arXiv subjects

Edward H. Kennedy

Publications and source records attributed to Edward H. Kennedy.

At least 37 records · Page 2Linked to original sources

arXiv2025

Discussion of "Causal and counterfactual views of missing data models" by Razieh Nabi, Rohit Bhattacharya, Ilya Shpitser, & James M. Robins

We congratulate Nabi et al. (2022) on their impressive and insightful paper, which illustrates the benefits of using causal/counterfactual perspectives and tools in missing data problems. This paper represents an important approach to missing-not-at-random (MNAR) problems, exploiting nonparametric independence restrictions for identification, as opposed to parametric/semiparametric models, or resorting to sensitivity analysis. Crucially, the authors represent these restrictions with missing data directed acyclic graphs (m-DAGs), which can be useful to determine identification in complex and interesting MNAR models. In this discussion we consider: (i) how/whether other tools from causal inference could be useful in missing data problems, (ii) problems that combine both missing data and causal inference together, and (iii) some work on estimation in one of the authors' example MNAR models.

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arXiv2025

The Fundamental Limits of Structure-Agnostic Functional Estimation

Many recent developments in causal inference, and functional estimation problems more generally, have been motivated by the fact that classical one-step (first-order) debiasing methods, or their more recent sample-split double machine-learning avatars, can outperform plugin estimators under surprisingly weak conditions. These first-order corrections improve on plugin estimators in a black-box fashion, and consequently are often used in conjunction with powerful off-the-shelf estimation methods. These first-order methods are however provably suboptimal in a minimax sense for functional estimation when the nuisance functions live in Holder-type function spaces. This suboptimality of first-order debiasing has motivated the development of "higher-order" debiasing methods. The resulting estimators are, in some cases, provably optimal over Holder-type spaces, but both the estimators which are minimax-optimal and their analyses are crucially tied to properties of the underlying function space. In this paper we investigate the fundamental limits of structure-agnostic functional estimation, where relatively weak conditions are placed on the underlying nuisance functions. We show that there is a strong sense in which existing first-order methods are optimal. We achieve this goal by providing a formalization of the problem of functional estimation with black-box nuisance function estimates, and deriving minimax lower bounds for this problem. Our results highlight some clear tradeoffs in functional estimation -- if we wish to remain agnostic to the underlying nuisance function spaces, impose only high-level rate conditions, and maintain compatibility with black-box nuisance estimators then first-order methods are optimal. When we have an understanding of the structure of the underlying nuisance functions then carefully constructed higher-order estimators can outperform first-order estimators.

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arXiv2025

Double Cross-fit Doubly Robust Estimators: Beyond Series Regression

Doubly robust estimators with cross-fitting have gained popularity in causal inference due to their favorable structure-agnostic error guarantees. However, when additional structure, such as Hölder smoothness, is available then more accurate "double cross-fit doubly robust" (DCDR) estimators can be constructed by splitting the training data and undersmoothing nuisance function estimators on independent samples. We study a DCDR estimator of the Expected Conditional Covariance, a functional of interest in causal inference and conditional independence testing. We first provide a structure-agnostic error analysis for the DCDR estimator with no assumptions on the nuisance functions or their estimators. Then, assuming the nuisance functions are Hölder smooth, but without assuming knowledge of the true smoothness level or the covariate density, we establish that DCDR estimators with several linear smoothers are $\sqrt{n}$-consistent and asymptotically normal under minimal conditions and achieve fast convergence rates in the non-$\sqrt{n}$ regime. When the covariate density and smoothnesses are known, we propose a minimax rate-optimal DCDR estimator based on undersmoothed kernel regression. Moreover, we show an undersmoothed DCDR estimator satisfies a slower-than-$\sqrt{n}$ central limit theorem, and that inference is possible even in the non-$\sqrt{n}$ regime. Finally, we support our theoretical results with simulations, providing intuition for double cross-fitting and undersmoothing, demonstrating where our estimator achieves $\sqrt{n}$-consistency while the usual "single cross-fit" estimator fails, and illustrating asymptotic normality for the undersmoothed DCDR estimator.

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arXiv2025

Causal Inference for Genomic Data with Multiple Heterogeneous Outcomes

With the evolution of single-cell RNA sequencing techniques into a standard approach in genomics, it has become possible to conduct cohort-level causal inferences based on single-cell-level measurements. However, the individual gene expression levels of interest are not directly observable; instead, only repeated proxy measurements from each individual's cells are available, providing a derived outcome to estimate the underlying outcome for each of many genes. In this paper, we propose a generic semiparametric inference framework for doubly robust estimation with multiple derived outcomes, which also encompasses the usual setting of multiple outcomes when the response of each unit is available. To reliably quantify the causal effects of heterogeneous outcomes, we specialize the analysis to standardized average treatment effects and quantile treatment effects. Through this, we demonstrate the use of the semiparametric inferential results for doubly robust estimators derived from both Von Mises expansions and estimating equations. A multiple testing procedure based on Gaussian multiplier bootstrap is tailored for doubly robust estimators to control the false discovery exceedance rate. Applications in single-cell CRISPR perturbation analysis and individual-level differential expression analysis demonstrate the utility of the proposed methods and offer insights into the usage of different estimands for causal inference in genomics.

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arXiv2024

Efficient Generalization and Transportation

When estimating causal effects, it is important to assess external validity, i.e., determine how useful a given study is to inform a practical question for a specific target population. One challenge is that the covariate distribution in the population underlying a study may be different from that in the target population. If some covariates are effect modifiers, the average treatment effect (ATE) may not generalize to the target population. To tackle this problem, we propose new methods to generalize or transport the ATE from a source population to a target population, in the case where the source and target populations have different sets of covariates. When the ATE in the target population is identified, we propose new doubly robust estimators and establish their rates of convergence and limiting distributions. Under regularity conditions, the doubly robust estimators provably achieve the efficiency bound and are locally asymptotic minimax optimal. A sensitivity analysis is provided when the identification assumptions fail. Simulation studies show the advantages of the proposed doubly robust estimator over simple plug-in estimators. Importantly, we also provide minimax lower bounds and higher-order estimators of the target functionals. The proposed methods are applied in transporting causal effects of dietary intake on adverse pregnancy outcomes from an observational study to the whole U.S. pregnant female population.

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arXiv2024

Doubly-robust inference and optimality in structure-agnostic models with smoothness

We study the problem of constructing an estimator of the average treatment effect (ATE) with observational data. The celebrated doubly-robust, augmented-IPW (AIPW) estimator generally requires consistent estimation of both nuisance functions for standard root-n inference, and moreover that the product of the errors of the nuisances should shrink at a rate faster than $n^{-1/2}$. A recent strand of research has aimed to understand the extent to which the AIPW estimator can be improved upon (in a minimax sense). Under structural assumptions on the nuisance functions, the AIPW estimator is typically not minimax-optimal, and improvements can be made using higher-order influence functions (Robins et al, 2017). Conversely, without any assumptions on the nuisances beyond the mean-square-error rates at which they can be estimated, the rate achieved by the AIPW estimator is already optimal (Balakrishnan et al, 2023; Jin and Syrgkanis, 2024). We make three main contributions. First, we propose a new hybrid class of distributions that combine structural agnosticism regarding the nuisance function space with additional smoothness constraints. Second, we calculate minimax lower bounds for estimating the ATE in the new class, as well as in the pure structure-agnostic one. Third, we propose a new estimator of the ATE that enjoys doubly-robust asymptotic linearity; it can yield asymptotically valid Wald-type confidence intervals even when the propensity score or the outcome model is inconsistently estimated, or estimated at a slow rate. Under certain conditions, we show that its rate of convergence in the new class can be much faster than that achieved by the AIPW estimator and, in particular, matches the minimax lower bound rate, thereby establishing its optimality. Finally, we complement our theoretical findings with simulations.

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arXiv2024

Stochastic interventions, sensitivity analysis, and optimal transport

Recent methodological research in causal inference has focused on effects of stochastic interventions, which assign treatment randomly, often according to subject-specific covariates. In this work, we demonstrate that the usual notion of stochastic interventions have a surprising property: when there is unmeasured confounding, bounds on their effects do not collapse when the policy approaches the observational regime. As an alternative, we propose to study generalized policies, treatment rules that can depend on covariates, the natural value of treatment, and auxiliary randomness. We show that certain generalized policy formulations can resolve the "non-collapsing" bound issue: bounds narrow to a point when the target treatment distribution approaches that in the observed data. Moreover, drawing connections to the theory of optimal transport, we characterize generalized policies that minimize worst-case bound width in various sensitivity analysis models, as well as corresponding sharp bounds on their causal effects. These optimal policies are new, and can have a more parsimonious interpretation compared to their usual stochastic policy analogues. Finally, we develop flexible, efficient, and robust estimators for the sharp nonparametric bounds that emerge from the framework.

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arXiv2024

Causal effects based on distributional distances

Comparing counterfactual distributions can provide more nuanced and valuable measures for causal effects, going beyond typical summary statistics such as averages. In this work, we consider characterizing causal effects via distributional distances, focusing on two kinds of target parameters. The first is the counterfactual outcome density. We propose a doubly robust-style estimator for the counterfactual density and study its rates of convergence and limiting distributions. We analyze asymptotic upper bounds on the $L_q$ and the integrated $L_q$ risks of the proposed estimator, and propose a bootstrap-based confidence band. The second is a novel distributional causal effect defined by the $L_1$ distance between different counterfactual distributions. We study three approaches for estimating the proposed distributional effect: smoothing the counterfactual density, smoothing the $L_1$ distance, and imposing a margin condition. For each approach, we analyze asymptotic properties and error bounds of the proposed estimator, and discuss potential advantages and disadvantages. We go on to present a bootstrap approach for obtaining confidence intervals, and propose a test of no distributional effect. We conclude with a numerical illustration and a real-world example.

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arXiv2024

Hierarchical and Density-based Causal Clustering

Understanding treatment effect heterogeneity is vital for scientific and policy research. However, identifying and evaluating heterogeneous treatment effects pose significant challenges due to the typically unknown subgroup structure. Recently, a novel approach, causal k-means clustering, has emerged to assess heterogeneity of treatment effect by applying the k-means algorithm to unknown counterfactual regression functions. In this paper, we expand upon this framework by integrating hierarchical and density-based clustering algorithms. We propose plug-in estimators that are simple and readily implementable using off-the-shelf algorithms. Unlike k-means clustering, which requires the margin condition, our proposed estimators do not rely on strong structural assumptions on the outcome process. We go on to study their rate of convergence, and show that under the minimal regularity conditions, the additional cost of causal clustering is essentially the estimation error of the outcome regression functions. Our findings significantly extend the capabilities of the causal clustering framework, thereby contributing to the progression of methodologies for identifying homogeneous subgroups in treatment response, consequently facilitating more nuanced and targeted interventions. The proposed methods also open up new avenues for clustering with generic pseudo-outcomes. We explore finite sample properties via simulation, and illustrate the proposed methods in voting and employment projection datasets.

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arXiv2024

Intervention effects based on potential benefit

Optimal treatment rules are mappings from individual patient characteristics to tailored treatment assignments that maximize mean outcomes. In this work, we introduce a conditional potential benefit (CPB) metric that measures the expected improvement under an optimally chosen treatment compared to the status quo, within covariate strata. The potential benefit combines (i) the magnitude of the treatment effect, and (ii) the propensity for subjects to naturally select a suboptimal treatment. As a consequence, heterogeneity in the CPB can provide key insights into the mechanism by which a treatment acts and/or highlight potential barriers to treatment access or adverse effects. Moreover, we demonstrate that CPB is the natural prioritization score for individualized treatment policies when intervention capacity is constrained. That is, in the resource-limited setting where treatment options are freely accessible, but the ability to intervene on a portion of the target population is constrained (e.g., if the population is large, and follow-up and encouragement of treatment uptake is labor-intensive), targeting subjects with highest CPB maximizes the mean outcome. Focusing on this resource-limited setting, we derive formulas for optimal constrained treatment rules, and for any given budget, quantify the loss compared to the optimal unconstrained rule. We describe sufficient identification assumptions, and propose nonparametric, robust, and efficient estimators of the proposed quantities emerging from our framework. Finally, we illustrate our methodology using data from a prospective cohort study in which we assess the impact of intensive care unit transfer on mortality.

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arXiv2024

Causal Effect Estimation after Propensity Score Trimming with Continuous Treatments

Propensity score trimming, which discards subjects with propensity scores below a threshold, is a common way to address positivity violations that complicate causal effect estimation. However, most works on trimming assume treatment is discrete and models for the outcome regression and propensity score are parametric. This work proposes nonparametric estimators for trimmed average causal effects in the case of continuous treatments based on efficient influence functions. For continuous treatments, an efficient influence function for a trimmed causal effect does not exist, due to a lack of pathwise differentiability induced by trimming and a continuous treatment. Thus, we target a smoothed version of the trimmed causal effect for which an efficient influence function exists. Our resulting estimators exhibit doubly-robust style guarantees, with error involving products or squares of errors for the outcome regression and propensity score, which allows for valid inference even when nonparametric models are used. Our results allow the trimming threshold to be fixed or defined as a quantile of the propensity score, such that confidence intervals incorporate uncertainty involved in threshold estimation. These findings are validated via simulation and an application, thereby showing how to efficiently-but-flexibly estimate trimmed causal effects with continuous treatments.

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arXiv2024

Continuous Treatment Effects with Surrogate Outcomes

In many real-world causal inference applications, the primary outcomes (labels) are often partially missing, especially if they are expensive or difficult to collect. If the missingness depends on covariates (i.e., missingness is not completely at random), analyses based on fully observed samples alone may be biased. Incorporating surrogates, which are fully observed post-treatment variables related to the primary outcome, can improve estimation in this case. In this paper, we study the role of surrogates in estimating continuous treatment effects and propose a doubly robust method to efficiently incorporate surrogates in the analysis, which uses both labeled and unlabeled data and does not suffer from the above selection bias problem. Importantly, we establish the asymptotic normality of the proposed estimator and show possible improvements on the variance compared with methods that solely use labeled data. Extensive simulations show our methods enjoy appealing empirical performance.

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arXiv2024

Time-uniform central limit theory and asymptotic confidence sequences

Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals, adding to the literature on confidence sequences (CS) -- sequences of confidence intervals that are uniformly valid over time -- which provide valid inference at arbitrary stopping times and incur no penalties for "peeking" at the data, unlike classical confidence intervals which require the sample size to be fixed in advance. Existing CSs in the literature are nonasymptotic, enjoying finite-sample guarantees but not the aforementioned broad applicability of asymptotic confidence intervals. This work provides a definition for "asymptotic CSs" and a general recipe for deriving them. Asymptotic CSs forgo nonasymptotic validity for CLT-like versatility and (asymptotic) time-uniform guarantees. While the CLT approximates the distribution of a sample average by that of a Gaussian for a fixed sample size, we use strong invariance principles (stemming from the seminal 1960s work of Strassen) to uniformly approximate the entire sample average process by an implicit Gaussian process. As an illustration, we derive asymptotic CSs for the average treatment effect in observational studies (for which nonasymptotic bounds are essentially impossible to derive even in the fixed-time regime) as well as randomized experiments, enabling causal inference in sequential environments.

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arXiv2024

Counterfactual Density Estimation using Kernel Stein Discrepancies

Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual distributions by minimizing kernel Stein discrepancies in a doubly robust manner. This enables the estimation of counterfactuals over large classes of distributions while exploiting the desired double robustness. We present a theoretical analysis of the proposed estimator, providing sufficient conditions for consistency and asymptotic normality, as well as an examination of its empirical performance.

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arXiv2024

Nonparametric identification and efficient estimation of causal effects with instrumental variables

Instrumental variables are widely used in econometrics and epidemiology for identifying and estimating causal effects when an exposure of interest is confounded by unmeasured factors. Despite this popularity, the assumptions invoked to justify the use of instruments differ substantially across the literature. Similarly, statistical approaches for estimating the resulting causal quantities vary considerably, and often rely on strong parametric assumptions. In this work, we compile and organize structural conditions that nonparametrically identify conditional average treatment effects, average treatment effects among the treated, and local average treatment effects, with a focus on identification formulae invoking the conditional Wald estimand. Moreover, we build upon existing work and propose nonparametric efficient estimators of functionals corresponding to marginal and conditional causal contrasts resulting from the various identification paradigms. We illustrate the proposed methods on an observational study examining the effects of operative care on adverse events for cholecystitis patients, and a randomized trial assessing the effects of market participation on political views.

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arXiv2024

Incremental Propensity Score Effects for Criminology: An Application Assessing the Relationship Between Homelessness, Behavioral Health Problems, and Recidivism

This study examines the relationship between homelessness and recidivism among people on probation with and without behavioral health problems. The study also illustrates a new way to summarize the effect of an exposure on an outcome, the Incremental Propensity Score (IPS) effect, which avoids pitfalls of other approaches commonly used in criminology. We assessed the impact of homelessness at probation start on rearrest within one year among a cohort of people on probation (n = 2,453). We estimated IPS effects, considering general and crime-specific recidivism if subjects were more or less likely to be unhoused, and assessed effect variation by behavioral health problem status. We used a doubly robust machine learning estimator to flexibly but efficiently estimate effects. A substantial intervention -- reducing homelessness by roughly 65% -- corresponded to a 9% reduction in the estimated average rate of recidivism (p < .05). Milder interventions showed smaller, non-significant effect sizes. Stratifying by behavioral health problem and rearrest type led to similar results without statistical significance. Minding limitations related to observational data and generalizability, this study suggests large reductions in homelessness lead to significant reductions in rearrest rates. Efforts to reduce recidivism should include interventions that make homelessness less likely, but notable differences in recidivism will require these interventions be sizable. Meanwhile, efforts to establish recidivism risk factors should consider alternative effects, like IPS effects, to maximize validity and reduce bias.

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arXiv2023

Minimax rates for heterogeneous causal effect estimation

Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but questions surrounding optimality have remained largely unanswered. In particular, a minimax theory of optimality has yet to be developed, with the minimax rate of convergence and construction of rate-optimal estimators remaining open problems. In this paper we derive the minimax rate for CATE estimation, in a Holder-smooth nonparametric model, and present a new local polynomial estimator, giving high-level conditions under which it is minimax optimal. Our minimax lower bound is derived via a localized version of the method of fuzzy hypotheses, combining lower bound constructions for nonparametric regression and functional estimation. Our proposed estimator can be viewed as a local polynomial R-Learner, based on a localized modification of higher-order influence function methods. The minimax rate we find exhibits several interesting features, including a non-standard elbow phenomenon and an unusual interpolation between nonparametric regression and functional estimation rates. The latter quantifies how the CATE, as an estimand, can be viewed as a regression/functional hybrid.

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arXiv2023

Flexibly Estimating and Interpreting Heterogeneous Treatment Effects of Laparoscopic Surgery for Cholecystitis Patients

Laparoscopic surgery has been shown through a number of randomized trials to be an effective form of treatment for cholecystitis. Given this evidence, one natural question for clinical practice is: does the effectiveness of laparoscopic surgery vary among patients? It might be the case that, while the overall effect is positive, some patients treated with laparoscopic surgery may respond positively to the intervention while others do not or may be harmed. In our study, we focus on conditional average treatment effects to understand whether treatment effects vary systematically with patient characteristics. Recent methodological work has developed a meta-learner framework for flexible estimation of conditional causal effects. In this framework, nonparametric estimation methods can be used to avoid bias from model misspecification while preserving statistical efficiency. In addition, researchers can flexibly and effectively explore whether treatment effects vary with a large number of possible effect modifiers. However, these methods have certain limitations. For example, conducting inference can be challenging if black-box models are used. Further, interpreting and visualizing the effect estimates can be difficult when there are multi-valued effect modifiers. In this paper, we develop new methods that allow for interpretable results and inference from the meta-learner framework for heterogeneous treatment effects estimation. We also demonstrate methods that allow for an exploratory analysis to identify possible effect modifiers. We apply our methods to a large database for the use of laparoscopic surgery in treating cholecystitis. We also conduct a series of simulation studies to understand the relative performance of the methods we develop. Our study provides key guidelines for the interpretation of conditional causal effects from the meta-learner framework.

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