arXiv subjects

Sean McGrath

Publications and source records attributed to Sean McGrath.

16 recordsLinked to original sources

arXiv2025

Illustrating implications of misaligned causal questions and statistics in settings with competing events and interest in treatment mechanisms

In the presence of competing events, many investigators are interested in a direct treatment effect on the event of interest that does not capture treatment effects on competing events. Classical survival analysis methods that treat competing events like censoring events, at best, target a controlled direct effect: the effect of the treatment under a difficult to imagine and typically clinically irrelevant scenario where competing events are somehow eliminated. A separable direct effect, quantifying the effect of a future modified version of the treatment, is an alternative direct effect notion that may better align with an investigator's underlying causal question. In this paper, we provide insights into the implications of naively applying an estimator constructed for a controlled direct effect (i.e., "censoring by competing events") when the actual causal effect of interest is a separable direct effect. We illustrate the degree to which controlled and separable direct effects may take different values, possibly even different signs, and the degree to which these two different effects may be differentially impacted by violation and/or near violation of their respective identifying conditions under a range of data generating scenarios. Finally, we provide an empirical comparison of inverse probability of censoring weighting to an alternative weighted estimator specifically structured for a separable effect using data from a randomized trial of estrogen therapy and prostate cancer mortality.

stat.ME↗

arXiv2025

Optimal Nuisance Function Tuning for Estimating a Doubly Robust Functional under Proportional Asymptotics

In this paper, we explore the asymptotically optimal tuning parameter choice in ridge regression for estimating nuisance functions of a statistical functional that has recently gained prominence in conditional independence testing and causal inference. Given a sample of size $n$, we study estimators of the Expected Conditional Covariance (ECC) between variables $Y$ and $A$ given a high-dimensional covariate $X \in \mathbb{R}^p$. Under linear regression models for $Y$ and $A$ on $X$ and the proportional asymptotic regime $p/n \to c \in (0, \infty)$, we evaluate three existing ECC estimators and two sample splitting strategies for estimating the required nuisance functions. Since no consistent estimator of the nuisance functions exists in the proportional asymptotic regime without imposing further structure on the problem, we first derive debiased versions of the ECC estimators that utilize the ridge regression nuisance function estimators. We show that our bias correction strategy yields $\sqrt{n}$-consistent estimators of the ECC across different sample splitting strategies and estimator choices. We then derive the asymptotic variances of these debiased estimators to illustrate the nuanced interplay between the sample splitting strategy, estimator choice, and tuning parameters of the nuisance function estimators for optimally estimating the ECC. Our analysis reveals that prediction-optimal tuning parameters (i.e., those that optimally estimate the nuisance functions) may not lead to the lowest asymptotic variance of the ECC estimator -- thereby demonstrating the need to be careful in selecting tuning parameters based on the final goal of inference. Finally, we verify our theoretical results through extensive numerical experiments.

math.ST↗

arXiv2025

Time-smoothed inverse probability weighted estimation of effects of generalized time-varying treatment strategies on repeated outcomes truncated by death

Researchers are often interested in estimating effects of generalized time-varying treatment strategies on the mean of an outcome at one or more selected follow-up times of interest. For example, the Medications and Weight Gain in PCORnet (MedWeight) study aimed to estimate effects of adhering to flexible medication regimes on future weight change using electronic health records (EHR) data. This problem presents several methodological challenges that have not been jointly addressed in the prior literature. First, this setting involves treatment strategies that vary over time and depend dynamically and non-deterministically on measured confounder history. Second, the outcome is repeatedly, non-monotonically, informatively, and sparsely measured in the data source. Third, some individuals die during follow-up, rendering the outcome of interest undefined at the follow-up time of interest. In this article, we pose a range of inverse probability weighted (IPW) estimators targeting effects of generalized time-varying treatment strategies in truncation by death settings that allow time-smoothing for precision gain. We conducted simulation studies that confirm precision gains of the time-smoothed IPW approaches over more conventional IPW approaches that do not leverage the repeated outcome measurements. We illustrate an application of the IPW approaches to estimate comparative effects of adhering to flexible antidepressant medication strategies on future weight change. The methods are implemented in the accompanying R package, smoothedIPW.

stat.ME↗

arXiv2025

A Tutorial on Conducting Mediation Analysis with Exposure Mixtures

Causal mediation analysis is a powerful tool in environmental health research, allowing researchers to uncover the pathways through which exposures influence health outcomes. While traditional mediation methods have been widely applied to individual exposures, real-world scenarios often involve complex mixtures. Such mixtures introduce unique methodological challenges, including multicollinearity, sparsity of active exposures, and potential nonlinear and interactive effects. This paper provides an overview of several commonly used approaches for mediation analysis under exposure mixture settings with clear strategies and code for implementation. The methods include: single exposure mediation analysis (SE-MA), principal component-based mediation analysis, environmental risk score-based mediation analysis, and Bayesian kernel machine regression causal mediation analysis. While SE-MA serves as a baseline that analyzes each exposure individually, the other methods are designed to address the correlation and complexity inherent in exposure mixtures. For each method, we aim to clarify the target estimand and the assumptions that each method is making to render a causal interpretation of the estimates obtained. We conduct a simulation study to systematically evaluate the operating characteristics of these four methods to estimate global indirect effects and to identify individual exposures contributing to the global mediation under varying sample sizes, effect sizes, and exposure-mediator-outcome structures. We also illustrate their real-world applicability by examining data from the PROTECT birth cohort, specifically analyzing the relationship between prenatal exposure to phthalate mixtures and neonatal head circumference Z-score, with leukotriene E4 as a mediator. This example offers practical guidance for conducting mediation analysis in complex environmental contexts.

stat.ME↗

arXiv2025

Meta-analysis of median survival times with inverse-variance weighting

We consider the problem of meta-analyzing outcome measures based on median survival times. Primary studies with time-to-event outcomes often report estimates of median survival times and confidence intervals based on the Kaplan-Meier estimator. However, outcome measures based on median survival are rarely meta-analyzed, as standard inverse-variance weighted methods require within-study standard errors that are typically not reported. In this article, we consider an inverse-variance weighted approach to meta-analyze median survival times that estimates the within-study standard errors from the reported confidence intervals. We show that this method consistently estimates the standard error of median survival when applied to confidence intervals constructed by the Brookmeyer-Crowley method. We conduct a series of simulation studies evaluating the performance of this approach at the study level (i.e., for estimating the standard error of median survival) and the meta-analytic level (i.e., for estimating the pooled median, difference of medians, and ratio of medians) for commonly used confidence intervals for median survival, including the Brookmeyer-Crowley method and nonparametric bootstrap. We find that this approach often performs comparably to a benchmark approach that uses the true within-study standard errors for meta-analyzing median-based outcome measures when within-study sample sizes are moderately large (e.g., above 50). However, when the effective sample sizes are small, the method can yield biased estimates of within-study standard errors. We illustrate an application of this approach in a meta-analysis evaluating survival benefits of being assigned to experimental arms versus comparator arms in randomized trials for non-small cell lung cancer therapies.

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arXiv2024

LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation

Low-rank matrix estimation is a fundamental problem in statistics and machine learning with applications across biomedical sciences, including genetics, medical imaging, drug discovery, and electronic health record data analysis. In the context of heterogeneous data generated from diverse sources, a key challenge lies in leveraging data from a source population to enhance the estimation of a low-rank matrix in a target population of interest. We propose an approach that leverages similarity in the latent row and column spaces between the source and target populations to improve estimation in the target population, which we refer to as LatEnt spAce-based tRaNsfer lEaRning (LEARNER). LEARNER is based on performing a low-rank approximation of the target population data which penalizes differences between the latent row and column spaces between the source and target populations. We present a cross-validation approach that allows the method to adapt to the degree of heterogeneity across populations. We conducted extensive simulations which found that LEARNER often outperforms the benchmark approach that only uses the target population data, especially as the signal-to-noise ratio in the source population increases. We also performed an illustrative application and empirical comparison of LEARNER and benchmark approaches in a re-analysis of summary statistics from a genome-wide association study in the BioBank Japan cohort. LEARNER is implemented in the R package learner and the Python package learner-py.

stat.ME↗

arXiv2024

CausalMetaR: An R package for performing causally interpretable meta-analyses

Researchers would often like to leverage data from a collection of sources (e.g., primary studies in a meta-analysis) to estimate causal effects in a target population of interest. However, traditional meta-analytic methods do not produce causally interpretable estimates for a well-defined target population. In this paper, we present the CausalMetaR R package, which implements efficient and robust methods to estimate causal effects in a given internal or external target population using multi-source data. The package includes estimators of average and subgroup treatment effects for the entire target population. To produce efficient and robust estimates of causal effects, the package implements doubly robust and non-parametric efficient estimators and supports using flexible data-adaptive (e.g., machine learning techniques) methods and cross-fitting techniques to estimate the nuisance models (e.g., the treatment model, the outcome model). We describe the key features of the package and demonstrate how to use the package through an example.

stat.ME↗

arXiv2023

When Does Uncertainty Matter?: Understanding the Impact of Predictive Uncertainty in ML Assisted Decision Making

As machine learning (ML) models are increasingly being employed to assist human decision makers, it becomes critical to provide these decision makers with relevant inputs which can help them decide if and how to incorporate model predictions into their decision making. For instance, communicating the uncertainty associated with model predictions could potentially be helpful in this regard. In this work, we carry out user studies (1,330 responses from 190 participants) to systematically assess how people with differing levels of expertise respond to different types of predictive uncertainty (i.e., posterior predictive distributions with different shapes and variances) in the context of ML assisted decision making for predicting apartment rental prices. We found that showing posterior predictive distributions led to smaller disagreements with the ML model's predictions, regardless of the shapes and variances of the posterior predictive distributions we considered, and that these effects may be sensitive to expertise in both ML and the domain. This suggests that posterior predictive distributions can potentially serve as useful decision aids which should be used with caution and take into account the type of distribution and the expertise of the human.

cs.LG↗

arXiv2023

metamedian: An R package for meta-analyzing studies reporting medians

When performing an aggregate data meta-analysis of a continuous outcome, researchers often come across primary studies that report the sample median of the outcome. However, standard meta-analytic methods typically cannot be directly applied in this setting. In recent years, there has been substantial development in statistical methods to incorporate primary studies reporting sample medians in meta-analysis, yet there are currently no comprehensive software tools implementing these methods. In this paper, we present the metamedian R package, a freely available and open-source software tool for meta-analyzing primary studies that report sample medians. We summarize the main features of the software and illustrate its application through real data examples involving risk factors for a severe course of COVID-19.

stat.ME↗

arXiv2022

Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functional

Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to estimate nuisance functions to obtain optimal rates of convergence for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. For several plug-in estimators and a first-order bias-corrected estimator, we illustrate the interplay between different tuning parameter choices for the nuisance function estimators and sample splitting strategies on the optimal rate of estimating the functional of interest. For each of these estimators and each sample splitting strategy, we show the necessity to either undersmooth or oversmooth the nuisance function estimators under low regularity conditions to obtain optimal rates of convergence for the functional of interest. Unlike the existing literature, we show that plug-in and first-order bias-corrected estimators can achieve minimax rates of convergence across all H\"older smoothness classes of the nuisance functions by careful combinations of sample splitting and nuisance function tuning strategies. We complement these results with numerical simulations illustrating the impact of different nuisance function tuning and sample splitting strategies.

math.ST↗

arXiv2022

Standard error estimation in meta-analysis of studies reporting medians

We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of the outcome and other studies report the sample median along with the first and third quartiles and/or minimum and maximum values. To perform meta-analysis in this context, a number of approaches have recently been developed to impute the sample mean and standard deviation from studies reporting medians. Then, standard meta-analytic approaches with inverse-variance weighting are applied based on the (imputed) study-specific sample means and standard deviations. In this paper, we illustrate how this common practice can severely underestimate the within-study standard errors, which results in overestimation of between-study heterogeneity in random effects meta-analyses. We propose a straightforward bootstrap approach to estimate the standard errors of the imputed sample means. Our simulation study illustrates how the proposed approach can improve estimation of the within-study standard errors and between-study heterogeneity. Moreover, we apply the proposed approach in a meta-analysis to identify risk factors of a severe course of COVID-19.

stat.ME↗

arXiv2021

Revisiting the g-null paradox

The parametric g-formula is an approach to estimating causal effects of sustained treatment strategies from observational data. An often cited limitation of the parametric g-formula is the g-null paradox: a phenomenon in which model misspecification in the parametric g-formula is guaranteed under the conditions that motivate its use (i.e., when identifiability conditions hold and measured time-varying confounders are affected by past treatment). Many users of the parametric g-formula know they must acknowledge the g-null paradox as a limitation when reporting results but still require clarity on its meaning and implications. Here we revisit the g-null paradox to clarify its role in causal inference studies. In doing so, we present analytic examples and a simulation-based illustration of the bias of parametric g-formula estimates under the conditions associated with this paradox. Our results highlight the importance of avoiding overly parsimonious models for the components of the g-formula when using this method.

stat.ME↗

arXiv2019

gfoRmula: An R package for estimating effects of general time-varying treatment interventions via the parametric g-formula

Researchers are often interested in using longitudinal data to estimate the causal effects of hypothetical time-varying treatment interventions on the mean or risk of a future outcome. Standard regression/conditioning methods for confounding control generally fail to recover causal effects when time-varying confounders are themselves affected by past treatment. In such settings, estimators derived from Robins's g-formula may recover time-varying treatment effects provided sufficient covariates are measured to control confounding by unmeasured risk factors. The package gfoRmula implements in R one such estimator: the parametric g-formula. This estimator easily adapts to binary or continuous time-varying treatments as well as contrasts defined by static or dynamic, deterministic or random treatment interventions, as well as interventions that depend on the natural value of treatment. The package accommodates survival outcomes as well as binary or continuous end of follow-up outcomes. For survival outcomes, the package has different options for handling competing events. This paper describes the gfoRmula package, along with motivating background, features, and examples.

stat.CO↗

arXiv2019

Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis

Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report the sample mean and standard deviation of the outcome. However, when the outcome is skewed, authors sometimes summarize the data by reporting the sample median and one or both of (i) the minimum and maximum values and (ii) the first and third quartiles, but do not report the mean or standard deviation. To include these studies in meta-analysis, several methods have been developed to estimate the sample mean and standard deviation from the reported summary data. A major limitation of these widely used methods is that they assume that the outcome distribution is normal, which is unlikely to be tenable for studies reporting medians. We propose two novel approaches to estimate the sample mean and standard deviation when data are suspected to be non-normal. Our simulation results and empirical assessments show that the proposed methods often perform better than the existing methods when applied to non-normal data.

stat.ME↗

arXiv2018

Two-sample aggregate data meta-analysis of medians

We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of medians. To include these studies in meta-analysis, several authors have recently proposed methods to estimate the sample mean and standard deviation from the median, sample size, and several commonly reported measures of spread. Researchers frequently apply these methods to estimate the difference of means and its variance for each primary study and pool the difference of means using inverse variance weighting. In this work, we develop several methods to directly meta-analyze the difference of medians. We conduct a simulation study evaluating the performance of the proposed median-based methods and the competing transformation-based methods. The simulation results show that the median-based methods outperform the transformation-based methods when meta-analyzing studies that report the median of the outcome, especially when the outcome is skewed. Moreover, we illustrate the various methods on a real-life data set.

stat.ME↗

arXiv2017

One-sample aggregate data meta-analysis of medians

An aggregate data meta-analysis is a statistical method that pools the summary statistics of several selected studies to estimate the outcome of interest. When considering a continuous outcome, typically each study must report the same measure of the outcome variable and its spread (e.g., the sample mean and its standard error). However, some studies may instead report the median along with various measures of spread. Recently, the task of incorporating medians in meta-analysis has been achieved by estimating the sample mean and its standard error from each study that reports a median in order to meta-analyze the means. In this paper, we propose two alternative approaches to meta-analyze data that instead rely on medians. We systematically compare these approaches via simulation study to each other and to methods that transform the study-specific medians and spread into sample means and their standard errors. We demonstrate that the proposed median-based approaches perform better than the transformation-based approaches, especially when applied to skewed data and data with high inter-study variance. In addition, when meta-analyzing data that consists of medians, we show that the median-based approaches perform considerably better than or comparably to the best-case scenario for a transformation approach: conducting a meta-analysis using the actual sample mean and standard error of the mean of each study. Finally, we illustrate these approaches in a meta-analysis of patient delay in tuberculosis diagnosis.

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