Causal Inference Literature Research Articles

Inverting estimating equations for causal inference on quantiles

Abstract The causal inference literature frequently focuses on estimating the mean of the potential outcome, whereas quantiles of the potential outcome may carry important additional information. We propose the inverse estimating equations framework to generalize a wide class of causal inference solutions from estimating the mean of the potential outcome to its quantiles. We assume that a moment function is available to identify the mean of the threshold-transformed potential outcome, based on which a convenient construction of the estimating equation of the quantiles of potential outcome is proposed. In addition, we give a general construction of the efficient influence functions of the mean and quantiles of potential outcomes, and establish their connection. We motivate estimators for the quantile estimands with the efficient influence function, and develop their asymptotic properties when either parametric models or data-adaptive machine learners are used to estimate the nuisance functions. A broad implication of our results is that one can rework the existing result for mean causal estimands to facilitate causal inference on quantiles. Our general results are illustrated by several analytical and numerical examples.

Parametric g-formula for Testing Time-Varying Causal Effects: What It Is, Why It Matters, and How to Implement It in Lavaan

Psychologists leverage longitudinal designs to examine the causal effects of a focal predictor (i.e., treatment or exposure) over time. But causal inference of naturally observed time-varying treatments is complicated by treatment-dependent confounding in which earlier treatments affect confounders of later treatments. In this tutorial article, we introduce psychologists to an established solution to this problem from the causal inference literature: the parametric g-computation formula. We explain why the g-formula is effective at handling treatment-dependent confounding. We demonstrate that the parametric g-formula is conceptually intuitive, easy to implement, and well-suited for psychological research. We first clarify that the parametric g-formula essentially utilizes a series of statistical models to estimate the joint distribution of all post-treatment variables. These statistical models can be readily specified as standard multiple linear regression functions. We leverage this insight to implement the parametric g-formula using lavaan, a widely adopted R package for structural equation modeling. Moreover, we describe how the parametric g-formula may be used to estimate a marginal structural model whose causal parameters parsimoniously encode time-varying treatment effects. We hope this accessible introduction to the parametric g-formula will equip psychologists with an analytic tool to address their causal inquiries using longitudinal data.

Enhancing Causal Pursuits in Organizational Science: Targeting the Effect of Treatment on the Treated in Research on Vulnerable Populations

Understanding the experiences of vulnerable workers is an important scientific pursuit. For example, research interest is often in quantifying the impacts of adverse exposures such as discrimination, exclusion, harassment, or job insecurity, among others. However, routine approaches have only focused on the average treatment effect, which encapsulates the impact of an exposure (e.g., discrimination) applied to the entire study population—including those who were not exposed. In this paper, we propose using a more refined causal quantity uniquely suited to address such causal queries: The effect of treatment on the treated (ETT) from the causal inference literature. We explain why the ETT is a more pertinent causal estimand for investigating the experiences of vulnerable workers by highlighting three appealing features: Better interpretability, greater accuracy, and enhanced robustness to violations of empirically untestable causal assumptions. We further describe how to estimate the ETT by introducing and comparing two estimators. Both estimators are conferred with a so-called doubly robust property. We hope the current proposal empowers organizational scholars in their crucial endeavors dedicated to understanding the vulnerable workforce.

A Causal Framework for the Comparability of Latent Variables

Measurement invariance (MI) describes the equivalence of measurement models of a construct across groups or time. When comparing latent means, MI is often stated as a prerequisite of meaningful group comparisons. The most common way to investigate MI is multi-group confirmatory factor analysis (MG-CFA). Although numerous guides exist, a recent review showed that MI is rarely investigated in practice. We argue that one reason might be that the results of MG-CFA are uninformative as to why MI does not hold between groups. Consequently, under this framework, it is difficult to regard the study of MI as an interesting and constructive step in the modeling process. We show how directed acyclic graphs (DAGs) from the causal inference literature can guide researchers in reasoning about the causes of non-invariance. For this, we first show how DAGs for measurement models can be translated into path diagrams used in the linear structural equation model (SEM) literature. We then demonstrate how insights gained from this causal perspective can be used to explicitly model encoded causal assumptions with moderated SEMs, allowing for a more enlightening investigation of MI. Ultimately, our goal is to provide a framework in which the investigation of MI is not deemed a “gateway test” that simply licenses further analyses. By enabling researchers to consider MI as an interesting part of the modeling process, we hope to increase the prevalence of investigations of MI altogether.

Mahalanobis balancing: A multivariate perspective on approximate covariate balancing

AbstractIn the past decade, various exact balancing‐based weighting methods were introduced to the causal inference literature. It eliminates covariate imbalance by imposing balancing constraints in a certain optimization problem, which can nevertheless be infeasible when there is bad overlap between the covariate distributions in the treated and control groups or when the covariates are high dimensional. Recently, approximate balancing was proposed as an alternative balancing framework. It resolves the feasibility issue by using inequality moment constraints instead. However, it can be difficult to select the threshold parameters. Moreover, moment constraints may not fully capture the discrepancy of covariate distributions. In this paper, we propose Mahalanobis balancing to approximately balance covariate distributions from a multivariate perspective. We use a quadratic constraint to control overall imbalance with a single threshold parameter, which can be tuned by a simple selection procedure. We show that the dual problem of Mahalanobis balancing is an norm‐based regularized regression problem, and establish interesting connection to propensity score models. We derive asymptotic properties, discuss the high‐dimensional scenario, and make extensive numerical comparisons with existing balancing methods.

The Incremental Propensity Score Approach for Diversity Science

Addressing core questions in diversity science requires quantifying causal effects (e.g., what drives social inequities and how to reduce them). Conventional approaches target the average causal effect (ACE), but ACE-based analyses suffer from limitations that undermine their relevance for diversity science. In this article, we introduce a novel alternative from the causal inference literature: the so-called incremental propensity score (IPS). First, we explain why the IPS is well suited for investigating core queries in diversity science. Unlike the ACE, the IPS does not demand conceptualizing unrealistic counterfactual scenarios in which everyone in the population is uniformly exposed versus unexposed to a causal factor. Instead, the IPS focuses on the effect of hypothetically shifting individuals’ chances of being exposed along a continuum. This allows seeing how the effect may be graded, offering a more realistic and policy-relevant quantification of the causal effect than a single ACE estimate. Moreover, the IPS does not require the positivity assumption, a necessary condition for estimating the ACE but which rarely holds in practice. Next, to broaden accessibility, we provide a step-by-step guide on estimating the IPS using R, a free and popular software. Finally, we illustrate the IPS using two real-world examples. The current article contributes to the methodological advancement in diversity science and offers researchers a more realistic, relevant, and meaningful approach.

Confounder-dependent Bayesian mixture model: Characterizing heterogeneity of causal effects in air pollution epidemiology.

Several epidemiological studies have provided evidence that long-term exposure to fine particulate matter (pm2.5) increases mortality rate. Furthermore, some population characteristics (e.g., age, race, and socioeconomic status) might play a crucial role in understanding vulnerability to air pollution. To inform policy, it is necessary to identify groups of the population that are more or less vulnerable to air pollution. In causal inference literature, the group average treatment effect (GATE) is a distinctive facet of the conditional average treatment effect. This widely employed metric serves to characterize the heterogeneity of a treatment effect based on some population characteristics. In this paper, we introduce a novel Confounder-Dependent Bayesian Mixture Model (CDBMM) to characterize causal effect heterogeneity. More specifically, our method leverages the flexibility of the dependent Dirichlet process to model the distribution of the potential outcomes conditionally to the covariates and the treatment levels, thus enabling us to: (i) identify heterogeneous and mutually exclusive population groups defined by similar GATEs in a data-driven way, and (ii) estimate and characterize the causal effects within each of the identified groups. Through simulations, we demonstrate the effectiveness of our method in uncovering key insights about treatment effects heterogeneity. We apply our method to claims data from Medicare enrollees in Texas. We found six mutually exclusive groups where the causal effects of pm2.5 on mortality rate are heterogeneous.

Comparing type 1 and type 2 error rates of different tests for heterogeneous treatment effects

Psychologists are increasingly interested in whether treatment effects vary in randomized controlled trials. A number of tests have been proposed in the causal inference literature to test for such heterogeneity, which differ in the sample statistic they use (either using the variance terms of the experimental and control group, their empirical distribution functions, or specific quantiles), and in whether they make distributional assumptions or are based on a Fisher randomization procedure. In this manuscript, we present the results of a simulation study in which we examine the performance of the different tests while varying the amount of treatment effect heterogeneity, the type of underlying distribution, the sample size, and whether an additional covariate is considered. Altogether, our results suggest that researchers should use a randomization test to optimally control for type 1 errors. Furthermore, all tests studied are associated with low power in case of small and moderate samples even when the heterogeneity of the treatment effect is substantial. This suggests that current tests for treatment effect heterogeneity require much larger samples than those collected in current research.

Causal Effects of Time-Varying Exposures: A Comparison of Structural Equation Modeling and Marginal Structural Models in Cross-Lagged Panel Research

The use of structural equation models for causal inference from panel data is critiqued in the causal inference literature for unnecessarily relying on a large number of parametric assumptions, and alternative methods originating from the potential outcomes framework have been recommended, such as inverse probability weighting (IPW) estimation of marginal structural models (MSMs). To better understand this criticism, we describe three phases of causal research. We explain (differences in) the assumptions that are made throughout these phases for structural equation modeling (SEM) and IPW-MSM approaches using an empirical example. Second, using simulations we compare the finite sample performance of SEM and IPW-MSM for the estimation of time-varying exposure effects on an end-of-study outcome under violations of parametric assumptions. Although increased reliance on parametric assumptions does not always translate to increased bias (even under model misspecification), researchers are still well-advised to acquaint themselves with causal methods from the potential outcomes framework.

The Causal Cookbook: Recipes for Propensity Scores, G-Computation, and Doubly Robust Standardization

Recent developments in the causal-inference literature have renewed psychologists’ interest in how to improve causal conclusions based on observational data. A lot of the recent writing has focused on concerns of causal identification (under which conditions is it, in principle, possible to recover causal effects?); in this primer, we turn to causal estimation (how do researchers actually turn the data into an effect estimate?) and modern approaches to it that are commonly used in epidemiology. First, we explain how causal estimands can be defined rigorously with the help of the potential-outcomes framework, and we highlight four crucial assumptions necessary for causal inference to succeed (exchangeability, positivity, consistency, and noninterference). Next, we present three types of approaches to causal estimation and compare their strengths and weaknesses: propensity-score methods (in which the independent variable is modeled as a function of controls), g-computation methods (in which the dependent variable is modeled as a function of both controls and the independent variable), and doubly robust estimators (which combine models for both independent and dependent variables). A companion R Notebook is available at github.com/ArthurChatton/CausalCookbook. We hope that this nontechnical introduction not only helps psychologists and other social scientists expand their causal toolbox but also facilitates communication across disciplinary boundaries when it comes to causal inference, a research goal common to all fields of research.

Can cognitive inflexibility reduce symptoms of anxiety and depression? Promoting the structural nested mean model in psychotherapy research

ABSTRACT Objective To estimate the causal effect of executive functioning on the remission of depression and anxiety symptoms in an observational dataset from a vocational rehabilitation program. It is also an aim to promote a method from the causal inference literature and to illustrate its value in this setting. Method With longitudinal (four-time points over 13 months) data from four independent sites, we compiled a dataset with 390 participants. At each time point, participants were tested on executive function and self-reported symptoms of anxiety and depression. We used g-estimation to evaluate whether objectively tested cognitive flexibility affected depressive/anxious symptoms and tested for moderation. Multiple imputations were used to handle missing data. Results The g-estimation showed a strong causal effect of cognitive inflexibility reducing depression and anxiety and modified by education level. In a counterfactual framework, a hypothetical intervention that could lower cognitive flexibility seemed to cause improvement in mental distress at the subsequent time-point (negative sign) for low education. The less flexibility, the larger improvement. For high education, the same but weaker effect was found, with a change in sign, negative during the intervention and positive during follow-up. Discussion An unexpected and strong effect was found from cognitive inflexibility on symptom improvement. This study demonstrates how to estimate causal psychological effects with standard software in an observational dataset with substantial missing and shows the value of such methods.

The Role of Exchangeability in Causal Inference

Though the notion of exchangeability has been discussed in the causal inference literature under various guises, it has rarely taken its original meaning as a symmetry property of probability distributions. As this property is a standard component of Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here, we propose a probabilistic between-group exchangeability property as an identifying condition for causal effects, relate it to alternative conditions for unconfounded inferences (commonly stated using potential outcomes) and define causal contrasts in the presence of exchangeability in terms of posterior predictive expectations for further exchangeable units. While our main focus is on a point treatment setting, we also investigate how this reasoning carries over to longitudinal settings.

A Tutorial on Causal Inference in Longitudinal Data With Time-Varying Confounding Using G-Estimation

In psychological research, longitudinal study designs are often used to examine the effects of a naturally observed predictor (i.e., treatment) on an outcome over time. But causal inference of longitudinal data in the presence of time-varying confounding is notoriously challenging. In this tutorial, we introduce g-estimation, a well-established estimation strategy from the causal inference literature. G-estimation is a powerful analytic tool designed to handle time-varying confounding variables affected by treatment. We offer step-by-step guidance on implementing the g-estimation method using standard parametric regression functions familiar to psychological researchers and commonly available in statistical software. To facilitate hands-on usage, we provide software code at each step using the open-source statistical software R. All the R code presented in this tutorial are publicly available online.

Estimating time-varying treatment effects in longitudinal studies.

Longitudinal study designs are frequently used to investigate the effects of a naturally observed predictor (treatment) on an outcome over time. Because the treatment at each time point or wave is not randomly assigned, valid inferences of its causal effects require adjusting for covariates that confound each treatment-outcome association. But adjusting for covariates which are inevitably time-varying is fraught with difficulties. On the one hand, standard regression adjustment for variables affected by treatment can lead to severe bias. On the other hand, omitting time-varying covariates from confounding adjustment precipitates spurious associations that can lead to severe bias. Thus, either including or omitting time-varying covariates for confounding adjustment can lead to incorrect inferences. In this article, we introduce an estimation strategy from the causal inference literature for evaluating the causal effects of time-varying treatments in the presence of time-varying confounding. G-estimation of the treatment effect at a particular wave proceeds by carefully adjusting for only pre-treatment instances of all variables while dispensing with any post-treatment instances. The introduced approach has various appealing features. Effect modification by time-varying covariates can be investigated using covariate-treatment interactions. Treatment may be either continuous or noncontinuous with any mean model permitted. Unbiased estimation requires correctly specifying a mean model for either the treatment or the outcome, but not necessarily both. The treatment and outcome models can be fitted with standard regression functions. In summary, g-estimation is effective, flexible, robust, and relatively straightforward to implement. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Principal Fairness for Human and Algorithmic Decision-Making

Using the concept of principal stratification from the causal inference literature, we introduce a new notion of fairness, called principal fairness, for human and algorithmic decision-making. Principal fairness states that one should not discriminate among individuals who would be similarly affected by the decision. Unlike the existing statistical definitions of fairness, principal fairness explicitly accounts for the fact that individuals can be impacted by the decision. This causal fairness formulation also enables online or post-hoc fairness evaluation and policy learning. We also explain how principal fairness relates to the existing causality-based fairness criteria. In contrast to the counterfactual fairness criteria, for example, principal fairness considers the effects of decision in question rather than those of protected attributes of interest. Finally, we discuss how to conduct empirical evaluation and policy learning under the proposed principal fairness criterion.

Conditional cross-design synthesis estimators for generalizability in Medicaid.

While much of the causal inference literature has focused on addressing internal validity biases, both internal and external validity are necessary for unbiased estimates in a target population of interest. However, few generalizability approaches exist for estimating causal quantities in a target population that is not well-represented by a randomized study but is reflected when additionally incorporating observational data. To generalize to a target population represented by a union of these data, we propose a novel class of conditional cross-design synthesis estimators that combine randomized and observational data, while addressing their estimates' respective biases-lack of overlap and unmeasured confounding. These methods enable estimating the causal effect of managed care plans on health care spending among Medicaid beneficiaries in New York City, which requires obtaining estimates for the 7% of beneficiaries randomized to a plan and 93% who choose a plan, who do not resemble randomized beneficiaries. Our new estimators include outcome regression, propensity weighting, and double robust approaches. All use the covariate overlap between the randomized and observational data to remove potential unmeasured confounding bias. Applying these methods, we find substantial heterogeneity in spending effects across managed care plans. This has major implications for our understanding of Medicaid, where this heterogeneity has previously been hidden. Additionally, we demonstrate that unmeasured confounding rather than lack of overlap poses a larger concern in thissetting.

Causal inference on distribution functions

Abstract Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space Rp. However, it is increasingly common that complex datasets are best summarized as data points in nonlinear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is nonlinear. We develop doubly robust estimators and associated asymptotic theory for these causal effects. As an illustration, we use our framework to quantify the causal effect of marriage on physical activity patterns using wearable device data collected through the National Health and Nutrition Examination Survey.

Causal inference on observational data: Opportunities and challenges in earthquake engineering

Collecting and analyzing observational data are essential to learning and implementing lessons in earthquake engineering. Historically, the methods that have been used to analyze and draw conclusions from empirical data have been limited to traditional statistics. The models developed using these techniques are able to capture associative relationships between important variables. However, the intervention decisions geared toward seismic risk mitigation should ideally be informed by an understanding of the causal mechanisms that drive infrastructure performance and community response. This article advocates for a paradigm shift in earthquake engineering where the language, tools, and models that have been (and continue to be) developed to draw causal conclusions from observational data are adopted. Several categories of data-driven earthquake engineering problems that can benefit from causal insights are examined. Two widely adopted frameworks from the broader causal inference literature are presented and linked to hypothetical earthquake engineering problems. The critical role of semi-parametric models and sensitivity analysis in justifying causal claims is also discussed. The article concludes with a discussion of specific opportunities and challenges toward the widespread use of causal inference as a tool for knowledge discovery in earthquake engineering. The ability to leverage the underlying physics of a problem within a causal inference framework is identified as both an opportunity and challenge for earthquake engineering researchers.

A Review of Generalizability and Transportability

When assessing causal effects, determining the target population to which the results are intended to generalize is a critical decision. Randomized and observational studies each have strengths and limitations for estimating causal effects in a target population. Estimates from randomized data may have internal validity but are often not representative of the target population. Observational data may better reflect the target population, and hence be more likely to have external validity, but are subject to potential bias due to unmeasured confounding. While much of the causal inference literature has focused on addressing internal validity bias, both internal and external validity are necessary for unbiased estimates in a target population. This article presents a framework for addressing external validity bias, including a synthesis of approaches for generalizability and transportability, and the assumptions they require, as well as tests for the heterogeneity of treatment effects and differences between study and target populations.

Estimating social influence in a social network using potential outcomes.

Social influence occurs when an individual's outcome is affected by another individual's actions. Current approaches in psychology that seek to examine social influence have focused on settings where individuals are nested in predefined groups and do not interact across groups. Such study designs permit using standard estimation methods such as multilevel models for estimating treatment effects but restrict social influence to originate only from individuals within the same group. In more general settings, such as social networks where an individual is free to interact with any other individual, the absence of discernible clusters or scientifically meaningful groups precludes existing estimation methods. In this article, we introduce a new class of methods for assessing social influence in social networks in the context of randomized experiments in psychology. Our proposal builds on the potential outcomes framework from the causal inference literature. In particular, we exploit the concept of (treatment) interference, which occurs between individuals when one individual's outcome is affected by other individuals' treatments. Estimation proceeds using randomization-based approaches that are established in other disciplines and guarantee valid inference by construction. We compared the proposed methods with standard methods empirically using Monte Carlo simulation studies. We illustrated the method using publicly available data from an experiment assessing the effects of an anticonflict intervention among students' peer networks. The R scripts used to implement the proposed methods in the simulation studies and the applied example are freely available online. (PsycInfo Database Record (c) 2022 APA, all rights reserved).