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Lance A. Waller

Publications and source records attributed to Lance A. Waller.

17 recordsLinked to original sources
arXiv2025

Inverse sampling intensity weighting for preferential sampling adjustment

Traditional geostatistical methods assume independence between observation locations and the spatial process of interest. Violations of this independence assumption are referred to as preferential sampling (PS). Standard methods to address PS rely on estimating complex shared latent variable models and can be difficult to apply in practice. We study the use of inverse sampling intensity weighting (ISIW) for PS adjustment in model-based geostatistics. ISIW is a two-stage approach wherein we estimate the sampling intensity of the observation locations then define intensity-based weights within a weighted likelihood adjustment. Prediction follows by substituting the adjusted parameter estimates within kriging. We introduce an implementation of ISIW based on the Vecchia approximation, enabling computational gains while maintaining strong predictive accuracy. Interestingly, we found that ISIW outpredicts standard PS methods under misspecification of the sampling design, and that accurate parameter estimation had little correlation with predictive performance, raising questions about the conditions driving optimal implementation of kriging-based predictors under PS. Our work highlights the potential of ISIW to adjust for PS in an intuitive, fast, and effective manner. We illustrate these ideas on spatial prediction of lead concentrations measured through moss biomonitoring data in Galicia, Spain, and PM2.5 concentrations from the U.S. EPA Air Quality System network in California.

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arXiv2025

Refining capture-recapture methods to estimate case counts in a finite population setting

In this paper, we expand upon and refine a monitoring strategy proposed for surveillance of diseases in finite, closed populations. This monitoring strategy consists of augmenting an arbitrarily non-representative data stream (such as a voluntary flu testing program) with a random sample (referred to as an "anchor stream"). This design allows for the use of traditional capture-recapture (CRC) estimators, as well as recently proposed anchor stream estimators that more efficiently utilize the data. Here, we focus on a particularly common situation in which the first data stream only records positive test results, while the anchor stream documents both positives and negatives. Due to the non-representative nature of the first data stream, along with the fact that inference is being performed on a finite, closed population, there are standard and non-standard finite population effects at play. Here, we propose two methods of incorporating finite population corrections (FPCs) for inference, along with an FPC-adjusted Bayesian credible interval. We compare these approaches with existing methods through simulation and demonstrate that the FPC adjustments can lead to considerable gains in precision. Finally, we provide a real data example by applying these methods to estimating the breast cancer recurrence count among Metro Atlanta-area patients in the Georgia Cancer Registry-based Cancer Recurrence Information and Surveillance Program (CRISP) database.

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arXiv2025

A Capture-Recapture Approach to Enhance Treatment Effect Evaluation in an Observational Cohort

We extend recently proposed design-based capture-recapture (CRC) methods for prevalence estimation among registry participants, in order to enhance treatment effect evaluation among a trial-eligible target population. The so-called ``anchor stream design" for CRC analysis integrates an observational study cohort with a randomized trial involving a small representative study sample, and enhances the generalizability and transportability of CRC findings. We show that a novel CRC-type estimator derived via multinomial distribution-based maximum-likelihood further exploits the design to deliver benefits in terms of validity and efficiency for comparing the effects of two treatments on a binary outcome. The design also unlocks a direct standardization-type estimator that allows efficient estimation of general means (e.g., for continuous outcomes such as biomarker levels) under a specific treatment. This provides an avenue to compare treatment responses within the target population in a more comprehensive manner. For inference, we recommend using a tailored Bayesian credible interval approach to improve coverage properties in conjunction with the proposed CRC estimator when estimating binary treatment effects, and a bootstrap percentile interval approach for use with continuous outcomes. Simulations demonstrate the validity and efficiency of the proposed estimators under the CRC design. Finally, we present an illustrative data application comparing Anti-S Antibody seropositive response rates for two major Covid-19 vaccines using an observational cohort from Tunisia.

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arXiv2025

The Hidden Toll of COVID-19 on Opioid Mortality in Georgia: A Bayesian Excess Opioid Mortality Analysis

COVID-19 has had a large scale negative impact on the health of opioid users exacerbating the health of an already vulnerable population. Critical information on the total impact of COVID-19 on opioid users is unknown due to a lack of comprehensive data on COVID-19 cases, inaccurate diagnostic coding, and lack of data coverage. To assess the impact of COVID-19 on small-area opioid mortality, we developed a Bayesian hierarchical excess opioid mortality modeling approach. We incorporate spatio-temporal autocorrelation structures to allow for sharing of information across small areas and time to reduce uncertainty in small area estimates. Excess mortality is defined as the difference between observed trends after a crisis and expected trends based on observed historical trends, which captures the total increase in observed mortality rates compared to what was expected prior to the crisis. We illustrate the application of our approach to assess excess opioid mortality risk estimates for 159 counties in GA. Using our proposed approach will help inform interventions in opioid-related public health responses, policies, and resource allocation. The application of this work also provides a general framework for improving the estimation and mapping of health indicators during crisis periods for the opioid user population.

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arXiv2025

What Influences the Field Goal Attempts of Professional Players? Analysis of Basketball Shot Charts via Log Gaussian Cox Processes with Spatially Varying Coefficients

Basketball shot charts provide valuable information regarding local patterns of in-game performance to coaches, players, sports analysts, and statisticians. The spatial patterns of where shots were attempted and whether the shots were successful suggest options for offensive and defensive strategies as well as historical summaries of performance against particular teams and players. The data represent a marked spatio-temporal point process with locations representing locations of attempted shots and an associated mark representing the shot's outcome (made/missed). Here, we develop a Bayesian log Gaussian Cox process model allowing joint analysis of the spatial pattern of locations and outcomes of shots across multiple games. We build a hierarchical model for the log intensity function using Gaussian processes, and allow spatially varying effects for various game-specific covariates. We aim to model the spatial relative risk under different covariate values. For inference via posterior simulation, we design a Markov chain Monte Carlo (MCMC) algorithm based on a kernel convolution approach. We illustrate the proposed method using extensive simulation studies. A case study analyzing the shot data of NBA legends Stephen Curry, LeBron James, and Michael Jordan highlights the effectiveness of our approach in real-world scenarios and provides practical insights into optimizing shooting strategies by examining how different playing conditions, game locations, and opposing team strengths impact shooting efficiency.

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arXiv2024

Utilizing a Capture-Recapture Strategy to Accelerate Infectious Disease Surveillance

Monitoring key elements of disease dynamics (e.g., prevalence, case counts) is of great importance in infectious disease prevention and control, as emphasized during the COVID-19 pandemic. To facilitate this effort, we propose a new capture-recapture (CRC) analysis strategy that takes misclassification into account from easily-administered, imperfect diagnostic test kits, such as the Rapid Antigen Test-kits or saliva tests. Our method is based on a recently proposed "anchor stream" design, whereby an existing voluntary surveillance data stream is augmented by a smaller and judiciously drawn random sample. It incorporates manufacturer-specified sensitivity and specificity parameters to account for imperfect diagnostic results in one or both data streams. For inference to accompany case count estimation, we improve upon traditional Wald-type confidence intervals by developing an adapted Bayesian credible interval for the CRC estimator that yields favorable frequentist coverage properties. When feasible, the proposed design and analytic strategy provides a more efficient solution than traditional CRC methods or random sampling-based biased-corrected estimation to monitor disease prevalence while accounting for misclassification. We demonstrate the benefits of this approach through simulation studies that underscore its potential utility in practice for economical disease monitoring among a registered closed population.

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arXiv2023

Enhanced Inference for Finite Population Sampling-Based Prevalence Estimation with Misclassification Errors

Epidemiologic screening programs often make use of tests with small, but non-zero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect test with known sensitivity and specificity to a sample of individuals from the population. In this setting, we propose an enhanced inferential approach for use in conjunction with sampling-based bias-corrected prevalence estimation. While ignoring the finite nature of the population can yield markedly conservative estimates, direct application of a standard finite population correction (FPC) conversely leads to underestimation of variance. We uncover a way to leverage the typical FPC indirectly toward valid statistical inference. In particular, we derive a readily estimable extra variance component induced by misclassification in this specific but arguably common diagnostic testing scenario. Our approach yields a standard error estimate that properly captures the sampling variability of the usual bias-corrected maximum likelihood estimator of disease prevalence. Finally, we develop an adapted Bayesian credible interval for the true prevalence that offers improved frequentist properties (i.e., coverage and width) relative to a Wald-type confidence interval. We report the simulation results to demonstrate the enhanced performance of the proposed inferential methods.

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arXiv2023

On some pitfalls of the log-linear modeling framework for capture-recapture studies in disease surveillance

In epidemiological studies, the capture-recapture (CRC) method is a powerful tool that can be used to estimate the number of diseased cases or potentially disease prevalence based on data from overlapping surveillance systems. Estimators derived from log-linear models are widely applied by epidemiologists when analyzing CRC data. The popularity of the log-linear model framework is largely associated with its accessibility and the fact that interaction terms can allow for certain types of dependency among data streams. In this work, we shed new light on significant pitfalls associated with the log-linear model framework in the context of CRC using real data examples and simulation studies. First, we demonstrate that the log-linear model paradigm is highly exclusionary. That is, it can exclude, by design, many possible estimates that are potentially consistent with the observed data. Second, we clarify the ways in which regularly used model selection metrics (e.g., information criteria) are fundamentally deceiving in the effort to select a best model in this setting. By focusing attention on these important cautionary points and on the fundamental untestable dependency assumption made when fitting a log-linear model to CRC data, we hope to improve the quality of and transparency associated with subsequent surveillance-based CRC estimates of case counts.

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arXiv2023

Impacts of Census Differential Privacy for Small-Area Disease Mapping to Monitor Health Inequities

The US Census Bureau will implement a new privacy-preserving disclosure avoidance system (DAS), which includes application of differential privacy, on the public-release 2020 census data. There are concerns that the DAS may bias small-area and demographically-stratified population counts, which play a critical role in public health research and policy, serving as denominators in estimation of disease/mortality rates. Employing three DAS demonstration products, we quantify errors attributable to reliance on DAS-protected denominators in standard small-area disease mapping models for characterizing health inequities. We conduct simulation studies and real data analyses of inequities in premature mortality at the census tract level in Massachusetts. Results show that overall patterns of inequity by racialized group and economic deprivation level are not compromised by the DAS. While early versions of DAS induce errors in mortality rate estimation that are larger for Black than for non-Hispanic white populations, this issue is ameliorated in newer DAS versions.

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arXiv2022

A Design and Analytic Strategy for Monitoring Disease Positivity and Case Characteristics in Accessible Closed Populations

We propose a monitoring strategy for efficient and robust estimation of disease prevalence and case numbers within closed and enumerated populations such as schools, workplaces, or retirement communities. The proposed design relies largely on voluntary testing, notoriously biased (e.g., in the case of COVID-19) due to non-representative sampling. The approach yields unbiased and comparatively precise estimates with no assumptions about factors underlying selection of individuals for voluntary testing, building on the strength of what can be a small random sampling component. This component unlocks a previously proposed "anchor stream" estimator, a well-calibrated alternative to classical capture-recapture (CRC) estimators based on two data streams. We show here that this estimator is equivalent to a direct standardization based on "capture", i.e., selection (or not) by the voluntary testing program, made possible by means of a key parameter identified by design. This equivalency simultaneously allows for novel two-stream CRC-like estimation of general means (e.g., of continuous variables such as antibody levels or biomarkers). For inference, we propose adaptations of a Bayesian credible interval when estimating case counts and bootstrapping when estimating means of continuous variables. We use simulations to demonstrate significant precision benefits relative to random sampling alone.

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arXiv2022

Tailoring Capture-Recapture Methods to Estimate Registry-Based Case Counts Based on Error-Prone Diagnostic Signals

Surveillance research is of great importance for effective and efficient epidemiological monitoring of case counts and disease prevalence. Taking specific motivation from ongoing efforts to identify recurrent cases based on the Georgia Cancer Registry, we extend recently proposed "anchor stream" sampling design and estimation methodology. Our approach offers a more efficient and defensible alternative to traditional capture-recapture (CRC) methods by leveraging a relatively small random sample of participants whose recurrence status is obtained through a principled application of medical records abstraction. This sample is combined with one or more existing signaling data streams, which may yield data based on arbitrarily non-representative subsets of the full registry population. The key extension developed here accounts for the common problem of false positive or negative diagnostic signals from the existing data stream(s). In particular, we show that the design only requires documentation of positive signals in these non-anchor surveillance streams, and permits valid estimation of the true case count based on an estimable positive predictive value (PPV) parameter. We borrow ideas from the multiple imputation paradigm to provide accompanying standard errors, and develop an adapted Bayesian credible interval approach that yields favorable frequentist coverage properties. We demonstrate the benefits of the proposed methods through simulation studies, and provide a data example targeting estimation of the breast cancer recurrence case count among Metro Atlanta area patients from the Georgia Cancer Registry-based Cancer Recurrence Information and Surveillance Program (CRISP) database.

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arXiv2022

An integrated abundance model for estimating county-level prevalence of opioid misuse in Ohio

Opioid misuse is a national epidemic and a significant drug related threat to the United States. While the scale of the problem is undeniable, estimates of the local prevalence of opioid misuse are lacking, despite their importance to policy-making and resource allocation. This is due, in part, to the challenge of directly measuring opioid misuse at a local level. In this paper, we develop a Bayesian hierarchical spatio-temporal abundance model that integrates indirect county-level data on opioid-related outcomes with state-level survey estimates on prevalence of opioid misuse to estimate the latent county-level prevalence and counts of people who misuse opioids. A simulation study shows that our integrated model accurately recovers the latent counts and prevalence. We apply our model to county-level surveillance data on opioid overdose deaths and treatment admissions from the state of Ohio. Our proposed framework can be applied to other applications of small area estimation for hard to reach populations, which is a common occurrence with many health conditions such as those related to illicit behaviors.

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arXiv2021

Multi-Objective Allocation of COVID-19 Testing Centers: Improving Coverage and Equity in Access

At the time of this article, COVID-19 has been transmitted to more than 42 million people and resulted in more than 673,000 deaths across the United States. Throughout this pandemic, public health authorities have monitored the results of diagnostic testing to identify hotspots of transmission. Such information can help reduce or block transmission paths of COVID-19 and help infected patients receive early treatment. However, most current schemes of test site allocation have been based on experience or convenience, often resulting in low efficiency and non-optimal allocation. In addition, the historical sociodemographic patterns of populations within cities can result in measurable inequities in access to testing between various racial and income groups. To address these pressing issues, we propose a novel test site allocation scheme to (a) maximize population coverage, (b) minimize prediction uncertainties associated with projections of outbreak trajectories, and (c) reduce inequities in access. We illustrate our approach with case studies comparing our allocation scheme with recorded allocation of testing sites in Georgia, revealing increases in both population coverage and improvements in equity of access over current practice.

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arXiv2016

Data Integration Model for Air Quality: A Hierarchical Approach to the Global Estimation of Exposures to Ambient Air Pollution

Air pollution is a major risk factor for global health, with both ambient and household air pollution contributing substantial components of the overall global disease burden. One of the key drivers of adverse health effects is fine particulate matter ambient pollution (PM$_{2.5}$) to which an estimated 3 million deaths can be attributed annually. The primary source of information for estimating exposures has been measurements from ground monitoring networks but, although coverage is increasing, there remain regions in which monitoring is limited. Ground monitoring data therefore needs to be supplemented with information from other sources, such as satellite retrievals of aerosol optical depth and chemical transport models. A hierarchical modelling approach for integrating data from multiple sources is proposed allowing spatially-varying relationships between ground measurements and other factors that estimate air quality. Set within a Bayesian framework, the resulting Data Integration Model for Air Quality (DIMAQ) is used to estimate exposures, together with associated measures of uncertainty, on a high resolution grid covering the entire world. Bayesian analysis on this scale can be computationally challenging and here approximate Bayesian inference is performed using Integrated Nested Laplace Approximations. Model selection and assessment is performed by cross-validation with the final model offering substantial increases in predictive accuracy, particularly in regions where there is sparse ground monitoring, when compared to current approaches: root mean square error (RMSE) reduced from 17.1 to 10.7, and population weighted RMSE from 23.1 to 12.1 $μ$gm$^{-3}$. Based on summaries of the posterior distributions for each grid cell, it is estimated that 92% of the world's population reside in areas exceeding the World Health Organization's Air Quality Guidelines.

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arXiv2016

Hierarchical multivariate space-time methods for modeling counts with an application to stroke mortality data

Geographic patterns in stroke mortality have been studied as far back as the 1960s, when a region of the southeastern United States became known as the "stroke belt" due to its unusually high rates of stroke mortality. While stroke mortality rates are known to increase exponentially with age, an investigation of spatiotemporal trends by age group at the county-level is daunting due to the preponderance of small population sizes and/or few stroke events by age group. Here, we harness the power of a complex, nonseparable multivariate space-time model which borrows strength across space, time, and age group to obtain reliable estimates of yearly county-level mortality rates from US counties between 1973 and 2013 for those aged 65+. Furthermore, we propose an alternative metric for measuring changes in event rates over time which accounts for the full trajectory of a county's event rates, as opposed to simply comparing the rates at the beginning and end of the study period. In our analysis of the stroke data, we identify differing spatiotemporal trends in mortality rates across age groups, shed light on the gains achieved in the Deep South, and provide evidence that a separable model is inappropriate for these data.

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arXiv2015

A Nonseparable Multivariate Space-Time Model for Analyzing County-Level Heart Disease Death Rates by Race and Gender

While death rates due to diseases of the heart have experienced a sharp decline over the past 50 years, these diseases continue to be the leading cause of death in the United States, and the rate of decline varies by geographic location, race, and gender. We look to harness the power of hierarchical Bayesian methods to obtain a clearer picture of the declines from county-level, temporally varying heart disease death rates for men and women of different races in the US. Specifically, we propose a nonseparable multivariate spatio-temporal Bayesian model which allows for group-specific temporal correlations and temporally-evolving covariance structures in the multivariate spatio-temporal component of the model. After verifying the effectiveness of our model via simulation, we apply our model to a dataset of over 200,000 county-level heart disease death rates. In addition to yielding a superior fit than other common approaches for handling such data, the richness of our model provides insight into racial, gender, and geographic disparities underlying heart disease death rates in the US which are not permitted by more restrictive models.

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