Ashesh Rambachan, Jonathan Roth · The Review of Economic Studies · 2023 · 1,117 citations

Abstract This paper proposes tools for robust inference in difference-in-differences and event-study designs where the parallel trends assumption may be violated. Instead of requiring that parallel trends holds exactly, we impose restrictions on how different the post-treatment violations of parallel trends can be from the pre-treatment differences in trends (“pre-trends”). The causal parameter of interest is partially identified under these restrictions. We introduce two approaches that guarantee uniformly valid inference under the imposed restrictions, and we derive novel results showing that they have desirable power properties in our context. We illustrate how economic knowledge can inform the restrictions on the possible violations of parallel trends in two economic applications. We also highlight how our approach can be used to conduct sensitivity analyses showing what causal conclusions can be drawn under various restrictions on the possible violations of the parallel trends assumption.

Interpreting findings from Mendelian randomization using the MR-Egger method

Stephen Burgess, Simon G. Thompson · European Journal of Epidemiology · 2017 · 4,791 citations

Mendelian randomization-Egger (MR-Egger) is an analysis method for Mendelian randomization using summarized genetic data. MR-Egger consists of three parts: (1) a test for directional pleiotropy, (2) a test for a causal effect, and (3) an estimate of the causal effect. While conventional analysis methods for Mendelian randomization assume that all genetic variants satisfy the instrumental variable assumptions, the MR-Egger method is able to assess whether genetic variants have pleiotropic effects on the outcome that differ on average from zero (directional pleiotropy), as well as to provide a consistent estimate of the causal effect, under a weaker assumption-the InSIDE (INstrument Strength Independent of Direct Effect) assumption. In this paper, we provide a critical assessment of the MR-Egger method with regard to its implementation and interpretation. While the MR-Egger method is a worthwhile sensitivity analysis for detecting violations of the instrumental variable assumptions, there are several reasons why causal estimates from the MR-Egger method may be biased and have inflated Type 1 error rates in practice, including violations of the InSIDE assumption and the influence of outlying variants. The issues raised in this paper have potentially serious consequences for causal inferences from the MR-Egger approach. We give examples of scenarios in which the estimates from conventional Mendelian randomization methods and MR-Egger differ, and discuss how to interpret findings in such cases.