Searcharxiv⌕ Search

arXiv subjects

Nicholas Williams

Publications and source records attributed to Nicholas Williams.

18 recordsLinked to original sources
arXiv2026

Improving reproducibility by controlling random seed stability in machine learning based estimation via bagging

Predictions from machine learning algorithms can vary across random seeds, inducing instability in downstream debiased machine learning estimators. We formalize random seed stability via a concentration condition and prove that subbagging guarantees stability for any bounded-outcome regression algorithm. We introduce a new cross-fitting procedure, adaptive cross-bagging, which simultaneously eliminates seed dependence from both nuisance estimation and sample splitting in debiased machine learning. Numerical experiments confirm that the method achieves the targeted level of stability whereas alternatives do not. Our method incurs a small computational penalty relative to standard practice whereas alternative methods incur large penalties.

stat.ME↗
arXiv2025

Everything all at once: On choosing an estimand for multi-component environmental exposures

Many research questions -- particularly those in environmental health -- do not involve binary exposures. In environmental epidemiology, this includes multivariate exposure mixtures with nondiscrete components. Causal inference estimands and estimators to quantify the relationship between an exposure mixture and an outcome are relatively few. We propose an approach to quantify a relationship between a shift in the exposure mixture and the outcome -- either in the single timepoint or longitudinal setting. The shift in the exposure mixture can be defined flexibly in terms of shifting one or more components, including examining interaction between mixture components, and in terms of shifting the same or different amounts across components. The estimand we discuss has a similar interpretation as a main effect regression coefficient. First, we focus on choosing a shift in the exposure mixture supported by observed data. We demonstrate how to assess extrapolation and modify the shift to minimize reliance on extrapolation. Second, we propose estimating the relationship between the exposure mixture shift and outcome completely nonparametrically, using machine learning in model-fitting. This is in contrast to other current approaches, which employ parametric modeling for at least some relationships, which we would like to avoid because parametric modeling assumptions in complex, nonrandomized settings are tenuous at best. We are motivated by longitudinal data on pesticide exposures among participants in the CHAMACOS Maternal Cognition cohort. We examine the relationship between longitudinal exposure to agricultural pesticides and risk of hypertension. We provide step-by-step code to facilitate the easy replication and adaptation of the approaches we use.

stat.ME↗
arXiv2025

Nonparametric estimation of an optimal treatment rule with fused randomized trials and missing effect modifiers

A fundamental principle of clinical medicine is that a treatment should only be administered to those patients who would benefit from it. Treatment strategies that assign treatment to patients as a function of their individual characteristics are known as dynamic treatment rules. The dynamic treatment rule that optimizes the outcome in the population is called the optimal dynamic treatment rule. Randomized clinical trials are considered the gold standard for estimating the marginal causal effect of a treatment on an outcome; they are often not powered to detect heterogeneous treatment effects, and thus, may rarely inform more personalized treatment decisions. The availability of multiple trials studying a common set of treatments presents an opportunity for combining data, often called data-fusion, to better estimate dynamic treatment rules. However, there may be a mismatch in the set of patient covariates measured across trials. We address this problem here; we propose a nonparametric estimator for the optimal dynamic treatment rule that leverages information across the set of randomized trials. We apply the estimator to fused randomized trials of medications for the treatment of opioid use disorder to estimate a treatment rule that would match patient subgroups with the medication that would minimize risk of return to regular opioid use.

stat.AP↗
arXiv2025

Longitudinal weighted and trimmed treatment effects with flip interventions

Weighting and trimming are popular methods for addressing positivity violations in causal inference. While well-studied with single-timepoint data, standard methods do not easily generalize to address non-baseline positivity violations in longitudinal data, and remain vulnerable to such violations. In this paper, we extend weighting and trimming to longitudinal data via stochastic ``flip'' interventions, which maintain the treatment status of subjects who would have received the target treatment, and flip others' treatment to the target with probability equal to their weight (e.g., overlap weight, trimming indicator). We first show, in single-timepoint data, that flip interventions yield a large class of weighted average treatment effects, ascribing a novel policy interpretation to these popular weighted estimands. With longitudinal data, we then show that flip interventions provide interpretable weighting or trimming on non-baseline covariates and, crucially, yield effects that are identifiable under arbitrary positivity violations. Moreover, we demonstrate that flip interventions are policy-relevant since they could be implemented in practice. By contrast, we show that alternative approaches for weighting on non-baseline covariates fail to achieve this property. We derive flexible and efficient estimators based on efficient influence functions when the weight is a smooth function of the propensity score. Namely, we construct multiply robust-style and sequentially doubly robust-style estimators that achieve root-n consistency and asymptotic normality under nonparametric conditions. Finally, we demonstrate our methods through an analysis of the effect of union membership on earnings.

stat.ME↗
arXiv2024

A drug classification pipeline for Medicaid claims using RxNorm

Objective: Freely preprocess drug codes recorded in electronic health records and insurance claims to drug classes that may then be used in biomedical research. Materials and Methods: We developed a drug classification pipeline for linking National Drug Codes to the World Health Organization Anatomical Therapeutic Chemical classification. To implement our solution, we created an R package interface to the National Library of Medicine's RxNorm API. Results: Using the classification pipeline, 59.4% of all unique NDC were linked to an ATC, resulting in 95.5% of all claims being successfully linked to a drug classification. We identified 12,004 unique NDC codes that were classified as being an opioid or non-opioid prescription for treating pain. Discussion: Our proposed pipeline performed similarly well to other NDC classification routines using commercial databases. A check of a small, random sample of non-active NDC found the pipeline to be accurate for classifying these codes. Conclusion: The RxNorm NDC classification pipeline is a practical and reliable tool for categorizing drugs in large-scale administrative claims data.

q-bio.QM↗
arXiv2024

Identification and estimation of mediational effects of longitudinal modified treatment policies

We demonstrate a comprehensive semiparametric approach to causal mediation analysis, addressing the complexities inherent in settings with longitudinal and continuous treatments, confounders, and mediators. Our methodology utilizes a nonparametric structural equation model and a cross-fitted sequential regression technique based on doubly robust pseudo-outcomes, yielding an efficient, asymptotically normal estimator without relying on restrictive parametric modeling assumptions. We are motivated by a recent scientific controversy regarding the effects of invasive mechanical ventilation (IMV) on the survival of COVID-19 patients, considering acute kidney injury (AKI) as a mediating factor. We highlight the possibility of "inconsistent mediation," in which the direct and indirect effects of the exposure operate in opposite directions. We discuss the significance of mediation analysis for scientific understanding and its potential utility in treatment decisions.

stat.ME↗
arXiv2024

Recanting twins: addressing intermediate confounding in mediation analysis

The presence of intermediate confounders, also called recanting witnesses, is a fundamental challenge to the investigation of causal mechanisms in mediation analysis, preventing the identification of natural path-specific effects. Proposed alternative parameters (such as randomizational interventional effects) are problematic because they can be non-null even when there is no mediation for any individual in the population; i.e., they are not an average of underlying individual-level mechanisms. In this paper we develop a novel method for mediation analysis in settings with intermediate confounding, with guarantees that the causal parameters are summaries of the individual-level mechanisms of interest. The method is based on recently proposed ideas that view causality as the transfer of information, and thus replace recanting witnesses by draws from their conditional distribution, what we call "recanting twins". We show that, in the absence of intermediate confounding, recanting twin effects recover natural path-specific effects. We present the assumptions required for identification of recanting twins effects under a standard structural causal model, as well as the assumptions under which the recanting twin identification formulas can be interpreted in the context of the recently proposed separable effects models. To estimate recanting-twin effects, we develop efficient semi-parametric estimators that allow the use of data driven methods in the estimation of the nuisance parameters. We present numerical studies of the methods using synthetic data, as well as an application to evaluate the role of new-onset anxiety and depressive disorder in explaining the relationship between gabapentin/pregabalin prescription and incident opioid use disorder among Medicaid beneficiaries with chronic pain.

stat.ME↗
arXiv2023

Studying continuous, time-varying, and/or complex exposures using longitudinal modified treatment policies

This tutorial discusses methodology for causal inference using longitudinal modified treatment policies. This method facilitates the mathematical formalization, identification, and estimation of many novel parameters, and mathematically generalizes many commonly used parameters, such as the average treatment effect. Longitudinal modified treatment policies apply to a wide variety of exposures, including binary, multivariate, and continuous, and can accommodate time-varying treatments and confounders, competing risks, loss-to-follow-up, as well as survival, binary, or continuous outcomes. Longitudinal modified treatment policies can be seen as an extension of static and dynamic interventions to involve the natural value of treatment, and, like dynamic interventions, can be used to define alternative estimands with a positivity assumption that is more likely to be satisfied than estimands corresponding to static interventions. This tutorial aims to illustrate several practical uses of the longitudinal modified treatment policy methodology, including describing different estimation strategies and their corresponding advantages and disadvantages. We provide numerous examples of types of research questions which can be answered using longitudinal modified treatment policies. We go into more depth with one of these examples--specifically, estimating the effect of delaying intubation on critically ill COVID-19 patients' mortality. We demonstrate the use of the open-source R package lmtp to estimate the effects, and we provide code on https://github.com/kathoffman/lmtp-tutorial.

stat.ME↗
arXiv2022

Nonparametric estimators of interventional (transported) direct and indirect effects that accommodate multiple mediators and multiple intermediate confounders

Mediation analysis is appealing for its ability to improve understanding of the mechanistic drivers of causal effects, but real-world data complexities challenge its successful implementation, including: 1) the existence of post-exposure variables that also affect mediators and outcomes (thus, confounding the mediator-outcome relationship), that may also be 2) multivariate, and 3) the existence of multivariate mediators. Interventional direct and indirect effects (IDE/IIE) accommodate post-exposure variables that confound the mediator-outcome relationship, but currently, no estimator for IDE/IIE exists that allows for both multivariate mediators and multivariate post-exposure intermediate confounders. This, again, represents a significant limitation for real-world analyses. We address this gap by extending two recently developed nonparametric estimators -- one that estimates the IDE/IIE and another that estimates the IDE/IIE transported to a new, target population -- to allow for multivariate mediators and multivariate intermediate confounders simultaneously. We use simulation to examine finite sample performance, and apply these estimators to longitudinal data from the Moving to Opportunity trial. In the application, we walk through a strategy for separating indirect effects into mediator- or mediator-group-specific indirect effects, while appropriately accounting for other, possibly co-occurring intermediate variables.

stat.ME↗
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.

stat.ME↗
arXiv2022

A novel decomposition to explain heterogeneity in observational and randomized studies of causality

This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study heterogeneity, identifying sources of variability in treatment effects across studies. The proposed methodology allows for robust estimation of causal parameters under various assumptions, addressing differences in pre-treatment covariate distributions, mediating variables, and the outcome mechanism. Our approach is validated through a simulation study and applied to data from the Moving to Opportunity (MTO) study, demonstrating its practical relevance. This work contributes to the broader understanding of causal inference in multi-study environments, with potential applications in evidence synthesis and policy-making.

stat.ME↗
arXiv2022

Efficient and flexible causal mediation with time-varying mediators, treatments, and confounders

Interventional effects have been proposed as a solution to the unidentifiability of natural (in)direct effects under mediator-outcome confounders affected by the exposure. Such confounders are an intrinsic characteristic of studies with time-varying exposures and mediators, yet the generalization of the interventional effect framework to the time-varying case has received little attention in the literature. We present an identification result for interventional effects in a general longitudinal data structure that allows flexibility in the specification of treatment-outcome, treatment-mediator, and mediator-outcome relationships. Identification is achieved under the standard no-unmeasured-confounders and positivity assumptions. We also present a theoretical and computational study of the properties of the identifying functional based on the efficient influence function (EIF). We use the EIF to propose a sequential regression estimation algorithm that yields doubly robust, $\sqrt{n}$-consistent, asymptotically Gaussian, and efficient estimators under slow convergence rates for the regression algorithms used. This allows the use of flexible machine learning for regression while permitting uncertainty quantification through confidence intervals and p-values. A free and open source \texttt{R} package implementing our proposed estimators is made available on GitHub. We apply the proposed estimator to an application from a comparative effectiveness trial of two medications for opioid use disorder. In the application, we estimate the extent to which differences between the two treatments' on subsequent risk of opioid use is mediated by craving symptoms.

stat.ME↗
arXiv2021

Causal mediation with instrumental variables

Mediation analysis is a strategy for understanding the mechanisms by which treatments or interventions affect later outcomes. Mediation analysis is frequently applied in randomized trial settings, but typically assumes: a) that randomized assignment is the exposure of interest as opposed to actual take-up of the intervention, and b) no unobserved confounding of the mediator-outcome relationship. In contrast to the rich literature on instrumental variable (IV) methods to estimate a total effect of a non-randomized exposure, there has been almost no research into using IV as an identification strategy in the presence of both exposure-outcome and mediator-outcome unobserved confounding. In response, we define and identify novel estimands -- complier interventional direct and indirect effects (i.e., IV mediational effects) in two scenarios: 1) with a single IV for the exposure, and 2) with two IVs, one for the exposure and another for the mediator, that may be related. We propose nonparametric, robust, efficient estimators, and apply them to a housing voucher experiment.

stat.ME↗
arXiv2021

Optimizing Precision and Power by Machine Learning in Randomized Trials, with an Application to COVID-19

The rapid finding of effective therapeutics requires the efficient use of available resources in clinical trials. The use of covariate adjustment can yield statistical estimates with improved precision, resulting in a reduction in the number of participants required to draw futility or efficacy conclusions. We focus on time-to-event and ordinal outcomes. A key question for covariate adjustment in randomized studies is how to fit a model relating the outcome and the baseline covariates to maximize precision. We present a novel theoretical result establishing conditions for asymptotic normality of a variety of covariate-adjusted estimators that rely on machine learning (e.g., l1-regularization, Random Forests, XGBoost, and Multivariate Adaptive Regression Splines), under the assumption that outcome data is missing completely at random. We further present a consistent estimator of the asymptotic variance. Importantly, the conditions do not require the machine learning methods to converge to the true outcome distribution conditional on baseline variables, as long as they converge to some (possibly incorrect) limit. We conducted a simulation study to evaluate the performance of the aforementioned prediction methods in COVID-19 trials using longitudinal data from over 1,500 patients hospitalized with COVID-19 at Weill Cornell Medicine New York Presbyterian Hospital. We found that using l1-regularization led to estimators and corresponding hypothesis tests that control type 1 error and are more precise than an unadjusted estimator across all sample sizes tested. We also show that when covariates are not prognostic of the outcome, l1-regularization remains as precise as the unadjusted estimator, even at small sample sizes (n = 100). We give an R package adjrct that performs model-robust covariate adjustment for ordinal and time-to-event outcomes.

stat.ME↗
arXiv2020

Non-parametric causal effects based on longitudinal modified treatment policies

Most causal inference methods consider counterfactual variables under interventions that set the treatment deterministically. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Furthermore, violations to the positivity assumption, necessary for identification, are exacerbated with continuous and multi-valued treatments and deterministic interventions. In this paper we propose longitudinal modified treatment policies (LMTPs) as a non-parametric alternative. LMTPs can be designed to guarantee positivity, and yield effects of immediate practical relevance with an interpretation that is familiar to regular users of linear regression adjustment. We study the identification of the LMTP parameter, study properties of the statistical estimand such as the efficient influence function, and propose four different estimators. Two of our estimators are efficient, and one is sequentially doubly robust in the sense that it is consistent if, for each time point, either an outcome regression or a treatment mechanism is consistently estimated. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on hypoxemia and mortality in Intensive Care Unit (ICU) patients. Software implementing our methods is provided in the form of the open source \texttt{R} package \texttt{lmtp} freely available on GitHub (\url{https://github.com/nt-williams/lmtp}).

stat.ME↗
arXiv2018

Quantifying Inactive Lithium in Lithium Metal Batteries

Inactive lithium (Li) formation is the immediate cause of capacity loss and catastrophic failure of Li metal batteries. However, the chemical component and the atomic level structure of inactive Li have rarely been studied due to the lack of effective diagnosis tools to accurately differentiate and quantify Li+ in solid electrolyte interphase (SEI) components and the electrically isolated unreacted metallic Li0, which together comprise the inactive Li. Here, by introducing a new analytical method, Titration Gas Chromatography (TGC), we can accurately quantify the contribution from metallic Li0 to the total amount of inactive Li. We uncover that the Li0, rather than the electrochemically formed SEI, dominates the inactive Li and capacity loss. Using cryogenic electron microscopies to further study the microstructure and nanostructure of inactive Li, we find that the Li0 is surrounded by insulating SEI, losing the electronic conductive pathway to the bulk electrode. Coupling the measurements of the Li0 global content to observations of its local atomic structure, we reveal the formation mechanism of inactive Li in different types of electrolytes, and identify the true underlying cause of low Coulombic efficiency in Li metal deposition and stripping. We ultimately propose strategies to enable the highly efficient Li deposition and stripping to enable Li metal anode for next generation high energy batteries.

cond-mat.mtrl-sci↗
arXiv2016

Galois covers of type (p,...,p), vanishing cycles formula, and the existence of torsor structures

In this article we prove a local Riemman-Hurwitz formula which compares the dimensions of the spaces of vanishing cycles in a finite Galois cover of type (p,p,...,p) between formal germs of p-adic curves and which generalises the formula proven by the first author in the case of Galois covers of degree p. We also investigate the problem of the existence of a torsor structure for a finite Galois cover of type (p,p,...,p) between p-adic schemes.

math.AG↗