arXiv subjects

Brian Gilbert

Publications and source records attributed to Brian Gilbert.

7 recordsLinked to original sources

arXiv2026

Data-Adaptive and Model-Robust Covariate Adjustment for Time-to-Event Outcomes in Stratified Randomized Trials

Time-to-event outcomes are commonly used as primary endpoints in randomized clinical trials. Despite this, relatively little work incorporates baseline covariate information while also accounting for stratified randomization, a common form of randomization. Moreover, leveraging efficiency gains using these approaches typically requires pre-specifying a subset of covariates that are most predictive of the outcome -- a challenging task in practice, as most trials collect dozens of potentially prognostic baseline variables. In this work, we build on existing literature to propose a data-adaptive and model-robust covariate adjustment method for time-to-event outcomes. Our approach, based on targeted minimum loss-based estimation, allows for data-adaptive covariate selection and model-robust efficient inference on functionals of the survival curve while accounting for stratification. Through extensive simulations and analysis, we showcase the simplicity and improved precision of our method when the covariate set is not known a priori.

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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.

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arXiv2023

Consistency of common spatial estimators under spatial confounding

This paper addresses the asymptotic performance of popular spatial regression estimators of the linear effect of an exposure on an outcome under ``spatial confounding" -- the presence of an unmeasured spatially-structured variable influencing both the exposure and the outcome. We first show that the estimators from ordinary least squares (OLS) and restricted spatial regression are asymptotically biased under spatial confounding. We then prove a novel main result on the consistency of the generalized least squares (GLS) estimator using a Gaussian process (GP) working covariance matrix in the presence of spatial confounding under infill (fixed domain) asymptotics. The result holds under very general conditions -- for any exposure with some non-spatial variation (noise), for any spatially continuous fixed confounder function, using any Mat\`ern or square exponential kernel used to construct the GLS estimator, and without requiring Gaussianity of errors. Finally, we prove that spatial estimators from GLS, GP regression, and spline models that are consistent under confounding by a fixed function will also be consistent under endogeneity or confounding by a random function, i.e., a stochastic process. We conclude that, contrary to claims in some literature on spatial confounding, traditional spatial estimators are capable of estimating linear exposure effects under spatial confounding as long as there is some noise in the exposure. We support our theoretical arguments with simulation studies.

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arXiv2023

Learning sources of variability from high-dimensional observational studies

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.

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arXiv2023

Visibility graph-based covariance functions for scalable spatial analysis in non-convex domains

We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not guaranteed to be positive definite on such domains, while existing non-Euclidean approaches fail to respect the partially Euclidean nature of these domains where the geodesic distance agrees with the Euclidean distances for some pairs of points. Using a visibility graph on the domain, we propose a class of covariance functions that preserve Euclidean-based covariances between points that are connected in the domain while incorporating the non-convex geometry of the domain via conditional independence relationships. We show that the proposed method preserves the partially Euclidean nature of the intrinsic geometry on the domain while maintaining validity (positive definiteness) and marginal stationarity of the covariance function over the entire parameter space, properties which are not always fulfilled by existing approaches to construct covariance functions on non-convex domains. We provide useful approximations to improve computational efficiency, resulting in a scalable algorithm. We compare the performance of our method with those of competing state-of-the-art methods using simulation studies on synthetic non-convex domains. The method is applied to data regarding acidity levels in the Chesapeake Bay, showing its potential for ecological monitoring in real-world spatial applications on irregular domains.

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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.

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arXiv2021

A causal inference framework for spatial confounding

Over the past few decades, addressing "spatial confounding" has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed solutions are tied to specific analysis models and do not address the issue of confounding as it is understood in causal inference. We offer an analysis-model-agnostic definition of spatial confounding as the existence of an unmeasured causal confounder variable with a spatial structure. We present a causal inference framework for nonparametric identification of the causal effect of a continuous exposure on an outcome in the presence of spatial confounding. In particular, we identify two critical additional assumptions that allow the use of the spatial coordinates as a proxy for the unmeasured spatial confounder: the measurability of the confounder as a function of space, which is required for conditional ignorability to hold, and the presence of a non-spatial component in the exposure, required for positivity to hold. We also propose studying a causal estimand based on a "shift intervention" that requires less stringent identifying assumptions than traditional estimands. We then turn to estimation and focus on "double machine learning" (DML), a procedure in which flexible models are used to regress both the exposure and outcome variables on confounders to arrive at a causal estimator with favorable robustness properties and convergence rates. This procedure avoids restrictive assumptions, such as linearity and effect homogeneity, which are typically made in spatial models and which can lead to bias when violated. We demonstrate the advantages of the DML approach analytically and via extensive simulation studies. We apply our methods and reasoning to a study of the effect of fine particulate matter exposure during pregnancy on birthweight in California.

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