arXiv subjects

Michael R. Elliott

Publications and source records attributed to Michael R. Elliott.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian Joint Modeling of Longitudinal Symptomatology Scale Responses and Fall Outcomes via Heterogeneous Latent Transition Analysis

The Study of Women's Health Across the Nation (SWAN) has followed women for over 30 years, from midlife premenopause until later life. The study has 16 surveys at approximately 2 years intervals that cover a wide range of physical and psychological symptoms. These multivariate categorical survey responses potentially contain rich health-related information. Temporal trajectories of the survey responses can be characterized by both the responses profiles and the evolving dynamics of the responses over time. To capture those two features and investigate how they inform subsequent health outcomes, we propose a joint multi-layer latent transition model. We combine a latent transition model that classifies individuals based on their response profiles over time with an additional layer of clustering of these latent class transition sequences, with the goal of connecting these cluster profiles with health outcomes: in this application, self-reported falls. In addition, we evaluate the operating characteristics of the method through simulation studies.

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arXiv2026

Bayesian Optimal Sample Design for Surveys with Heteroscedasticity

We develop a Bayesian optimal sample allocation approach for stratified sampling in heteroscedastic populations. Existing optimal allocation theory typically assumes knowledge of certain design parameters (e.g., strata variances) that may be unknown, leading practitioners to substitute in survey-based estimates when planning samples, often without considering the effects of this substitution on sample efficiency. Bayesian decision theory for optimal experimental design avoids such substitutions and can be applied to sample allocation. Bayesian sample optimization methods were studied heavily from the mid-1960s through early 1980s, but have been overlooked since, in spite of modern computing advances that have facilitated a proliferation of Bayesian methods in other areas of statistics. A limitation of this early Bayesian sample design work is that it did not accommodate heteroscedastic error structures, which underlie commonly used ratio estimation models. Our paper, which optimizes the design under a univariate regression model with heteroscedastic errors, addresses this limitation of earlier work, while illustrating the Bayesian approach to design. We identify the optimal Bayesian allocation under our model, then compare performance of the proposed Bayesian sampling strategy with that of key design-based and model-assisted alternatives across several settings, finding that the proposed methods do as well or better than the alternatives under the scenarios considered. We apply our methods in analyzing revenues of public charities, using publicly available IRS Form 990 data.

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arXiv2026

Propensity score adjustment when errors in achievement measures inform treatment assignment

U.S. state education agencies mark schools displaying achievement gaps between demographic subgroups as needing improvement. Some schools may have few students in these subgroups, such that average end-of-year test scores only noisily measure the average "true" score-the score one would expect if students took the test many times. This, in addition to the masking of small subgroup averages in publicly available assessment data, poses challenges for evaluating interventions aimed at closing achievement gaps. We introduce propensity score estimates designed to achieve balance on subgroup average true scores. These estimates are available even when noisy measurements are not and improve overlap compared to those that ignore measurement error, leading to greater bias reduction of matching estimators. We demonstrate our methods through simulation and an application to a statewide initiative in Texas for curbing summer learning loss.

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arXiv2025

Using Subject-Level Variability to Predict Time-Varying Outcomes: Investigating the Association between Hormone Variability and BMD Trajectories over the Menopausal Transition

Women are at increased risk of bone loss during the menopausal transition; in fact, nearly 50\% of women's lifetime bone loss occurs during this time. The longitudinal relationships between estradiol (E2) and follicle-stimulating hormone (FSH), two hormones that change have characteristic changes during the menopausal transition, and bone health outcomes are complex. However, in addition to level and rate of change in E2 and FSH, variability in these hormones across the menopausal transition may be an important predictor of bone health, but this question has yet to be well explored. We introduce a joint model that characterizes individual mean estradiol (E2) trajectories and the individual residual variances and links these variances to bone health trajectories. In our application, we found that higher FSH variability was associated with declines in bone mineral density (BMD) before menopause, but this association was moderated over time after the menopausal transition. Additionally, higher mean E2, but not E2 variability, was associated with slower decreases in during the menopausal transition. We also include a simulation study that shows that naive two-stage methods often fail to propagate uncertainty in the individual-level variance estimates, resulting in estimation bias and invalid interval coverage.

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arXiv2025

Sensitivity Analysis when Generalizing Causal Effects from Multiple Studies to a Target Population: Motivation from the ECHO Program

Unobserved effect modifiers can induce bias when generalizing causal effect estimates to target populations. In this work, we extend a sensitivity analysis framework assessing the robustness of study results to unobserved effect modification that adapts to various generalizability scenarios, including multiple (conditionally) randomized trials, observational studies, or combinations thereof. This framework is interpretable and does not rely on distributional or functional assumptions about unknown parameters. We demonstrate how to leverage the multi-study setting to detect violation of the generalizability assumption through hypothesis testing, showing with simulations that the proposed test achieves high power under real-world sample sizes. Finally, we apply our sensitivity analysis framework to analyze the generalized effect estimate of secondhand smoke exposure on birth weight using cohort sites from the Environmental influences on Child Health Outcomes (ECHO) study.

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arXiv2025

Joint Modeling of Multiple Longitudinal Biomarkers and Survival Outcomes via Threshold Regression: Variability as a Predictor

Longitudinal biomarker data and health outcomes are routinely collected in many studies to assess how biomarker trajectories predict health outcomes. Existing methods primarily focus on mean biomarker profiles, treating variability as a nuisance. However, excess variability may indicate system dysregulations that may be associated with poor outcomes. In this paper, we address the long-standing problem of using variability information of multiple longitudinal biomarkers in time-to-event analyses by formulating and studying a Bayesian joint model. We first model multiple longitudinal biomarkers, some of which are subject to limit-of-detection censoring. We then model the survival times by incorporating random effects and variances from the longitudinal component as predictors through threshold regression that admits non-proportional hazards. We demonstrate the operating characteristics of the proposed joint model through simulations and apply it to data from the Study of Women's Health Across the Nation (SWAN) to investigate the impact of the mean and variability of follicle-stimulating hormone (FSH) and anti-Mullerian hormone (AMH) on age at the final menstrual period (FMP).

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arXiv2024

Investigating Mode Effects in Interviewer Variances Using Two Representative Multi-mode Surveys

This study examines whether interviewer variances remain consistent across different modes in mixed-mode studies, using data from two distinct designs. In the first design, when interviewers are responsible for either face-to-face or telephone mode, we examine whether there are mode differences in interviewer variances for 1) sensitive political questions, 2) international items, 3) and item missing indicators on international items, using the Arab Barometer wave 6 Jordan data. In the second design, we draw on Health and Retirement Study (HRS) 2016 core survey data to examine the question on three topics when interviewers are responsible for both modes. The topics cover 1) the CESD depression scale, 2) interviewer observations, and 3) the physical activity scale. To account for the lack of interpenetrated designs in both data sources, we include respondent-level covariates in our models. We find significant differences in interviewer variances on one item (twelve items in total) in the Arab Barometer study; whereas for HRS, the results are three out of eighteen. Overall, we find the magnitude of the interviewer variances larger in FTF than TEL on sensitive items. We conduct simulations to understand the power to detect mode effects in the typically modest interviewer sample sizes.

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arXiv2024

A Bayesian Approach to Modeling Variance of Intensive Longitudinal Biomarker Data as a Predictor of Health Outcomes

Intensive longitudinal biomarker data are increasingly common in scientific studies that seek temporally granular understanding of the role of behavioral and physiological factors in relation to outcomes of interest. Intensive longitudinal biomarker data, such as those obtained from wearable devices, are often obtained at a high frequency typically resulting in several hundred to thousand observations per individual measured over minutes, hours, or days. Often in longitudinal studies, the primary focus is on relating the means of biomarker trajectories to an outcome, and the variances are treated as nuisance parameters, although they may also be informative for the outcomes. In this paper, we propose a Bayesian hierarchical model to jointly model a cross-sectional outcome and the intensive longitudinal biomarkers. To model the variability of biomarkers and deal with the high intensity of data, we develop subject-level cubic B-splines and allow the sharing of information across individuals for both the residual variability and the random effects variability. Then different levels of variability are extracted and incorporated into an outcome submodel for inferential and predictive purposes. We demonstrate the utility of the proposed model via an application involving bio-monitoring of hertz-level heart rate information from a study on social stress.

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arXiv2022

Surrogacy Validation for Time-to-Event Outcomes with Illness-Death Frailty Models

A common practice in clinical trials is to evaluate a treatment effect on an intermediate endpoint when the true outcome of interest would be difficult or costly to measure. We consider how to validate intermediate endpoints in a causally-valid way when the trial outcomes are time-to-event. Using counterfactual outcomes, those that would be observed if the counterfactual treatment had been given, the causal association paradigm assesses the relationship of the treatment effect on the surrogate $S$ with the treatment effect on the true endpoint $T$. In particular, we propose illness death models to accommodate the censored and semi-competing risk structure of survival data. The proposed causal version of these models involves estimable and counterfactual frailty terms. Via these multi-state models, we characterize what a valid surrogate would look like using a causal effect predictiveness plot. We evaluate the estimation properties of a Bayesian method using Markov Chain Monte Carlo and assess the sensitivity of our model assumptions. Our motivating data source is a localized prostate cancer clinical trial where the two survival endpoints are time to distant metastasis and time to death.

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arXiv2022

Variance as a predictor of health outcomes: Subject-level trajectories and variability of sex hormones to predict body fat changes in peri- and post-menopausal women

Longitudinal biomarker data and cross-sectional outcomes are routinely collected in modern epidemiology studies, often with the goal of informing tailored early intervention decisions. For example, hormones such as estradiol and follicle-stimulating hormone may predict changes in womens' health during the midlife. Most existing methods focus on constructing predictors from mean marker trajectories. However, subject-level biomarker variability may also provide critical information about disease risks and health outcomes. In this paper, we develop a joint model that estimates subject-level means and variances of longitudinal biomarkers to predict a cross-sectional health outcome. Simulations demonstrate excellent recovery of true model parameters. The proposed method provides less biased and more efficient estimates, relative to alternative approaches that either ignore subject-level differences in variances or perform two-stage estimation where estimated marker variances are treated as observed. Analyses of women's health data reveal larger variability of E2 or larger variability of FSH were associated with higher levels of fat mass change and higher levels of lean mass change across the menopausal transition.

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arXiv2022

Robust Model-based Inference for Non-Probability Samples

With the ubiquitous availability of unstructured data, growing attention is paid as how to adjust for selection bias in such non-probability samples. The majority of the robust estimators proposed by prior literature are either fully or partially design-based, which may lead to inefficient estimates if outlying (pseudo-)weights are present. In addition, correctly reflecting the uncertainty of the adjusted estimator remains a challenge when the available reference survey is complex in the sample design. This article proposes a fully model-based method for inference using non-probability samples where the goal is to predict the outcome variable for the entire population units. We employ a Bayesian bootstrap method with Rubin's combing rules to derive the adjusted point and interval estimates. Using Gaussian process regression, our method allows for kernel matching between the non-probability sample units and population units based on the estimated selection propensities when the outcome model is misspecified. The repeated sampling properties of our method are evaluated through two Monte Carlo simulation studies. Finally, we examine it on a real-world non-probability sample with the aim to estimate crash-attributed injury rates in different body regions in the United States.

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arXiv2022

Robust and Efficient Bayesian Inference for Non-Probability Samples

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian outcomes and may perform poorly in presence of influential pseudo-weights. Furthermore, their variance estimator lacks a unified framework and rely often on asymptotic theory. To address these gaps, we propose an alternative Bayesian approach using a partially linear Gaussian process regression that utilizes a prediction model with a flexible function of the pseudo-inclusion probabilities to impute the outcome variable for the reference survey. By efficiency, we mean not only computational scalability but also superiority with respect to variance. We also show that Gaussian process regression behaves as a kernel matching technique based on the estimated propensity scores, which yields double robustness and lowers sensitivity to influential pseudo-weights. Using the simulated posterior predictive distribution, one can directly quantify the uncertainty of the proposed estimator and derive associated $95\%$ credible intervals. We assess the repeated sampling properties of our method in two simulation studies. The application of this study deals with modeling count data with varying exposures under a non-probability sample setting.

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arXiv2022

Robust Bayesian Inference for Big Data: Combining Sensor-based Records with Traditional Survey Data

Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches assume that the conditional mean structures have been correctly specified for the selection indicator or key substantive measures. In the presence of a reference probability sample, these methods rely on a pseudo-likelihood method to account for the sampling weights of the reference sample, which is parametric in nature. Under a Bayesian framework, handling the sampling weights is an even bigger hurdle. To further protect against model misspecification, we expand the idea of double robustness such that more flexible non-parametric methods, as well as Bayesian models, can be used for prediction. In particular, we employ Bayesian additive regression trees, which not only capture non-linear associations automatically but permit direct quantification of the uncertainty of point estimates through its posterior predictive draws. We apply our method to sensor-based naturalistic driving data from the second Strategic Highway Research Program using the 2017 National Household Travel Survey as a benchmark.

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arXiv2021

Deriving Priors for Bayesian Prediction of Daily Response Propensity in Responsive Survey Design: Historical Data Analysis vs. Literature Review

Responsive Survey Design (RSD) aims to increase the efficiency of survey data collection via live monitoring of paradata and the introduction of protocol changes when survey errors and increased costs seem imminent. Daily predictions of response propensity for all active sampled cases are among the most important quantities for live monitoring of data collection outcomes, making sound predictions of these propensities essential for the success of RSD. Because it relies on real-time updates of prior beliefs about key design quantities, such as predicted response propensities, RSD stands to benefit from Bayesian approaches. However, empirical evidence of the merits of these approaches is lacking in the literature, and the derivation of informative prior distributions is required for these approaches to be effective. In this paper, we evaluate the ability of two approaches to deriving prior distributions for the coefficients defining daily response propensity models to improve predictions of daily response propensity in a real data collection employing RSD. The first approach involves analyses of historical data from the same survey, and the second approach involves literature review. We find that Bayesian methods based on these two approaches result in higher-quality predictions of response propensity than more standard approaches ignoring prior information. This is especially true during the early-to-middle periods of data collection when interventions are often considered in an RSD framework.

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arXiv2020

Using Multiple Imputation to Classify Potential Outcomes Subgroups

With medical tests becoming increasingly available, concerns about over-testing and over-treatment dramatically increase. Hence, it is important to understand the influence of testing on treatment selection in general practice. Most statistical methods focus on average effects of testing on treatment decisions. However, this may be ill-advised, particularly for patient subgroups that tend not to benefit from such tests. Furthermore, missing data are common, representing large and often unaddressed threats to the validity of statistical methods. Finally, it is desirable to conduct analyses that can be interpreted causally. We propose to classify patients into four potential outcomes subgroups, defined by whether or not a patient's treatment selection is changed by the test result and by the direction of how the test result changes treatment selection. This subgroup classification naturally captures the differential influence of medical testing on treatment selections for different patients, which can suggest targets to improve the utilization of medical tests. We can then examine patient characteristics associated with patient potential outcomes subgroup memberships. We used multiple imputation methods to simultaneously impute the missing potential outcomes as well as regular missing values. This approach can also provide estimates of many traditional causal quantities. We find that explicitly incorporating causal inference assumptions into the multiple imputation process can improve the precision for some causal estimates of interest. We also find that bias can occur when the potential outcomes conditional independence assumption is violated; sensitivity analyses are proposed to assess the impact of this violation. We applied the proposed methods to examine the influence of 21-gene assay, the most commonly used genomic test, on chemotherapy selection among breast cancer patients.

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arXiv2018

Accounting for selection bias due to death in estimating the effect of wealth shock on cognition for the Health and Retirement Study

The Health and Retirement Study is a longitudinal study of US adults enrolled at age 50 and older. We were interested in investigating the effect of a sudden large decline in wealth on the cognitive score of subjects. Our analysis was complicated by the lack of randomization, confounding by indication, and a substantial fraction of the sample and population will die during follow-up leading to some of our outcomes being censored. Common methods to handle these problems for example marginal structural models, may not be appropriate because it upweights subjects who are more likely to die to obtain a population that over time resembles that would have been obtained in the absence of death. We propose a refined approach by comparing the treatment effect among subjects who would survive under both sets of treatment regimes being considered. We do so by viewing this as a large missing data problem and impute the survival status and outcomes of the counterfactual. To improve the robustness of our imputation, we used a modified version of the penalized spline of propensity methods in treatment comparisons approach. We found that our proposed method worked well in various simulation scenarios and our data analysis.

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arXiv2018

P-splines with an l1 penalty for repeated measures

P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for within-subject variability. In addition to $\ell_2$ penalties, $\ell_1$-type penalties have been used in nonparametric and semiparametric regression to achieve greater flexibility, such as in locally adaptive regression splines, $\ell_1$ trend filtering, and the fused lasso additive model. However, there has been less focus on using $\ell_1$ penalties in P-splines, particularly for estimating conditional means. In this paper, we demonstrate the potential benefits of using an $\ell_1$ penalty in P-splines with an emphasis on fitting non-smooth functions. We propose an estimation procedure using the alternating direction method of multipliers and cross validation, and provide degrees of freedom and approximate confidence bands based on a ridge approximation to the $\ell_1$ penalized fit. We also demonstrate potential uses through simulations and an application to electrodermal activity data collected as part of a stress study.

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arXiv2018

"Robust-squared" Imputation Models Using BART

Examples of "doubly robust" estimator for missing data include augmented inverse probability weighting (AIPWT) models (Robins et al., 1994) and penalized splines of propensity prediction (PSPP) models (Zhang and Little, 2009). Doubly-robust estimators have the property that, if either the response propensity or the mean is modeled correctly, a consistent estimator of the population mean is obtained. However, doubly-robust estimators can perform poorly when modest misspecification is present in both models (Kang and Schafer, 2007). Here we consider extensions of the AIPWT and PSPP models that use Bayesian Additive Regression Trees (BART; Chipman et al., 2010) to provide highly robust propensity and mean model estimation. We term these "robust-squared" in the sense that the propensity score, the means, or both can be estimated with minimal model misspecification, and applied to the doubly-robust estimator. We consider their behavior via simulations where propensities and/or mean models are misspecified. We apply our proposed method to impute missing instantaneous velocity (delta-v) values from the 2014 National Automotive Sampling System Crashworthiness Data System dataset and missing Blood Alcohol Concentration values from the 2015 Fatality Analysis Reporting System dataset. We found that BART applied to PSPP and AIPWT, provides a more robust and efficient estimate compared to PSPP and AIPWT, with the BART-estimated propensity score combined with PSPP providing the most efficient estimator with close to nominal coverage.

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