arXiv subjects

Ziren Jiang

Publications and source records attributed to Ziren Jiang.

7 recordsLinked to original sources

arXiv2026

BAMIFun: Bayesian Multiple Imputation for Functional Data

Missing data are pervasive in modern functional datasets, where trajectories are often sparsely or irregularly observed. Although Functional Principal Component Analysis (FPCA) is widely used to reconstruct incomplete curves, existing approaches typically employ single imputation, leading to overly optimistic inferences in downstream analyses. To address these challenges, we develop a novel Bayesian multiple imputation framework for functional data (BAMIFun). For single-level functional data, we impose a Bayesian low-rank model that incorporates penalized spline representations to enforce smoothness of the functional domain and derive an efficient Gibbs sampler algorithm for posterior computation. In addition, we demonstrate and validate how to properly account for estimation uncertainties in downstream analysis. Furthermore, we extend the framework to multiway functional data using Functional Tensor Singular Value Decomposition (FTSVD) model, enabling Bayesian multiple imputation in settings not supported by existing methods. Simulation studies show that BAMIFun achieves substantially improved coverage and more reliable downstream inference compared to existing methods, while maintaining similar imputation accuracy. Case studies using a physical activity dataset and an infant gut microbiome dataset further demonstrate the practical advantages of our proposed methods under severe missingness. The code is available at https://github.com/ZirenJiang/BAMIFun.

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arXiv2026

Heterogeneous readmission prediction with hierarchical effect decomposition and regularization

Accurately predicting hospital readmission risks using electronic health records (EHRs) is critical for effective patient management and healthcare resource allocation. Patient populations in health systems are highly heterogeneous across different primary diagnoses, necessitating tailored yet interpretable prediction models. We propose a hierarchical modeling framework incorporating hierarchical nested re-parameterization and structured regularization methods, which we call hierNest. Specifically, our approach leverages the inherent hierarchical structure present in primary diagnoses and groupings of these diagnoses into major diagnostic categories. Our methodology facilitates information borrowing across related patient subgroups and preserves interpretability at different hierarchical levels. Simulation studies demonstrate superior predictive accuracy of the proposed method, particularly with small subgroup sample sizes and varying degrees of hierarchical effects. We apply our methods to a large EHR dataset comprising Medicare patients.

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arXiv2026

Tutorial on Bayesian Functional Regression Using Stan

This manuscript provides step-by-step instructions for implementing Bayesian functional regression models using Stan. Extensive simulations indicate that the inferential performance of the methods is comparable to that of state-of-the-art frequentist approaches. However, Bayesian approaches allow for more flexible modeling and provide an alternative when frequentist methods are not available or may require additional development. Methods and software are illustrated using the accelerometry data from the National Health and Nutrition Examination Survey (NHANES).

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arXiv2026

Estimating causal effects of functional treatments with modified functional treatment policies

Functional data are increasingly prevalent in biomedical research. While functional data analysis has been established for decades, causal inference with functional treatments remains largely unexplored. Existing methods typically focus on estimating the causal average dose response functional (ADRF), which requires strong positivity assumptions and offers limited interpretability. In this work, we target a new causal estimand, the modified functional treatment policy (MFTP), which focuses on estimating the average potential outcome when each individual slightly modifies their treatment trajectory from the observed one. A major challenge for this new estimand is the need to define an average over an infinite-dimensional object with no density. By proposing a novel definition of the population average over a functional variable using a functional principal component analysis (FPCA) decomposition, we establish the causal identifiability of the MFTP estimand. We further derive outcome regression, inverse probability weighting, and doubly robust estimators for the MFTP, and provide theoretical guarantees under mild regularity conditions. The proposed estimators are validated through extensive simulation studies. Applying our MFTP framework to the National Health and Nutrition Examination Survey (NHANES) accelerometer data, we estimate the causal effects of reducing disruptive nighttime activity and low-activity duration on all-cause mortality.

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arXiv2025

Exploring the effects of mechanical ventilator settings with modified vector-valued treatment policies

Mechanical ventilation is critical for managing respiratory failure, but inappropriate ventilator settings can lead to ventilator-induced lung injury (VILI), increasing patient morbidity and mortality. Evaluating the causal impact of ventilator settings is challenging due to the complex interplay of multiple treatment variables and strong confounding due to ventilator guidelines. In this paper, we propose a modified vector-valued treatment policy (MVTP) framework coupled with energy balancing weights to estimate causal effects involving multiple continuous ventilator parameters simultaneously in addition to sensitivity analysis to unmeasured confounding. Our approach mitigates common challenges in causal inference for vector-valued treatments, such as infeasible treatment combinations, stringent positivity assumptions, and interpretability concerns. Using the MIMIC-III database, our analyses suggest that equal reductions in the total power of ventilation (i.e., the mechanical power) through different ventilator parameters result in different expected patient outcomes. Specifically, lowering airway pressures may yield greater reductions in patient mortality compared to proportional adjustments of tidal volume alone. Moreover, controlling for respiratory-system compliance and minute ventilation, we found a significant benefit of reducing driving pressure in patients with acute respiratory distress syndrome (ARDS). Our analyses help shed light on the contributors to VILI.

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arXiv2025

Modified treatment policy effect estimation with weighted energy distance

The causal effects of continuous treatments are often characterized through the average dose response function, which is challenging to estimate from observational data due to confounding and positivity violations. Modified treatment policies (MTPs) are an alternative approach that aim to assess the effect of a modification to observed treatment values and work under relaxed assumptions. Estimators for MTPs generally focus on estimating the conditional density of treatment given covariates and using it to construct weights. However, weighting using conditional density models has well-documented challenges. Further, MTPs with larger treatment modifications have stronger confounding and no tools exist to help choose an appropriate modification magnitude. This paper investigates the role of weights for MTPs showing that to control confounding, weights should balance the weighted data to an unobserved hypothetical target population that can be characterized with observed data. Leveraging this insight, we present a versatile set of tools to enhance estimation for MTPs. We introduce a distance that measures imbalance of covariate distributions under the MTP and use it to develop new weighting methods and tools to aid in the estimation of MTPs. Using our methods we study the effect of mechanical power of ventilation on in-hospital mortality.

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arXiv2024

BAMITA: Bayesian Multiple Imputation for Tensor Arrays

Data increasingly take the form of a multi-way array, or tensor, in several biomedical domains. Such tensors are often incompletely observed. For example, we are motivated by longitudinal microbiome studies in which several timepoints are missing for several subjects. There is a growing literature on missing data imputation for tensors. However, existing methods give a point estimate for missing values without capturing uncertainty. We propose a multiple imputation approach for tensors in a flexible Bayesian framework, that yields realistic simulated values for missing entries and can propagate uncertainty through subsequent analyses. Our model uses efficient and widely applicable conjugate priors for a CANDECOMP/PARAFAC (CP) factorization, with a separable residual covariance structure. This approach is shown to perform well with respect to both imputation accuracy and uncertainty calibration, for scenarios in which either single entries or entire fibers of the tensor are missing. For two microbiome applications, it is shown to accurately capture uncertainty in the full microbiome profile at missing timepoints and used to infer trends in species diversity for the population. Documented R code to perform our multiple imputation approach is available at https://github.com/lockEF/MultiwayImputation .

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