arXiv subjects

Erica E. M. Moodie

Publications and source records attributed to Erica E. M. Moodie.

At least 19 recordsLinked to original sources

arXiv2026

A Bayesian framework for multilevel data under model mis-specification

We propose a Bayesian framework for uncertainty quantification from the perspective that the working model is mis-specified in settings of a multilevel data-generating process. We focus on settings in which the mis-specification fails to match the functional form of the mean structure, and discuss Bayesian estimation of target parameters under dependence induced by a mismatch between working and data-generating models. The proposal represents a Bayesian semi-parametric procedure aimed at estimating population-level parameters while accounting for cluster- and unit-level variation in the estimating function. The proposal extends the regular Bayesian bootstrap to account for cluster- and unit-level variation using multilevel weights from an enriched Dirichlet model. Simulation studies indicate that the proposed approach has good frequentist properties when the data-generating process and the proposed model induce a partially exchangeable sequence associated with the unknown quantity of interest. Applications to radon (Gelman and Hill, 2007), Programme for International Student Assessment 2022 (OECD, 2023), and tuberculosis (Nobre et al., 2023) datasets are presented for illustrative purposes. The results demonstrate that the proposed method is competitive with variations of multilevel models, with major differences observed in the range of credible intervals, which are justified by the nonparametric assumptions underlying the proposed method.

stat.ME↗

arXiv2026

Kernel weighted importance sampling for off-policy evaluation in contextual bandits

This article presents a novel estimator for performing off-policy evaluation using only offline data for contextual bandits. The proposed estimator, Kernel-WIS is demonstrated to be asymptotically consistent and to empirically outperform strong baselines (including weighted importance sampling), particularly under behaviour policy miss-specification. The benefit of Kernel-WIS is derived from combining the bounded property of weighted importance sampling with the linearity of vanilla importance sampling.

cs.LG↗

arXiv2026

Framing Causal Questions in Sports Analytics: A Tutorial on Estimand Choice Illustrated Through Crossing in Soccer

Causal inference has become an accepted analytic framework in sports analytics, where experimentation is rarely feasible. A key consideration is the choice of estimand, specifically, whether to target the Average Treatment Effect (ATE), which reflects the effect of an action across the entire population, or the Average Treatment Effect on the Treated (ATT), which reflects the effect among those who actually took the action. Using data from nearly all 240 matches of the 2019 Chinese Super League season, we apply propensity score matching to estimate the causal effect of crossing on shot creation in soccer. The ATE and ATT are nearly identical (0.033 and 0.035 respectively), a result we attribute to substantial overlap in propensity score distributions between plays where a cross was and was not attempted. To illustrate when these estimands diverge, we construct two simulation scenarios with known ground truth: one reproducing the high-overlap structure of the real data, where ATE and ATT coincide, and one engineered to exhibit severe confounding and low overlap, where they diverge substantially. While empirical findings are specific to the 2019 Chinese Super League season, the case study and simulations provide a principled guide to estimand choice in causal analyses of sports data.

stat.AP↗

arXiv2026

Simulation-based Power Analysis for Sequential Multiple Assignment Randomized Trials

Sequential Multiple Assignment Randomized Trials (SMARTs) provide evidence for treatment sequences based on patient profiles, which is relevant in chronic disease settings. Sample size formulae implemented in calculators are the primary tool available to power SMARTs, though they require strong assumptions. We propose a simulation-based procedure omitting these assumptions, instead generating realistic synthetic SMART data by fitting models to real pilot data, to power SMARTs to compare treatment strategies. The proposed framework powers designs in two ways: by fixing the data generating mechanism and estimating effect size under different designs, or by fixing effect size and varying operational decisions within the SMART. Comparing our results to a calculator (SMARTsize), estimated sample sizes at varying power levels were similar at larger fixed effect sizes, whereas a discrepancy was apparent at smaller effect sizes due to differences between fixed and observed effect sizes in the simulated trials. The simulation-based procedure's ability to capture this effect size fluctuation is advantageous for smaller expected effect sizes, as it is essential to ensure adequate sample size to avoid a type II error. In providing flexible tools to power competing SMART designs, the full potential of SMARTs to build treatment sequences can be better realized.

stat.OT↗

arXiv2026

Inference on summaries of a model-agnostic longitudinal variable importance trajectory with application to suicide prevention

Risk of suicide attempt varies over time. Understanding the importance of risk factors measured at a mental health visit can help clinicians evaluate future risk and provide appropriate care during the visit. In prediction settings where data are collected over time, such as in mental health care, it is often of interest to understand both the importance of variables for predicting the response at each time point and the importance summarized over the time series. Building on recent advances in estimation and inference for variable importance measures, we define summaries of variable importance trajectories and corresponding estimators. The same approaches for inference can be applied to these measures regardless of the choice of the algorithm(s) used to estimate the prediction function. We propose a nonparametric efficient estimation and inference procedure as well as a null hypothesis testing procedure that are valid even when complex machine learning tools are used for prediction. Through simulations, we demonstrate that our proposed procedures have good operating characteristics. We use these approaches to analyze electronic health records data from two large health systems to investigate the longitudinal importance of risk factors for suicide attempt to inform future suicide prevention research and clinical workflow.

stat.ME↗

arXiv2026

Semi- and non-parametric approaches to individualized treatment regimes in the presence of causal mediation

Individualized treatment rules (ITRs) map an individual patient's characteristics to their recommended treatment value. Typically, the optimal ITR is defined as the rule which maximizes a mean counterfactual outcome; the resulting ITR maximizes the effect of treatment along all causal pathways to the outcome, including indirect pathways through mediating variables. Although maximizing the total effect is often sufficient, explicitly incorporating causal mediation in an ITR analysis has several potential benefits such as enhanced interpretability, and additional flexibility in targeting specific causal pathways. For this purpose, we introduce novel Bayesian semiparametric and nonparametric estimators for conditional mediation effects in the presence of multiple mediators and show how they can be used to estimate optimal ITRs. We demonstrate the proposed methodology via an application to optimal kidney allocation with hepatitis C positive donors.

stat.ME↗

arXiv2026

A Bayesian adaptive enrichment design using aggregate historical data to inform individualized treatment recommendations

Adaptive enrichment trials aim to identify and recruit participants most likely to benefit from treatment based on evolving biomarker evidence, with the goal of informing individualized treatment recommendations. Bayesian methods are well suited to these designs because they allow external information to be incorporated in a principled manner. In practice, prior studies often provide only summary-level information, with subgroup-specific estimates unavailable due to design or privacy constraints. Existing dynamic borrowing approaches therefore rely on aggregate measures, such as the average treatment effect, and implicitly assume that historical information maps directly onto model parameters. In adaptive enrichment settings aimed at identifying individualized treatment effects, however, subgroup-specific treatment parameters are not identifiable when only marginal historical effects are available. To address this gap, we propose a Bayesian adaptive enrichment design that borrows information from external studies using a normalized power prior anchored on one or more summary measures, such as the average treatment effect. { To our knowledge, no existing method addresses this gap.} Interim analyses use posterior probabilities to guide early stopping for efficacy or futility, or to continue recruitment within promising biomarker-defined subgroups. Simulation studies evaluate operating characteristics across historical bias, sample size, and prior informativeness. Together with a motivating future trial in obstructive sleep apnea, the results show efficiency gains versus non-borrowing designs, including improved power, earlier stopping, and reduced expected sample size.

stat.ME↗

arXiv2026

Information Borrowing from Partially Compatible Trajectories for Estimation of Dynamic Treatment Regimes

Dynamic Treatment Regimes (DTRs) provide a systematic framework for optimizing sequential decision-making in chronic disease management, where therapies must adapt to patients' evolving clinical profiles. Inverse probability weighting (IPW) is a cornerstone methodology for estimating regime values from observational data due to its intuitive formulation and established theoretical properties, yet standard IPW estimators face significant limitations, including variance instability and data inefficiency. A fundamental but underexplored source of inefficiency lies in the strict alignment requirement between observed and target treatment trajectories, which fails to account for partial compatibility and discards substantial information from individuals with only minimal deviations from the regime. We propose two novel methodologies that relax the strict inclusion rule through flexible compatibility mechanisms. Both methods provide computationally tractable alternatives that can be easily integrated into existing IPW workflows, offering more efficient approaches to DTR estimation. Theoretical analysis demonstrates that both estimators preserve consistency while achieving superior finite-sample efficiency compared to standard IPW, and comprehensive simulation studies confirm improved stability. We illustrate the practical utility of our methods through an application to HIV treatment data from the AIDS Clinical Trials Group Study 175 (ACTG175).

stat.ME↗

arXiv2026

Near-Equivalent Q-learning Policies for Dynamic Treatment Regimes

Precision medicine aims to tailor therapeutic decisions to individual patient characteristics. This objective is commonly formalized through dynamic treatment regimes, which use statistical and machine learning methods to derive sequential decision rules adapted to evolving clinical information. In most existing formulations, these approaches produce a single optimal treatment at each stage, leading to a unique decision sequence. However, in many clinical settings, several treatment options may yield similar expected outcomes, and focusing on a single optimal policy may conceal meaningful alternatives. We extend the Q-learning framework for retrospective data by introducing a worst-value tolerance criterion controlled by a hyperparameter $\varepsilon$, which specifies the maximum acceptable deviation from the optimal expected value. Rather than identifying a single optimal policy, the proposed approach constructs sets of $\varepsilon$-optimal policies whose performance remains within a controlled neighborhood of the optimum. This formulation shifts Q-learning from a vector-valued representation to a matrix-valued one, allowing multiple admissible value functions to coexist during backward recursion. The approach yields families of near-equivalent treatment strategies and explicitly identifies regions of treatment indifference where several decisions achieve comparable outcomes. We illustrate the framework in two settings: a single-stage problem highlighting indifference regions around the decision boundary, and a multi-stage decision process based on a simulated oncology model describing tumor size and treatment toxicity dynamics.

stat.ML↗

arXiv2026

Doubly-Robust Bayesian Estimation of Optimal Individualized Treatment Rules using Network Meta-Analysis

An optimal individualized treatment rule (ITR) is a function that takes a patient's characteristics, such as demographics, biomarkers, and treatment history, and outputs a treatment that is expected to give the best outcome for that patient. Major Depressive Disorder (MDD) is a common and disabling mental health condition for which an optimal ITR is of interest. Unfortunately, the power to detect treatment-covariate interactions in individual studies of MDD treatments is low. Additionally, all treatments of interest are not compared head-to-head in a single study. Network meta-analysis (NMA) is a method of synthesizing data from multiple studies to estimate the relative effects of a set of treatments. Recently, two-stage ITR NMA was proposed as a method to estimate ITRs that has the potential to improve power and simultaneously consider all relevant treatment options. In the first stage, study-specific ITRs are estimated, and in the second stage, they are pooled using a Bayesian NMA model. The existing approach is vulnerable to model misspecification and fails to address missing outcomes, which occur in the MDD data. We overcome these challenges by proposing Bayesian Bootstrap dynamic Weighted Ordinary Least Squares (BBdWOLS), a doubly-robust approach to ITR estimation that accounts for missing at random outcomes and naturally quantifies the uncertainty in estimation. We also propose an improvement to the NMA model that incorporates the full variance-covariance matrix of study-specific estimates. In a simulation study, we show that our fully Bayesian ITR NMA method is more robust and efficient than the existing approach. We apply our method to the motivating dataset consisting of three studies of pharmacological treatments for MDD, and explore how ITR NMA results can support personalized decision making in this context.

stat.ME↗

arXiv2026

Personalized Treatment Hierarchies in Bayesian Network Meta-Analysis

Network Meta-Analysis (NMA) is an increasingly popular evidence synthesis tool that can provide a ranking of competing treatments, also known as a treatment hierarchy. Treatment-Covariate Interactions (TCIs) can be included in NMA models to allow relative treatment effects to vary with covariate values. We show that in an NMA model that includes TCIs, treatment hierarchies should be created with a particular covariate profile in mind. We outline the typical approach for creating a treatment hierarchy in standard Bayesian NMA and show how a treatment hierarchy for a particular covariate profile can be created from an NMA model that estimates TCIs. We demonstrate our methods using a real network of studies for treatments of major depressive disorder.

stat.ME↗

arXiv2025

Incorporating Missingness in a Framework for Generating Realistic Synthetic Randomized Controlled Trial Data

The current literature regarding generation of complex, realistic synthetic tabular data, particularly for randomized controlled trials (RCTs), often ignores missing data. However, missing data are common in RCT data and often are not Missing Completely At Random. We bridge the gap of determining how best to generate realistic synthetic data while also accounting for the missingness mechanism. We demonstrate how to generate synthetic missing values while ensuring that synthetic data mimic the targeted real data distribution. We propose and empirically compare several data generation frameworks utilizing various strategies for handling missing data (complete case, inverse probability weighting, and multiple imputation) by quantifying generation performance through a range of metrics. Focusing on the Missing At Random setting, we find that incorporating additional models to account for the missingness always outperformed a complete case approach.

stat.OT↗

arXiv2025

Individualized treatment regimens under correlated data with multiple outcomes

Precision medicine involves developing individualized treatment regimes (ITRs) which allow for treatment decisions to be tailored to patient characteristics. Naturally, the identification of the optimal regime, that is, the rule which maximizes patient outcomes, is of interest. Several procedures for estimating optimal ITRs from observational data have been proposed; however, relatively few methods exist for estimating optimal ITRs in the presence of competing risks. Previous approaches either target one particular cause of failure, or rely on singly-robust estimators. We propose a novel doubly-robust regression-based method for estimating optimal ITRs which accounts for the uncertainty related to the unobserved cause of failure by averaging over all possible causes, or targeting the most likely cause. Our approach is straightforward to implement, and we demonstrate an extension to incorporate clustering, motivated by the question of for whom kidney transplantation with hepatitis C virus (HCV)-positive donors is safe, using data from the Organ Procurement and Transplantation Network. Our analysis suggests that a large portion of HCV-negative kidney recipients would see their overall survival unchanged if they were instead provided a kidney from an HCV-positive donor. The estimated treatment rules could be used to provide more efficient allocation of HCV-positive kidneys, increasing the donor pool.

stat.ME↗

arXiv2025

A Precision Trial Case Study for Heterogeneous Treatment Effects in Obstructive Sleep Apnea

Precision medicine tailors treatments to individual patient characteristics, which is especially valuable for conditions like obstructive sleep apnea (OSA), where treatment responses vary widely. Traditional trials often overlook subgroup differences, leading to suboptimal recommendations. Current approaches rely on pre-specified thresholds with inherent uncertainty, assuming these thresholds are correct-a flawed assumption. This case study compares pre-specified thresholds to two advanced Bayesian methods: the established FK-BMA method and its novel variant, FK. The FK approach retains the flexibility of free-knot splines but omits variable selection, providing stable, interpretable models. Using biomarker data from large studies, this design identifies subgroups dynamically, allowing early trial termination or enrollment adjustments. Simulations in this specific context show FK improves precision, efficiency, and subgroup detection, offering practical benefits over FK-BMA and advancing precision medicine for OSA.

stat.AP↗

arXiv2025

fkbma: An R Package for Detecting Tailoring Variables with Free-Knot B-Splines and Bayesian Model Averaging

Precision medicine aims to optimize treatment by identifying patient subgroups most likely to benefit from specific interventions. To support this goal, we introduce fkbma, an R package that implements a Bayesian model averaging approach with free-knot B-splines for identifying tailoring variables. The package employs a reversible jump Markov chain Monte Carlo algorithm to flexibly model treatment effect heterogeneity while accounting for uncertainty in both variable selection and non-linear relationships. fkbma provides a comprehensive framework for detecting predictive biomarkers, integrating Bayesian adaptive enrichment strategies, and enabling robust subgroup identification in clinical trials and observational studies. This paper details the statistical methodology underlying fkbma, outlines its computational implementation, and demonstrates its application through simulations and real-world examples. The package's flexibility makes it a valuable tool for precision medicine research, offering a principled approach to treatment personalization.

stat.ME↗

arXiv2025

A Framework for Generating Realistic Synthetic Tabular Data in a Randomized Controlled Trial Setting

Generation of realistic synthetic data has garnered considerable attention in recent years, particularly in the health research domain due to its utility in, for instance, sharing data while protecting patient privacy or determining optimal clinical trial design. While much work has been concentrated on synthetic image generation, generation of realistic and complex synthetic tabular data of the type most commonly encountered in classic epidemiological or clinical studies is still lacking, especially with regards to generating data for randomized controlled trials (RTCs). There is no consensus regarding the best way to generate synthetic tabular RCT data such that the underlying multivariate data distribution is preserved. Motivated by an RCT in the treatment of Human Immunodeficiency Virus, we empirically compared the ability of several strategies and two generation techniques (one machine learning, the other a more classical statistical method) to faithfully reproduce realistic data. Our results suggest that using a sequential generation approach with a R-vine copula model to generate baseline variables, followed by a simple random treatment allocation to mimic the RCT setting, and subsequent regression models for variables post-treatment allocation (such as the trial outcome) is the most effective way to generate synthetic tabular RCT data that capture important and realistic features of the real data.

stat.OT↗

arXiv2024

Plasmode simulation for the evaluation of causal inference methods in homophilous social networks

Typical simulation approaches for evaluating the performance of statistical methods on populations embedded in social networks may fail to capture important features of real-world networks. It can therefore be unclear whether inference methods for causal effects due to interference that have been shown to perform well in such synthetic networks are applicable to social networks which arise in the real world. Plasmode simulation studies use a real dataset created from natural processes, but with part of the data-generation mechanism known. However, given the sensitivity of relational data, many network data are protected from unauthorized access or disclosure. In such case, plasmode simulations cannot use released versions of real datasets which often omit the network links, and instead can only rely on parameters estimated from them. A statistical framework for creating replicated simulation datasets from private social network data is developed and validated. The approach consists of simulating from a parametric exponential family random graph model fitted to the network data and resampling from the observed exposure and covariate distributions to preserve the associations among these variables.

stat.CO↗

arXiv2024

Sparse two-stage Bayesian meta-analysis for individualized treatments

Individualized treatment rules tailor treatments to patients based on clinical, demographic, and other characteristics. Estimation of individualized treatment rules requires the identification of individuals who benefit most from the particular treatments and thus the detection of variability in treatment effects. To develop an effective individualized treatment rule, data from multisite studies may be required due to the low power provided by smaller datasets for detecting the often small treatment-covariate interactions. However, sharing of individual-level data is sometimes constrained. Furthermore, sparsity may arise in two senses: different data sites may recruit from different populations, making it infeasible to estimate identical models or all parameters of interest at all sites, and the number of non-zero parameters in the model for the treatment rule may be small. To address these issues, we adopt a two-stage Bayesian meta-analysis approach to estimate individualized treatment rules which optimize expected patient outcomes using multisite data without disclosing individual-level data beyond the sites. Simulation results demonstrate that our approach can provide consistent estimates of the parameters which fully characterize the optimal individualized treatment rule. We estimate the optimal Warfarin dose strategy using data from the International Warfarin Pharmacogenetics Consortium, where data sparsity and small treatment-covariate interaction effects pose additional statistical challenges.

stat.ME↗