arXiv subjects

Joseph Antonelli

Publications and source records attributed to Joseph Antonelli.

At least 19 recordsLinked to original sources

arXiv2026

Multivariate incremental effects for continuous treatments: Studying the health effects of environmental mixtures

Evaluating the causal health effects of multivariate, continuous exposures, such as air pollution mixtures, is a critical public health challenge. A primary obstacle is the frequent violation of the positivity assumption, which renders the effects of standard deterministic interventions unidentified or heavily reliant on unreliable model extrapolation. In this paper, we develop a novel causal inference framework to address this challenge. We extend exponential tilting to multivariate exposures and address the critical question of how to compare different intervention directions fairly. This establishes a systematic framework for defining and evaluating various policy-relevant causal estimands, allowing researchers to address diverse scientific questions. We develop numerous methodological advancements, including efficient one-step estimation strategies, a Riemannian BFGS algorithm to solve a constrained manifold optimization problem, semiparametric efficiency bounds for causal estimands, minimax rates for estimators, and establishing asymptotic normality. We demonstrate our framework's utility by applying it to a nationwide environmental health dataset to identify the optimal strategy for reducing adverse health outcomes associated with a PM$_{2.5}$ chemical mixture.

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arXiv2025

Envelope-based partial least squares in functional regression

In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional Euclidean space before fitting the model using existing approaches to envelope models. We first develop an estimator under a linear model with continuous outcomes and then extend this procedure to the more general class of generalized linear models, which allow for a variety of outcome types. We provide asymptotic theory for these estimators showing that they are root-$n$ consistent and asymptotically normal when the regression coefficient is finite-rank. Additionally we show that consistency can be obtained even when the regression coefficient has rank that grows with the sample size. Extensive simulation studies confirm our theoretical results and show strong prediction performance of the proposed estimators. Additionally, we provide multiple data analyses showing that the proposed approach performs well in real-world settings under a variety of outcome types compared with existing dimension reduction approaches.

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arXiv2025

Borrowing Strength Across Exposures and Outcomes via Index Models for Multi-pollutant Mixtures

An important goal of environmental health research is to assess the health risks posed by mixtures of multiple environmental exposures. In these mixtures analyses, flexible models like Bayesian kernel machine regression and multiple index models are appealing because they allow for arbitrary non-linear exposure-outcome relationships. However, this flexibility comes at the cost of low power, particularly when exposures are highly correlated and the health effects are weak, as is typical in environmental health studies. We propose a multivariate index modelling strategy that borrows strength across exposures and outcomes by exploiting similar mixture component weights and exposure-response relationships. In the special case of distributed lag models, in which exposures are measured repeatedly over time, we jointly encourage co-clustering of lag profiles and exposure-response curves to more efficiently identify critical windows of vulnerability and characterize important exposure effects. We then extend the proposed approach to the multiple index model setting where the true index structure -- the number of indices and their composition -- is unknown, and introduce variable importance measures to quantify component contributions to mixture effects. Using time series data from the National Morbidity, Mortality and Air Pollution Study, we demonstrate the proposed methods by jointly modelling three mortality outcomes and two cumulative air pollution measurements with a maximum lag of 14 days.

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arXiv2024

Partial identification of principal causal effects under violations of principal ignorability

Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail in this manuscript. Our first key contribution is studying a commonly used strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption. We show that even if the joint distribution of principal strata is known, this strategy necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability leads to point identification in this setting, we discuss alternative, weaker assumptions and show how they can lead to informative partial identification regions. An additional contribution is that we provide theoretical support to strategies used in the literature for identifying association parameters that govern the joint distribution of principal strata. We prove that this is possible, but only if the principal ignorability assumption is violated. Additionally, due to partial identifiability of causal effects even when these association parameters are known, we show that these association parameters are only identifiable under strong parametric constraints. Lastly, we extend these results to more flexible semiparametric and nonparametric Bayesian models.

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arXiv2024

Causal inference and racial bias in policing: New estimands and the importance of mobility data

Studying racial bias in policing is a critically important problem, but one that comes with a number of inherent difficulties due to the nature of the available data. In this manuscript we tackle multiple key issues in the causal analysis of racial bias in policing. First, we formalize race and place policing, the idea that individuals of one race are policed differently when they are in neighborhoods primarily made up of individuals of other races. We develop an estimand to study this question rigorously, show the assumptions necessary for causal identification, and develop sensitivity analyses to assess robustness to violations of key assumptions. Additionally, we investigate difficulties with existing estimands targeting racial bias in policing. We show for these estimands, and the estimands developed in this manuscript, that estimation can benefit from incorporating mobility data into analyses. We apply these ideas to a study in New York City, where we find a large amount of racial bias, as well as race and place policing, and that these findings are robust to large violations of untestable assumptions. We additionally show that mobility data can make substantial impacts on the resulting estimates, suggesting it should be used whenever possible in subsequent studies.

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arXiv2024

Autoregressive models for panel data causal inference with application to state-level opioid policies

Motivated by the study of state opioid policies, we propose a novel approach that uses autoregressive models for causal effect estimation in settings with panel data and staggered treatment adoption. Specifically, we seek to estimate the impact of key opioid-related policies by quantifying the effects of must access prescription drug monitoring programs (PDMPs), naloxone access laws (NALs), and medical marijuana laws on opioid prescribing. Existing methods, such as differences-in-differences and synthetic controls, are challenging to apply in these types of dynamic policy landscapes where multiple policies are implemented over time and sample sizes are small. Autoregressive models are an alternative strategy that have been used to estimate policy effects in similar settings, but until this paper have lacked formal justification. We outline a set of assumptions that tie these models to causal effects, and we study biases of estimates based on this approach when key causal assumptions are violated. In a set of simulation studies that mirror the structure of our application, we show that our proposed estimators frequently outperform existing estimators. In short, we justify the use of autoregressive models to evaluate the effectiveness of four state policies in combating the opioid crisis.

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arXiv2024

Smooth and shape-constrained quantile distributed lag models

Exposure to environmental pollutants during the gestational period can significantly impact infant health outcomes, such as birth weight and neurological development. Identifying critical windows of susceptibility, which are specific periods during pregnancy when exposure has the most profound effects, is essential for developing targeted interventions. Distributed lag models (DLMs) are widely used in environmental epidemiology to analyze the temporal patterns of exposure and their impact on health outcomes. However, traditional DLMs focus on modeling the conditional mean, which may fail to capture heterogeneity in the relationship between predictors and the outcome. Moreover, when modeling the distribution of health outcomes like gestational birthweight, it is the extreme quantiles that are of most clinical relevance. We introduce two new quantile distributed lag model (QDLM) estimators designed to address the limitations of existing methods by leveraging smoothness and shape constraints, such as unimodality and concavity, to enhance interpretability and efficiency. We apply our QDLM estimators to the Colorado birth cohort data, demonstrating their effectiveness in identifying critical windows of susceptibility and informing public health interventions.

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arXiv2024

Treatment Effect Heterogeneity and Importance Measures for Multivariate Continuous Treatments

Estimating the joint effect of a multivariate, continuous exposure is crucial, particularly in environmental health where interest lies in simultaneously evaluating the impact of multiple environmental pollutants on health. We develop novel methodology that addresses two key issues for estimation of treatment effects of multivariate, continuous exposures. We use nonparametric Bayesian methodology that is flexible to ensure our approach can capture a wide range of data generating processes. Additionally, we allow the effect of the exposures to be heterogeneous with respect to covariates. Treatment effect heterogeneity has not been well explored in the causal inference literature for multivariate, continuous exposures, and therefore we introduce novel estimands that summarize the nature and extent of the heterogeneity, and propose estimation procedures for new estimands related to treatment effect heterogeneity. We provide theoretical support for the proposed models in the form of posterior contraction rates and show that it works well in simulated examples both with and without heterogeneity. Our approach is motivated by a study of the health effects of simultaneous exposure to the components of PM$_{2.5}$, where we find that the negative health effects of exposure to environmental pollutants are exacerbated by low socioeconomic status, race and age.

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arXiv2024

Causal Analysis of Air Pollution Mixtures: Estimands, Positivity, and Extrapolation

Causal inference for air pollution mixtures is an increasingly important issue with appreciable challenges. When the exposure is a multivariate mixture, there are many exposure contrasts that may be of nominal interest for causal effect estimation, but the complex joint mixture distribution often renders observed data extremely limited in their ability to inform estimates of many commonly-defined causal effects. We use potential outcomes to 1) define causal effects of air pollution mixtures, 2) formalize the key assumption of mixture positivity required for estimation and 3) offer diagnostic metrics for positivity violations in the mixture setting that allow researchers to assess the extent to which data can actually support estimation of mixture effects of interest. For settings where there is limited empirical support, we redefine causal estimands that apportion causal effects according to whether they can be directly informed by observed data versus rely entirely on model extrapolation, isolating key sources of information on the causal effect of an air pollution mixture. The ideas are deployed to assess the ability of a national United States data set on the chemical components of ambient particulate matter air pollution to support estimation of a variety of causal mixture effects.

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arXiv2023

Partial identification and unmeasured confounding with multiple treatments and multiple outcomes

Estimating the health effects of multiple air pollutants is a crucial problem in public health, but one that is difficult due to unmeasured confounding bias. Motivated by this issue, we develop a framework for partial identification of causal effects in the presence of unmeasured confounding in settings with multiple treatments and multiple outcomes. Under a factor confounding assumption, we show that joint partial identification regions for multiple estimands can be more informative than considering partial identification for individual estimands one at a time. We show how assumptions related to the strength of confounding or magnitude of plausible effect sizes for one estimand can reduce the partial identification regions for other estimands. As a special case of this result, we explore how negative control assumptions reduce partial identification regions and discuss conditions under which point identification can be obtained. We develop novel computational approaches to finding partial identification regions under a variety of these assumptions. We then estimate the causal effect of PM$_{2.5}$ components on a variety of public health outcomes in the United States Medicare cohort, where we find that the detrimental effect of certain air pollutants are robust to the potential presence of unmeasured confounding bias.

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arXiv2023

Principal stratification with continuous treatments and continuous post-treatment variables

Principal stratification (PS) is a commonly used approach for understanding the mechanisms through which a treatment affects an outcome. The goal of this work is to extend the PS framework to studies with continuous treatments, which introduces a number of both challenges and opportunities in terms of defining causal effects and performing inference. This manuscript provides multiple key methodological contributions: 1) we introduce principal causal estimands for continuous treatments that provide insights into different causal mechanisms, 2) we show that nonparametric identification is possible under a principal ignorability assumption, but only under a restrictive assumption on the joint distribution of potential mediators, which can be dropped under mild parametric assumptions, 3) we utilize nonparametric Bayesian models for the joint distribution of the potential mediating variables to ensure our approach is robust to model misspecification, and 4) we provide theoretical justification for utilizing an outcome model to identify the joint distribution of the potential mediating variables, and show that this is only possible if a principal ignorability assumption is violated. Lastly, we apply our methodology to a novel study of the relationship between the economy and arrest rates, and how this is potentially mediated by police capacity.

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arXiv2023

A spatial interference approach to account for mobility in air pollution studies with multivariate continuous treatments

We develop new methodology to improve our understanding of the causal effects of multivariate air pollution exposures on public health accounting for mobility. Typically, in environmental health studies, exposure to air pollution for an individual is assigned based on their residential address, though many people spend time in different regions with potentially different levels of air pollution. To account for this, we incorporate estimates of the mobility of individuals from cell phone mobility data to obtain a more accurate estimate of their air pollution exposure. We treat this as an interference problem, where individuals in one geographic region can be affected by exposures in other regions due to mobility into those areas. We propose policy-relevant estimands and derive expressions showing the extent of bias one would obtain by ignoring individuals' mobility. We additionally highlight the benefits of the proposed interference framework relative to a measurement error framework to account for mobility. Utilizing flexible Bayesian methodology we develop novel estimation strategies to estimate causal effects that account for this spatial spillover. Lastly, we use the proposed methodology to study the health effects of ambient air pollution on mortality among Medicare enrollees in the United States

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arXiv2023

Heterogeneous causal effects of neighborhood policing in New York City with staggered adoption of the policy

In New York City, neighborhood policing was adopted at the police precinct level over the years 2015-2018, and it is of interest to both (1) evaluate the impact of the policy, and (2) understand what types of communities are most impacted by the policy, raising questions of heterogeneous treatment effects. We develop novel statistical approaches that are robust to unmeasured confounding bias to study the causal effect of policies implemented at the community level. We find that neighborhood policing decreases discretionary arrests in certain areas of the city, but has little effect on crime or racial disparities in arrest rates.

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arXiv2022

All models are wrong, but which are useful? Comparing parametric and nonparametric estimation of causal effects in finite samples

There is a long-standing debate in the statistical, epidemiological and econometric fields as to whether nonparametric estimation that uses data-adaptive methods, like machine learning algorithms in model fitting, confer any meaningful advantage over simpler, parametric approaches in real-world, finite sample estimation of causal effects. We address the question: when trying to estimate the effect of a treatment on an outcome, across a universe of reasonable data distributions, how much does the choice of nonparametric vs.~parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach evaluating performance across thousands of data-generating mechanisms drawn from non-parametric models with semi-informative priors. We call this approach a Universal Monte-Carlo Simulation. We compare performance of estimating the average treatment effect across two parametric estimators (a g-computation estimator that uses a parametric outcome model and an inverse probability of treatment weighted estimator) and two nonparametric estimators (Bayesian additive regression trees and a targeted minimum loss-based estimator that uses an ensemble of machine learning algorithms in model fitting). We summarize estimator performance in terms of bias, confidence interval coverage, and mean squared error. We find that the nonparametric estimators nearly always outperform the parametric estimators with the exception of having similar performance in terms of bias and similar-to-slightly-worse performance in terms of coverage under the smallest sample size of N=100.

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arXiv2022

Improved inference for doubly robust estimators of heterogeneous treatment effects

We propose a doubly robust approach to characterizing treatment effect heterogeneity in observational studies. We develop a frequentist inferential procedure that utilizes posterior distributions for both the propensity score and outcome regression models to provide valid inference on the conditional average treatment effect even when high-dimensional or nonparametric models are used. We show that our approach leads to conservative inference in finite samples or under model misspecification, and provides a consistent variance estimator when both models are correctly specified. In simulations, we illustrate the utility of these results in difficult settings such as high-dimensional covariate spaces or highly flexible models for the propensity score and outcome regression. Lastly, we analyze environmental exposure data from NHANES to identify how the effects of these exposures vary by subject-level characteristics.

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arXiv2021

Multiple exposure distributed lag models with variable selection

Distributed lag models are useful in environmental epidemiology as they allow the user to investigate critical windows of exposure, defined as the time period during which exposure to a pollutant adversely affects health outcomes. Recent studies have focused on estimating the health effects of a large number of environmental exposures, or an environmental mixture, on health outcomes. In such settings, it is important to understand which environmental exposures affect a particular outcome, while acknowledging the possibility that different exposures have different critical windows. Further, in the studies of environmental mixtures, it is important to identify interactions among exposures, and to account for the fact that this interaction may occur between two exposures having different critical windows. Exposure to one exposure early in time could cause an individual to be more or less susceptible to another exposure later in time. We propose a Bayesian model to estimate the temporal effects of a large number of exposures on an outcome. We use spike-and-slab priors and semiparametric distributed lag curves to identify important exposures and exposure interactions, and discuss extensions with improved power to detect harmful exposures. We then apply these methods to estimate the effects of exposure to multiple air pollutants during pregnancy on birthweight from vital records in Colorado.

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arXiv2021

Robust inference for geographic regression discontinuity designs: assessing the impact of police precincts

We study variation in policing outcomes attributable to differential policing practices in New York City (NYC) using geographic regression discontinuity designs (GeoRDDs). By focusing on small geographic windows near police precinct boundaries we can estimate local average treatment effects of police precinct practices on arrest rates. We propose estimands and develop estimators for the GeoRDD when the data come from a spatial point process. Standard GeoRDDs rely on continuity assumptions of the potential outcome surface or a local randomization assumption within a window around the boundary. These assumptions, however, can easily be violated in real applications. We develop a novel and robust approach to testing whether there are differences in policing outcomes that are caused by differences in police precinct policies across NYC. Importantly, this approach is applicable to standard regression discontinuity designs with both numeric and point process data. This approach is robust to violations of traditional assumptions made, and is valid under weaker assumptions. We use a unique form of resampling to provide a valid estimate of our test statistic's null distribution even under violations of standard assumptions. This procedure gives substantially different results in the analysis of NYC arrest rates than those that rely on standard assumptions.

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arXiv2021

Estimation and false discovery control for the analysis of environmental mixtures

The analysis of environmental mixtures is of growing importance in environmental epidemiology, and one of the key goals in such analyses is to identify exposures and their interactions that are associated with adverse health outcomes. Typical approaches utilize flexible regression models combined with variable selection to identify important exposures and estimate a potentially nonlinear relationship with the outcome of interest. Despite this surge in interest, no approaches to date can identify exposures and interactions while controlling any form of error rates with respect to exposure selection. We propose two novel approaches to estimating the health effects of environmental mixtures that simultaneously 1) Estimate and provide valid inference for the overall mixture effect, and 2) identify important exposures and interactions while controlling the false discovery rate. We show that this can lead to substantial power gains to detect weak effects of environmental exposures. We apply our approaches to a study of persistent organic pollutants and find that our approach is able to identify more interactions than existing approaches.

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