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David Benkeser

Publications and source records attributed to David Benkeser.

At least 19 recordsLinked to original sources
arXiv2026

Nonparametric Motion Control in Functional Connectivity Studies in Children with Autism Spectrum Disorder

Autism Spectrum Disorder (ASD) is a neurodevelopmental condition associated with difficulties with social interactions, communication, and restricted or repetitive behaviors. To characterize ASD, investigators often use functional connectivity derived from resting-state functional magnetic resonance imaging of the brain. However, participants' head motion during the scanning session can induce motion artifacts. Many studies remove participants with excessive motion, and then estimate the effect of diagnosis on functional connectivity using linear regression. However, participant exclusions and linearity assumptions can cause biases. We propose an estimand that quantifies the difference in average functional connectivity in autistic and non-ASD children while standardizing motion relative to the low motion distribution in scans that pass motion quality control. We introduce a nonparametric estimator for motion control, called MoCo, that uses all participants and flexibly models the impacts of motion and other relevant features using an ensemble of machine learning methods. We establish large-sample efficiency and multiple robustness of our proposed estimator. The framework is applied to estimate the difference in functional connectivity between 132 autistic and 245 non-ASD children, of which 34 and 126 pass motion quality control, respectively. MoCo appears to dramatically reduce motion artifacts compared to a standard approach with no participant removal, while more efficiently utilizing participant data and accounting for possible selection biases compared to participant removal.

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arXiv2026

Flexible Nonparametric Inference for Causal Effects under the Front-Door Model

Evaluating causal treatment effects in observational studies requires addressing confounding. While the back-door criterion enables identification through adjustment for observed covariates, it fails in the presence of unmeasured confounding. The front-door criterion offers an alternative by leveraging variables that fully mediate the treatment effect and are unaffected by unmeasured confounders of the treatment-outcome pair. We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions. Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid modeling the mediator density entirely, and are compatible with flexible, machine learning-based nuisance estimation. We establish conditions for root-n consistency and asymptotic linearity by deriving second-order remainder bounds. We also develop flexible tests for assessing identification assumptions, including a doubly robust testing procedure, within a semiparametric extension of the front-door model that encodes generalized (Verma) independence constraints. We further show how these constraints can be leveraged to improve the efficiency of causal effect estimators. Simulation studies confirm favorable finite-sample performance, and real-data applications in education and emergency medicine illustrate the practical utility of our methods.

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arXiv2026

Causal Vaccine Effects on Post-infection Outcomes in the Naturally Infected

Understanding vaccine effects on post-infection outcomes is critical for evaluating the full value proposition of a vaccine. However, defining appropriate causal effects on such outcomes is challenging because infection is affected by vaccination. Existing principal stratification approaches focus on the \emph{Doomed} stratum, individuals who would be infected regardless of vaccine receipt. For many relevant outcomes, however, this estimand will understate vaccine benefit by excluding individuals whose adverse post-infection outcomes are improved because vaccination prevented infection. We therefore propose causal estimands for post-infection outcomes in the \emph{Naturally Infected}, individuals who would be infected in absence of vaccine. We derive bounds under minimal assumptions and give point identification results under an exclusion restriction and/or a partial principal ignorability assumption. For point-identified settings, we develop efficient one-step estimators with robustness properties under inconsistent nuisance parameter estimation. We further show under what conditions the same identification functional can be interpreted as targeting an effect among individuals exposed to a sufficiently infectious dose of the pathogen, thereby avoiding direct reliance on cross-world parameters and fundamentally untestable causal assumptions. Simulations show that the bounds are valid but often wide, and that the point estimators perform well when their identifying assumptions hold. In a reanalysis of a rotavirus vaccine trial, marginal and Doomed-stratum analyses showed little evidence of an effect on antibiotic use, whereas analyses targeting the Naturally Infected suggested a protective effect under principal ignorability-based assumptions.

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arXiv2025

Causal Inference with the Napkin Graph

Unmeasured confounding can render identification strategies based on adjustment functionals invalid. We study the "Napkin" graph, a causal structure that encapsulates features of M-bias, instrumental variables, and classical back-door and front-door settings, yet identifies the average treatment effect through a nonstandard ratio of two g-formulas. We develop influence-function-based estimators for this functional, including doubly-robust one-step and targeted minimum loss-based estimators that remain asymptotically linear under slower-than-parametric nuisance estimation using machine learning. A distinguishing feature of the Napkin graph is that it imposes a generalized independence restriction, known as a Verma constraint, rather than ordinary conditional independence restrictions, on the observed data distribution. We develop semiparametric efficiency theory for causal effects under a moment restriction corresponding to this Verma constraint, characterizing the orthocomplement of the tangent space, deriving the class of influence functions, and obtaining the semiparametric efficiency bound. More broadly, our analysis provides a framework for semiparametric inference in causal models defined by Verma constraints and demonstrates how such restrictions may yield efficiency gains. Simulations confirm the estimators' theoretical properties and demonstrate substantial efficiency gains. A real-data application using the Finnish Life Course Study estimates the effect of educational attainment on income. An accompanying R package, napkincausal, implements our methods.

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arXiv2025

Statistical learning for constrained functional parameters in infinite-dimensional models

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and machine learning, where estimated parameters must satisfy structural requirements such as moment restrictions, policy benchmarks, calibration criteria, or fairness considerations. To address these problems, we characterize the solution as the minimizer of a penalized population risk using a Lagrange-type formulation, and analyze it through a statistical functional lens. Central to our approach is a constraint-specific path through the unconstrained parameter space that defines the constrained solutions. For a broad class of constraint-risk pairs, this path admits closed-form expressions and reveals how constraints shape optimal adjustments. When closed forms are unavailable, we derive recursive representations that support tractable estimation. Our results also suggest natural estimators of the constrained parameter, constructed by combining estimates of unconstrained components of the data-generating distribution. Thus, our procedure can be integrated with any statistical learning approach and implemented using standard software. We provide general conditions under which the resulting estimators achieve optimal risk and constraint satisfaction, and we demonstrate the flexibility and effectiveness of the proposed method through various examples, simulations, and real-data applications.

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arXiv2025

Assessing Racial Disparities in Healthcare Expenditures via Mediator Distribution Shifts

Racial disparities in healthcare expenditures are well-documented, yet the underlying drivers remain complex. This study develops a framework to decompose such disparities through shifts in the distributions of mediating variables, rather than treating race itself as a manipulable exposure. We define disparities as differences in covariate-adjusted outcome distributions across racial groups, and decompose the total disparity into a component attributable to differences in mediator distributions, and a residual component that remains after equalizing those distributions. Using data from the Medical Expenditures Panel Survey (MEPS), we examine the extent to which expenditure disparities would persist or be reduced if mediators such as socioeconomic status (SES), insurance access, health behaviors, or health status were equalized across racial groups. To ensure valid inference, we derive asymptotically linear estimators based on influence-function techniques and flexible machine learning, including super learners and a two-part model designed for the zero-inflated, right-skewed nature of expenditure data. Applying this framework to MEPS data from 2009 and 2016, substantial disparities were observed across all pairwise racial comparisons, with the largest gaps observed between non-Hispanic Whites and Hispanics in both years. Differences in SES and health status were the largest contributors to these disparities, with insurance access also playing a meaningful role, particularly for Hispanic populations, whereas health behaviors contributed minimally. Residual disparities persisted, especially in comparisons involving non-Hispanic Whites, suggesting the influence of unmeasured or structural factors.

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arXiv2025

Target trial emulation without matching: a more efficient approach for evaluating vaccine effectiveness using observational data

Real-world vaccine effectiveness has increasingly been studied using matching-based approaches, particularly in observational cohort studies following the target trial emulation framework. Although matching is appealing in its simplicity, it suffers important limitations in terms of clarity of the target estimand and the efficiency or precision with which is it estimated. Scientifically justified causal estimands of vaccine effectiveness may be difficult to define owing to the fact that vaccine uptake varies over calendar time when infection dynamics may also be rapidly changing. We propose a causal estimand of vaccine effectiveness that summarizes vaccine effectiveness over calendar time, similar to how vaccine efficacy is summarized in a randomized controlled trial. We describe the identification of our estimand, including its underlying assumptions, and propose simple-to-implement estimators based on two hazard regression models. We apply our proposed estimator in simulations and in a study to assess the effectiveness of the Pfizer-BioNTech COVID-19 vaccine to prevent infections with SARS-CoV2 in children 5-11 years old. In both settings, we find that our proposed estimator yields similar scientific inferences while providing significant efficiency gains over commonly used matching-based estimators.

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arXiv2025

Monte Carlo Integration in Simple and Complex Simulation Designs

Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand, of interest. However, in many simulation designs, the true value of the estimand is difficult to compute analytically. Here, we illustrate the use of Monte Carlo integration to compute true estimand values in simple and complex simulation designs. We provide general pseudocode that can be replicated in any software program of choice to demonstrate key principles in using Monte Carlo integration in two scenarios: a simple three variable simulation where interest lies in the marginally adjusted odds ratio; and a more complex causal mediation analysis where interest lies in the controlled direct effect in the presence of mediator-outcome confounders affected by the exposure. We discuss general strategies that can be used to minimize Monte Carlo error, and to serve as checks on the simulation program to avoid coding errors. R programming code is provided illustrating the application of our pseudocode in these settings.

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arXiv2024

Comparing HIV Vaccine Immunogenicity across Trials with Different Populations and Study Designs

Safe and effective preventive vaccines have the potential to help stem the HIV epidemic. The efficacy of such vaccines is typically measured in randomized, double-blind phase IIb/III trials and described as a reduction in newly acquired HIV infections. However, such trials are often expensive, time-consuming, and/or logistically challenging. These challenges lead to a great interest in immune responses induced by vaccination, and in identifying which immune responses predict vaccine efficacy. These responses are termed vaccine correlates of protection. Studies of vaccine-induced immunogenicity vary in size and design, ranging from small, early phase trials, to case-control studies nested in a broader late-phase randomized trial. Moreover, trials can be conducted in geographically diverse study populations across the world. Such diversity presents a challenge for objectively comparing vaccine-induced immunogenicity. To address these practical challenges, we propose a framework that is capable of identifying appropriate causal estimands and estimators, which can be used to provide standardized comparisons of vaccine-induced immunogenicity across trials. We evaluate the performance of the proposed estimands via extensive simulation studies. Our estimators are well-behaved and enjoy robustness properties. The proposed technique is applied to compare vaccine immunogenicity using data from three recent HIV vaccine trials.

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arXiv2024

A Density Ratio Super Learner

The estimation of the ratio of two density probability functions is of great interest in many statistics fields, including causal inference. In this study, we develop an ensemble estimator of density ratios with a novel loss function based on super learning. We show that this novel loss function is qualified for building super learners. Two simulations corresponding to mediation analysis and longitudinal modified treatment policy in causal inference, where density ratios are nuisance parameters, are conducted to show our density ratio super learner's performance empirically.

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arXiv2024

Fair Risk Minimization under Causal Path-Specific Effect Constraints

This paper introduces a framework for estimating fair optimal predictions using machine learning where the notion of fairness can be quantified using path-specific causal effects. We use a recently developed approach based on Lagrange multipliers for infinite-dimensional functional estimation to derive closed-form solutions for constrained optimization based on mean squared error and cross-entropy risk criteria. The theoretical forms of the solutions are analyzed in detail and described as nuanced adjustments to the unconstrained minimizer. This analysis highlights important trade-offs between risk minimization and achieving fairnes. The theoretical solutions are also used as the basis for construction of flexible semiparametric estimation strategies for these nuisance components. We describe the robustness properties of our estimators in terms of achieving the optimal constrained risk, as well as in terms of controlling the value of the constraint. We study via simulation the impact of using robust estimators of pathway-specific effects to validate our theory. This work advances the discourse on algorithmic fairness by integrating complex causal considerations into model training, thus providing strategies for implementing fair models in real-world applications.

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arXiv2022

Efficient estimation of modified treatment policy effects based on the generalized propensity score

Continuous treatments have posed a significant challenge for causal inference, both in the formulation and identification of scientifically meaningful effects and in their robust estimation. Traditionally, focus has been placed on techniques applicable to binary or categorical treatments with few levels, allowing for the application of propensity score-based methodology with relative ease. Efforts to accommodate continuous treatments introduced the generalized propensity score, yet estimators of this nuisance parameter commonly utilize parametric regression strategies that sharply limit the robustness and efficiency of inverse probability weighted estimators of causal effect parameters. We formulate and investigate a novel, flexible estimator of the generalized propensity score based on a nonparametric function estimator that provably converges at a suitably fast rate to the target functional so as to facilitate statistical inference. With this estimator, we demonstrate the construction of nonparametric inverse probability weighted estimators of a class of causal effect estimands tailored to continuous treatments. To ensure the asymptotic efficiency of our proposed estimators, we outline several non-restrictive selection procedures for utilizing a sieve estimation framework to undersmooth estimators of the generalized propensity score. We provide the first characterization of such inverse probability weighted estimators achieving the nonparametric efficiency bound in a setting with continuous treatments, demonstrating this in numerical experiments. We further evaluate the higher-order efficiency of our proposed estimators by deriving and numerically examining the second-order remainder of the corresponding efficient influence function in the nonparametric model. Open source software implementing our proposed estimation techniques, the haldensify R package, is briefly discussed.

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arXiv2022

A Huber loss-based super learner with applications to healthcare expenditures

Complex distributions of the healthcare expenditure pose challenges to statistical modeling via a single model. Super learning, an ensemble method that combines a range of candidate models, is a promising alternative for cost estimation and has shown benefits over a single model. However, standard approaches to super learning may have poor performance in settings where extreme values are present, such as healthcare expenditure data. We propose a super learner based on the Huber loss, a "robust" loss function that combines squared error loss with absolute loss to down-weight the influence of outliers. We derive oracle inequalities that establish bounds on the finite-sample and asymptotic performance of the method. We show that the proposed method can be used both directly to optimize Huber risk, as well as in finite-sample settings where optimizing mean squared error is the ultimate goal. For this latter scenario, we provide two methods for performing a grid search for values of the robustification parameter indexing the Huber loss. Simulations and real data analysis demonstrate appreciable finite-sample gains in cost prediction and causal effect estimation using our proposed method.

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arXiv2021

Efficient Estimation of Pathwise Differentiable Target Parameters with the Undersmoothed Highly Adaptive Lasso

We consider estimation of a functional parameter of a realistically modeled data distribution based on observing independent and identically distributed observations. We define an $m$-th order Spline Highly Adaptive Lasso Minimum Loss Estimator (Spline HAL-MLE) of a functional parameter that is defined by minimizing the empirical risk function over an $m$-th order smoothness class of functions. We show that this $m$-th order smoothness class consists of all functions that can be represented as an infinitesimal linear combination of tensor products of $\leq m$-th order spline-basis functions, and involves assuming $m$-derivatives in each coordinate. By selecting $m$ with cross-validation we obtain a Spline-HAL-MLE that is able to adapt to the underlying unknown smoothness of the true function, while guaranteeing a rate of convergence faster than $n^{-1/4}$, as long as the true function is cadlag (right-continuous with left-hand limits) and has finite sectional variation norm. The $m=0$-smoothness class consists of all cadlag functions with finite sectional variation norm and corresponds with the original HAL-MLE defined in van der Laan (2015). In this article we establish that this Spline-HAL-MLE yields an asymptotically efficient estimator of any smooth feature of the functional parameter under an easily verifiable global undersmoothing condition. A sufficient condition for the latter condition is that the minimum of the empirical mean of the selected basis functions is smaller than a constant times $n^{-1/2}$, which is not parameter specific and enforces the selection of the $L_1$-norm in the lasso to be large enough to include sparsely supported basis. We demonstrate our general result for the $m=0$-HAL-MLE of the average treatment effect and of the integral of the square of the data density. We also present simulations for these two examples confirming the theory.

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arXiv2021

Inference for natural mediation effects under case-cohort sampling with applications in identifying COVID-19 vaccine correlates of protection

Combating the SARS-CoV2 pandemic will require the fast development of effective preventive vaccines. Regulatory agencies may open accelerated approval pathways for vaccines if an immunological marker can be established as a mediator of a vaccine's protection. A rich source of information for identifying such correlates are large-scale efficacy trials of COVID-19 vaccines, where immune responses are measured subject to a case-cohort sampling design. We propose two approaches to estimation of mediation parameters in the context of case-cohort sampling designs. We establish the theoretical large-sample efficiency of our proposed estimators and evaluate them in a realistic simulation to understand whether they can be employed in the analysis of COVID-19 vaccine efficacy trials.

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arXiv2020

Nonparametric inference for interventional effects with multiple mediators

Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects. Interventional direct and indirect effects provide one such decomposition. Existing estimators of these effects are based on parametric models with confidence interval estimation facilitated via the nonparametric bootstrap. We provide theory that allows for more flexible, possibly machine learning-based, estimation techniques to be considered. In particular, we establish weak convergence results that facilitate the construction of closed-form confidence intervals and hypothesis tests. Finally, we demonstrate multiple robustness properties of the proposed estimators. Simulations show that inference based on large-sample theory has adequate small-sample performance. Our work thus provides a means of leveraging modern statistical learning techniques in estimation of interventional mediation effects.

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arXiv2019

Design and analysis considerations for a sequentially randomized HIV prevention trial

TechStep is a randomized trial of a mobile health interventions targeted towards transgender adolescents. The interventions include a short message system, a mobile-optimized web application, and electronic counseling. The primary outcomes are self-reported sexual risk behaviors and uptake of HIV preventing medication. In order that we may evaluate the efficacy of several different combinations of interventions, the trial has a sequentially randomized design. We use a causal framework to formalize the estimands of the primary and key secondary analyses of the TechStep trial data. Targeted minimum loss-based estimators of these quantities are described and studied in simulation.

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arXiv2019

Robust inference on the average treatment effect using the outcome highly adaptive lasso

Many estimators of the average effect of a treatment on an outcome require estimation of the propensity score, the outcome regression, or both. It is often beneficial to utilize flexible techniques such as semiparametric regression or machine learning to estimate these quantities. However, optimal estimation of these regressions does not necessarily lead to optimal estimation of the average treatment effect, particularly in settings with strong instrumental variables. A recent proposal addressed these issues via the outcome-adaptive lasso, a penalized regression technique for estimating the propensity score that seeks to minimize the impact of instrumental variables on treatment effect estimators. However, a notable limitation of this approach is that its application is restricted to parametric models. We propose a more flexible alternative that we call the outcome highly adaptive lasso. We discuss large sample theory for this estimator and propose closed form confidence intervals based on the proposed estimator. We show via simulation that our method offers benefits over several popular approaches.

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