To conduct causal inference in observational settings, researchers must rely on certain identifying assumptions. In practice, these assumptions are unlikely to hold exactly. This paper considers the bias of selection-on-observables, instrumental variables, and proximal inference estimates under violations of their identifying assumptions. We develop bias expressions for IV and proximal inference that show how violations of their respective assumptions are amplified by any unmeasured confounding in the outcome variable. We propose a set of sensitivity tools that quantify the sensitivity of different identification strategies, and an augmented bias contour plot visualizes the relationship between these strategies. We argue that the act of choosing an identification strategy implicitly expresses a belief about the degree of violations that must be present in alternative identification strategies. Even when researchers intend to conduct an IV or proximal analysis, a sensitivity analysis comparing different identification strategies can help to better understand the implications of each set of assumptions. Throughout, we compare the different approaches on a re-analysis of the impact of state surveillance on the incidence of protest in Communist Poland.

Standard approaches in generalizability often focus on generalizing the intent-to-treat (ITT). However, in practice, a more policy-relevant quantity is the generalized impact of an intervention across compliers. While instrumental variable (IV) methods are commonly used to estimate the complier average causal effect (CACE) within samples, standard approaches cannot be applied to a target population with a different distribution from the study sample. This paper makes several key contributions. First, we introduce a new set of identifying assumptions in the form of a population-level exclusion restriction that allows for identification of the target complier average causal effect (T-CACE) in both randomized experiments and observational studies. This allows researchers to identify the T-CACE without relying on standard principal ignorability assumptions. Second, we propose a class of inverse-weighted estimators for the T-CACE and derive their asymptotic properties. We provide extensions for settings in which researchers have access to auxiliary compliance information across the target population. Finally, we introduce a sensitivity analysis for researchers to evaluate the robustness of the estimators in the presence of unmeasured confounding. We illustrate our proposed method through extensive simulations and a study evaluating the impact of deep canvassing on reducing exclusionary attitudes.

In a clustered observational study, treatment is assigned to groups and all units within the group are exposed to the treatment. Here, we use a clustered observational study (COS) design to estimate the effectiveness of Magnet Nursing certificates for emergency surgery patients. Recent research has introduced specialized weighting estimators for the COS design that balance baseline covariates at the unit and cluster level. These methods allow researchers to adjust for observed confounders, but are sensitive to unobserved confounding. In this paper, we develop new sensitivity analysis methods tailored to weighting estimators for COS designs. We provide several key contributions. First, we introduce a key bias decomposition, tailored to the specific confounding structure that arises in a COS. Second, we develop a sensitivity framework for weighted COS designs that constrain the error in the underlying weights. We introduce both a marginal sensitivity model and a variance-based sensitivity model, and extend both to accommodate multiple estimands. Finally, we propose amplification and benchmarking methods to better interpret the results. Throughout, we illustrate our proposed methods by analyzing the effectiveness of Magnet nursing hospitals.

Recent methodological developments have introduced new black-box approaches to better estimate heterogeneous treatment effects; however, these methods fall short of providing interpretable characterizations of the underlying individuals who may be most at risk or benefit most from receiving the treatment, thereby limiting their practical utility. In this work, we introduce a novel method, causal distillation trees (CDT), to estimate interpretable subgroups. CDT allows researchers to fit any machine learning model of their choice to estimate the individual-level treatment effect, and then leverages a simple, second-stage tree-based model to 'distill' the estimated treatment effect into meaningful subgroups. As a result, CDT inherits the improvements in predictive performance from black-box machine learning models while preserving the interpretability of a simple decision tree. We derive theoretical guarantees for the consistency of the estimated subgroups using CDT, and introduce stability-driven diagnostics for researchers to evaluate the quality of the estimated subgroups. We illustrate our proposed method on a randomized controlled trial of antiretroviral treatment for HIV from the AIDS Clinical Trials Group Study 175 and show that CDT out-performs state-of-the-art approaches in constructing stable, clinically relevant subgroups.

To test scientific theories and develop individualized treatment rules, researchers often wish to learn heterogeneous treatment effects that can be consistently found across diverse populations and contexts. We consider the problem of generalizing heterogeneous treatment effects (HTE) based on data from multiple sites. A key challenge is that a target population may differ from the source sites in unknown and unobservable ways. This means that the estimates from site-specific models lack external validity, and a simple pooled analysis risks bias. We develop a robust CATE (conditional average treatment effect) estimation methodology with multisite data from heterogeneous populations. We propose a minimax-regret framework that learns a generalizable CATE model by minimizing the worst-case regret over a class of target populations whose CATE can be represented as convex combinations of site-specific CATEs. Using robust optimization, the proposed methodology accounts for distribution shifts in both individual covariates and treatment effect heterogeneity across sites. We show that the resulting CATE model has an interpretable closed-form solution, expressed as a weighted average of site-specific CATE models. Thus, researchers can utilize a flexible CATE estimation method within each site and aggregate site-specific estimates to produce the final model. Through simulations and a real-world application, we show that the proposed methodology improves the robustness and generalizability of existing approaches.

The use of Artificial Intelligence (AI), or more generally data-driven algorithms, has become ubiquitous in today's society. Yet, in many cases and especially when stakes are high, humans still make final decisions. The critical question, therefore, is whether AI helps humans make better decisions compared to a human-alone or AI-alone system. We introduce a new methodological framework to empirically answer this question with a minimal set of assumptions. We measure a decision maker's ability to make correct decisions using standard classification metrics based on the baseline potential outcome. We consider a single-blinded and unconfounded treatment assignment, where the provision of AI-generated recommendations is assumed to be randomized across cases with humans making final decisions. Under this study design, we show how to compare the performance of three alternative decision-making systems--human-alone, human-with-AI, and AI-alone. Importantly, the AI-alone system includes any individualized treatment assignment, including those that are not used in the original study. We also show when AI recommendations should be provided to a human-decision maker, and when one should follow such recommendations. We apply the proposed methodology to our own randomized controlled trial evaluating a pretrial risk assessment instrument. We find that the risk assessment recommendations do not improve the classification accuracy of a judge's decision to impose cash bail. Furthermore, we find that replacing a human judge with algorithms--the risk assessment score and a large language model in particular--leads to a worse classification performance.

Careful design and pre-registration of a treated-control comparison in an observational study enhances the quality of its evidence. However, sensitivity to unmeasured confounding is not typically a primary consideration in the pre-analysis design stage. In the following paper, we introduce a framework for weighted estimators that allows researchers to optimize for robustness to omitted variable bias at the design stage using a measure called design sensitivity. Inspired by a similar measure for matching estimators, design sensitivity describes the asymptotic power of a sensitivity analysis, and allows researchers to transparently evaluate the impact of different estimation strategies on sensitivity to omitted confounders prior to outcome analysis. We apply this general framework to two commonly-used sensitivity models, the marginal sensitivity model and the variance-based sensitivity model. By comparing design sensitivities, we interrogate how key features of weighted observational designs, including trimming weights, choosing between different treatment versions, and altering the study's inclusion criteria, impact robustness to unmeasured confounding. We illustrate the proposed framework on a study examining drivers of support for the 2016 Colombian peace agreement.

Estimating externally valid causal effects is a foundational problem in the social and biomedical sciences. Generalizing or transporting causal estimates from an experimental sample to a target population of interest relies on an overlap assumption between the experimental sample and the target population--i.e., all units in the target population must have a non-zero probability of being included in the experiment. In practice, having full overlap between an experimental sample and a target population can be implausible. In the following paper, we introduce a framework for considering external validity in the presence of overlap violations. We propose a novel bias decomposition that parameterizes the bias from an overlap violation into two components: (1) the proportion of units omitted, and (2) the degree to which omitting the units moderates the treatment effect. The bias decomposition offers an intuitive and straightforward approach to conducting sensitivity analysis to assess robustness to overlap violations. Furthermore, we introduce a suite of sensitivity tools in the form of summary measures and benchmarking, which help researchers consider the plausibility of the overlap violations. We apply the proposed framework on an experiment evaluating the impact of a cash transfer program in Northern Uganda.

Weighting methods are popular tools for estimating causal effects; assessing their robustness under unobserved confounding is important in practice. In the following paper, we introduce a new set of sensitivity models called 'variance-based sensitivity models.' Variance-based sensitivity models characterize the bias from omitting a confounder by bounding the distributional differences that arise in the weights from omitting a confounder, with several notable innovations over existing approaches. First, the variance-based sensitivity models can be parameterized with respect to a simple R^2 parameter that is both standardized and bounded. We introduce a formal benchmarking procedure that allows researchers to use observed covariates to reason about plausible parameter values in an interpretable and transparent way. Second, we show that researchers can estimate valid confidence intervals under a set of variance-based sensitivity models, and provide extensions for researchers to incorporate their substantive knowledge about the confounder to help tighten the intervals. Last, we highlight the connection between our proposed approach and existing sensitivity analyses, and demonstrate both, empirically and theoretically, that variance-based sensitivity models can provide improvements on both the stability and tightness of the estimated confidence intervals over existing methods. We illustrate our proposed approach on a study examining blood mercury levels using the National Health and Nutrition Examination Survey (NHANES).

Randomized Controlled Trials (RCTs) are pivotal in generating internally valid estimates with minimal assumptions, serving as a cornerstone for researchers dedicated to advancing causal inference methods. However, extending these findings beyond the experimental cohort to achieve externally valid estimates is crucial for broader scientific inquiry. This paper delves into the forefront of addressing these external validity challenges, encapsulating the essence of a multidisciplinary workshop held at the Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University, in Fall 2023. The workshop congregated experts from diverse fields including social science, medicine, public health, statistics, computer science, and education, to tackle the unique obstacles each discipline faces in extrapolating experimental findings. Our study presents three key contributions: we integrate ongoing efforts, highlighting methodological synergies across fields; provide an exhaustive review of generalizability and transportability based on the workshop’s discourse; and identify persistent hurdles while suggesting avenues for future research. By doing so, this paper aims to enhance the collective understanding of the generalizability and transportability of causal effects, fostering cross-disciplinary collaboration and offering valuable insights for researchers working on refining and applying causal inference methods.

Randomized controlled trials (RCT’s) allow researchers to estimate causal effects in an experimental sample with minimal identifying assumptions. However, to generalize or transport a causal effect from an RCT to a target population, researchers must adjust for a set of treatment effect moderators. In practice, it is impossible to know whether the set of moderators has been properly accounted for. In the following paper, I propose a two parameter sensitivity analysis for generalizing or transporting experimental results using weighted estimators. The contributions in the paper are three-fold. First, I show that the sensitivity parameters are scale-invariant and standardized, and introduce an estimation approach for researchers to simultaneously account for the bias in their estimates from omitting a moderator, as well as potential changes to their inference. Second, I propose several tools researchers can use to perform sensitivity analysis: (1) different numerical measures to summarize the uncertainty in an estimated effect to unobserved confounding; (2) graphical summary tools for researchers to visualize the sensitivity in their estimated effects, as the confounding strength of the omitted variable changes; and (3) a formal benchmarking approach for researchers to estimate potential sensitivity parameter values using existing data. Finally, I demonstrate that the proposed framework can be easily extended to the class of doubly robust, augmented weighted estimators. The sensitivity analysis framework is applied to a set of Jobs Training Program experiments.

andomized control trials are often considered the gold standard in causal inference due to their high internal validity. Despite its importance, generalizing experimental results to a target population is challenging in social and biomedical sciences. Recent papers clarify the assumptions necessary for generalization and develop various weighting estimators for the population average treatment effect (PATE). However, in practice, many of these methods result in large variance and little statistical power, thereby limiting the value of the PATE inference. In this article, we propose post-residualized weighting, in which information about the outcome measured in the observational population data is used to improve the efficiency of many existing popular methods without making additional assumptions. We empirically demonstrate the efficiency gains through simulations and apply our proposed method to a set of jobs training program experiments.

Even in the best-designed experiment, noncompliance with treatment assignment can complicate analysis. Under one-way noncompliance, researchers typically rely on an instrumental variables approach, under an exclusion restriction assumption, to identify the complier average causal effect (CACE). This approach suffers from high variance, particularly when the experiment has a low compliance rate. The following paper suggests blocking designs that can help overcome precision losses in the face of high rates of noncompliance in experiments when a placebo-controlled design is infeasible. We also introduce the principal ignorability assumption and a class of principal score weighted estimators, which are largely absent from the experimental political science literature. We then introduce the ''block principal ignorability'' assumption which, when combined with a blocking design, suggests a simple difference-in-means estimator for estimating the CACE. We show that blocking can improve precision of both IV and principal score weighting approaches, and further show that our simple, design-based solution has superior performance to both principal score weighting and instrumental variables under blocking. Finally, in a re-evaluation of the Gerber, Green, and Nickerson (2003) study, we find that blocked, principal ignorability approaches to estimation of the CACE, including our blocked difference-in-means and principal score weighting estimators, result in confidence intervals roughly half the size of traditional instrumental variable approaches.

Survey weighting allows researchers to account for bias in survey samples, due to unit nonresponse or convenience sampling, using measured demographic covariates. Unfortunately, in practice, it is impossible to know whether the estimated survey weights are sufficient to alleviate concerns about bias due to unobserved confounders or incorrect functional forms used in weighting. In the following paper, we propose two sensitivity analyses for the exclusion of important covariates: (1) a sensitivity analysis for partially observed confounders (i.e., variables measured across the survey sample, but not the target population) and (2) a sensitivity analysis for fully unobserved confounders (i.e., variables not measured in either the survey or the target population). We provide graphical and numerical summaries of the potential bias that arises from such confounders, and introduce a benchmarking approach that allows researchers to quantitatively reason about the sensitivity of their results. We demonstrate our proposed sensitivity analyses using state-level 2020 U.S. Presidential Election polls.

We expand upon a simulation study that compared three promising methods for estimating weights for assessing the average treatment effect on the treated for binary treatments: generalized boosted models, covariate-balancing propensity scores, and entropy balance. The original study showed that generalized boosted models can outperform covariate-balancing propensity scores, and entropy balance when there are likely to be non-linear associations in both the treatment assignment and outcome models and when the other two models are fine-tuned to obtain balance only on first-order moments. We explore the potential benefit of using higher-order moments in the balancing conditions for covariate-balancing propensity scores and entropy balance. Our findings showcase that these two models should, by default, include higher order moments and focusing only on first moments can result in substantial bias in estimated treatment effect estimates from both models that could be avoided using higher moments.