The "Why" behind including "Y" in your imputation model.

Missing data is a common challenge when analyzing epidemiological data, and imputation is often used to address this issue. Here, we investigate the scenario where a covariate used in an analysis has missingness and will be imputed. There are recommendations to include the outcome from the analysis model in the imputation model for missing covariates, but it is not necessarily clear if this recommendation always holds and why this is sometimes true. We examine deterministic imputation (i.e. single imputation with fixed values) and stochastic imputation (i.e. single or multiple imputation with random values) methods and their implications for estimating the relationship between the imputed covariate and the outcome. We mathematically demonstrate that including the outcome variable in imputation models is not just a recommendation but a requirement to achieve unbiased results when using stochastic imputation methods. Moreover, we dispel common misconceptions about deterministic imputation models and demonstrate why the outcome should not be included in these models. This article aims to bridge the gap between imputation in theory and in practice, providing mathematical derivations to explain common statistical recommendations. We offer a better understanding of the considerations involved in imputing missing covariates and emphasize when it is necessary to include the outcome variable in the imputation model.

Homogenized gridded dataset for drought and hydrometeorological modeling for the continental United States.

We present a novel data set for drought in the continental US (CONUS) built to enable computationally efficient spatio-temporal statistical and probabilistic models of drought. We converted drought data obtained from the widely-used US Drought Monitor (USDM) from its native geo-referenced polygon format to a 0.5 degree regular grid. We merged known environmental drivers of drought, including those obtained from the North American Land Data Assimilation System (NLDAS-2), US Geological Survey (USGS) streamflow data, and National Oceanic and Atmospheric Administration (NOAA) teleconnections data. The resulting data set permits statistical and probabilistic modeling of drought with explicit spatial and/or temporal dependence. Such models could be used to forecast drought at short-range, seasonal to sub-seasonal, and inter-annual timescales with uncertainty, extending the reach and value of the current US Drought Outlook from the National Weather Service Climate Prediction Center. This novel data product provides the first common gridded dataset that includes critical variables used to inform hydrological and meteorological drought.

Estimation of opioid misuse prevalence in New York State counties, 2007-2018. A Bayesian spatio-temporal abundance model approach.

An important challenge to addressing the opioid overdose crisis is the lack of information on the size of the population of people who misuse opioids (PWMO) in local areas. This estimate is needed for better resource allocation, estimation of treatment and overdose outcome rates using appropriate denominators (i.e., the population at risk), and proper evaluation of intervention effects. In this study, we used a Bayesian hierarchical spatio-temporal integrated abundance model that integrates multiple types of county-level surveillance outcome data, state-level information on opioid misuse, and covariates to estimate the latent (hidden) counts and prevalence of PWMO across New York State counties (2007-2018). The model assumes that each opioid-related outcome reflects a partial count of the number of PWMO, and leverages these multiple sources of data to circumvent limitations of parameter estimation associated with other types of abundance models. Model estimates showed a reduction in the prevalence of PWMO during the study period, with important spatial and temporal variability. The model also provided county-level estimates of rates of treatment and opioid overdoses using the PWMO as denominators. This modeling approach can identify the size of hidden populations to guide public health efforts to confront the opioid overdose crisis across local areas.

Interplay of competition and facilitation in grazing succession by migrant Serengeti herbivores.

Competition, facilitation, and predation offer alternative explanations for successional patterns of migratory herbivores. However, these interactions are difficult to measure, leaving uncertainty about the mechanisms underlying body-size-dependent grazing-and even whether succession occurs at all. We used data from an 8-year camera-trap survey, GPS-collared herbivores, and fecal DNA metabarcoding to analyze the timing, arrival order, and interactions among migratory grazers in Serengeti National Park. Temporal grazing succession is characterized by a "push-pull" dynamic: Competitive grazing nudges zebra ahead of co-migrating wildebeest, whereas grass consumption by these large-bodied migrants attracts trailing, small-bodied gazelle that benefit from facilitation. "Natural experiments" involving intense wildfires and rainfall respectively disrupted and strengthened these effects. Our results highlight a balance between facilitative and competitive forces in co-regulating large-scale ungulate migrations.

A Bayesian Spatio-temporal Model to Optimize Allocation of Buprenorphine in North Carolina.

The opioid epidemic is an ongoing public health crisis. In North Carolina, overdose deaths due to illicit opioid overdose have sharply increased over the last 5-7 years. Buprenorphine is a U.S. Food and Drug Administration approved medication for treatment of opioid use disorder and is obtained by prescription. Prior to January 2023, providers had to obtain a waiver and were limited in the number of patients that they could prescribe buprenorphine. Thus, identifying counties where increasing buprenorphine would yield the greatest overall reduction in overdose death can help policymakers target certain geographical regions to inform an effective public health response. We propose a Bayesian spatiotemporal model that relates yearly, county-level changes in illicit opioid overdose death rates to changes in buprenorphine prescriptions. We use our model to forecast the statewide count and rate of illicit opioid overdose deaths in future years, and we use nonlinear constrained optimization to identify the optimal buprenorphine increase in each county under a set of constraints on available resources. Our model estimates a negative relationship between death rate and increasing buprenorphine after accounting for other covariates, and our identified optimal single-year allocation strategy is estimated to reduce opioid overdose deaths by over 5.

State-Level History of Overdose Deaths Involving Stimulants in the United States, 1999‒2020.

Objectives. To examine the state-level history of US overdose deaths involving stimulants with and without opioids from 1999 to 2020. Methods. We used death certificate data from the National Center for Health Statistics to categorize deaths into 4 groups of interest: cocaine with and without opioids, and psychostimulants with and without opioids. We used a Bayesian multiple change point model to describe the timing and magnitude of changes in overdose death rates involving stimulants for each state and year. Results. There was little change in the death rates of cocaine without opioids. Death rates involving cocaine and opioids sharply increased around 2015, particularly in the Northeast and Mid-Atlantic. We also observed steady increases in deaths involving psychostimulants without opioids just before 2010, particularly in states in the West and South. Deaths involving psychostimulants with opioids increased around 2015 with largest increases concentrated in Appalachian states. Conclusions. There is significant geographic heterogeneity in the co-involvement of stimulants in the US overdose crisis. Results can inform public health efforts to inform state-level overdose efforts such as naloxone distribution. (Am J Public Health. 2023;113(9):991-999. https://doi.org/10.2105/AJPH.2023.307337).

A spatio-temporal hierarchical model to account for temporal misalignment in American Community Survey explanatory variables.

The American Community Survey (ACS) is one of the most vital public sources for demographic and socioeconomic characteristics of communities in the United States and is administered by the U.S. Census Bureau every year. The ACS publishes 5-year estimates of community characteristics for all geographical areas and 1-year estimates for areas with population of at least 65,000. Many epidemiological and public health studies use 5-year ACS estimates as explanatory variables in models. However, doing so ignores the uncertainty and averages over variability during the time-period which may lead to biased estimates of covariate effects of interest. In this paper, we propose a Bayesian hierarchical model that accounts for the uncertainty and disentangles the temporal misalignment in the ACS multi-year time-period estimates. We show via simulation that our proposed model more accurately recovers covariate effects compared to models that ignore the temporal misalignment. Lastly, we implement our proposed model to quantify the relationship between yearly, county-level characteristics and the prevalence of frequent mental distress for counties in North Carolina from 2014 to 2018.

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.

A Descriptive Study on Opioid Misuse Prevalence and Office-Based Buprenorphine Access in Ohio Prior to the Removal of the Drug Addiction Treatment Act of 2000 Waiver.

Background Medications for the treatment of opioid use disorder (MOUD) are effective evidence-based strategies to reduce opioid overdose deaths. Strategies to optimize MOUD availability and uptake are needed. Objective We aim to describe the spatial relationship between the estimated prevalence of opioid misuse and office-based buprenorphine access in the state of Ohio prior to the removal of the Drug Addiction Treatment Act of 2000 (DATA 2000) waiver requirement. Methods We conducted a descriptive ecological study of county-level (N=88) opioid misuse prevalence and office-based buprenorphine prescribing access in Ohio in 2018. Counties were categorized into urban (with and without a major metropolitan area) and rural. The county-level prevalence estimates of opioid misuse per 100,000 were derived from integrated abundance modeling. Utilizing data from the Ohio Department of Mental Health and Addiction Services, as well as the state's Physician Drug Monitoring Program (PDMP), buprenorphine access per 100,000 was estimated by the number of patients in each county that could be served by office-based buprenorphine (prescribing capacity) and the number of patients served by office-based buprenorphine (prescribing frequency) for opioid use disorder. The ratios of opioid misuse prevalence to both prescribing capacity and frequency were calculated by county and mapped. Results Less than half of the 1,828 waivered providers in the state of Ohio in 2018 were prescribing buprenorphine, and 25% of counties had no buprenorphine access. The median estimated opioid misuse prevalence and buprenorphine prescribing capacity per 100,000 were highest in urban counties, particularly those with a major metropolitan area. Although the median estimated opioid misuse prevalence was lower in rural counties, all counties in the highest quartile of estimated misuse prevalence were rural. In addition, the median buprenorphine prescribing frequency was highest in rural counties. While the ratio of opioid misuse prevalence to buprenorphine prescribing capacity was lowest in urban counties, the ratio of opioid misuse prevalence to buprenorphine prescribing frequency was lowest in rural counties. Opioid misuse prevalence and buprenorphine prescribing frequency demonstrated similar spatial patterns, with highest levels in the southern and eastern portions of the state, while office-based buprenorphine prescribing capacity did not. Conclusion Urban counties had higher buprenorphine capacity relative to their burden of opioid misuse; however, access was limited by buprenorphine prescribing frequency. In contrast, in rural counties, a minimal gap was evident between prescribing capacity and frequency, suggesting that buprenorphine prescribing capacity was the major factor limiting access. While the recent deregulation of buprenorphine prescribing should help improve buprenorphine access, future research should investigate whether deregulation similarly impacts buprenorphine prescribing capacity and buprenorphine prescribing frequency.

A Dynamic Spatial Factor Model to Describe the Opioid Syndemic in Ohio.

BACKGROUND: The opioid epidemic has been ongoing for over 20 years in the United States. As opioid misuse has shifted increasingly toward injection of illicitly produced opioids, it has been associated with HIV and hepatitis C transmission. These epidemics interact to form the opioid syndemic. METHODS: We obtain annual county-level counts of opioid overdose deaths, treatment admissions for opioid misuse, and newly diagnosed cases of acute and chronic hepatitis C and newly diagnosed HIV from 2014 to 2019. Aligned with the conceptual framework of syndemics, we develop a dynamic spatial factor model to describe the opioid syndemic for counties in Ohio and estimate the complex synergies between each of the epidemics. RESULTS: We estimate three latent factors characterizing variation of the syndemic across space and time. The first factor reflects overall burden and is greatest in southern Ohio. The second factor describes harms and is greatest in urban counties. The third factor highlights counties with higher than expected hepatitis C rates and lower than expected HIV rates, which suggests elevated localized risk for future HIV outbreaks. CONCLUSIONS: Through the estimation of dynamic spatial factors, we are able to estimate the complex dependencies and characterize the synergy across outcomes that underlie the syndemic. The latent factors summarize shared variation across multiple spatial time series and provide new insights into the relationships between the epidemics within the syndemic. Our framework provides a coherent approach for synthesizing complex interactions and estimating underlying sources of variation that can be applied to other syndemics.

Integrating Public Health Surveillance and Environmental Data to Model Presence of Histoplasma in the United States.

BACKGROUND: In the United States, the true geographic distribution of the environmental fungus Histoplasma capsulatum remains poorly understood but appears to have changed since it was first characterized. Histoplasmosis is caused by inhalation of the fungus and can range in severity from asymptomatic to life threatening. Due to limited public health surveillance and under detection of infections, it is challenging to directly use reported case data to characterize spatial risk. METHODS: Using monthly and yearly county-level public health surveillance data and various environmental and socioeconomic characteristics, we use a spatio-temporal occupancy model to estimate latent, or unobserved, presence of H. capsulatum , accounting for imperfect detection of histoplasmosis cases. RESULTS: We estimate areas with higher probabilities of the presence of H. capsulatum in the East North Central states around the Great Lakes, reflecting a shift of the endemic region to the north from previous estimates. The presence of H. capsulatum was strongly associated with higher soil nitrogen levels. CONCLUSIONS: In this investigation, we were able to mitigate challenges related to reporting and illustrate a shift in the endemic region from historical estimates. This work aims to help inform future surveillance needs, clinical awareness, and testing decisions for histoplasmosis.

A MULTIVARIATE SPATIOTEMPORAL CHANGE-POINT MODEL OF OPIOID OVERDOSE DEATHS IN OHIO.

Ohio is one of the states most impacted by the opioid epidemic and experienced the second highest age-adjusted fatal drug overdose rate in 2017. Initially it was believed prescription opioids were driving the opioid crisis in Ohio. However, as the epidemic evolved, opioid overdose deaths due to fentanyl have drastically increased. In this work we develop a Bayesian multivariate spatiotemporal model for Ohio county overdose death rates from 2007 to 2018 due to different types of opioids. The log-odds are assumed to follow a spatially varying change point regression model. By assuming the regression coefficients are a multivariate conditional autoregressive process, we capture spatial dependence within each drug type and also dependence across drug types. The proposed model allows us to not only study spatiotemporal trends in overdose death rates but also to detect county-level shifts in these trends over time for various types of opioids.

Spatiotemporal Trends in Opioid Overdose Deaths by Race for Counties in Ohio.

BACKGROUND: The opioid epidemic continues to be an ongoing public health crisis in the United States. Initially, large increases in overdose death rates were observed in largely rural, White communities, leading to the initial perception that the opioid epidemic was primarily a problem for the White population. Recent findings have shown increasing rates of overdose death among Blacks. We compare overdose rates between Blacks and Whites and explore county-level spatiotemporal heterogeneity in Ohio. METHODS: We obtained county-level opioid overdose death counts for Whites and Blacks from 2007 to 2018 in Ohio. We fit a Bayesian multivariate spatial rates model to estimate annual standardized mortality ratios for Whites and Blacks for each county. We accounted for correlation between racial groups in the same county and across space and time. We also estimated differences in the mean trends between urban and rural counties for each racial group. RESULTS: The overall overdose death rate in the state was increasing until 2018. County-level death rates for Whites were higher than Blacks throughout the state early in the study period. Death rates for Blacks increased throughout the study period and were comparable to the rates for Whites by the end of the study in many counties. CONCLUSIONS: County-level opioid overdose death rates increased faster for Blacks than Whites during the study. By 2018, death rates were comparable for Blacks and Whites in many counties. The opioid epidemic spans racial groups in Ohio and trends indicate that overdose is a growing problem among Blacks.

Estimating the burden of the opioid epidemic for adults and adolescents in Ohio counties.

Quantifying the opioid epidemic at the local level is a challenging problem that has important consequences on resource allocation. Adults and adolescents may exhibit different spatial trends and require different interventions and resources so it is important to examine the problem for each age group. In Ohio, surveillance data are collected at the county level for each age group on measurable outcomes of the opioid epidemic, overdose deaths, and treatment admissions. However, our interest lies in quantifying the unmeasurable construct, representing the burden of the opioid epidemic, which drives rates of the outcomes. We propose jointly modeling adult and adolescent surveillance outcomes through a multivariate spatial factor model. A generalized spatial factor model within each age group quantifies a latent factor related to the number of opioid-associated treatment admissions and deaths. By assuming a multivariate conditional autoregressive model for the spatial factors of adults and adolescents, we allow the adolescent model to borrow strength from the adult model (and vice versa), improving estimation. We also incorporate county-level covariates to help explain spatial heterogeneity in each of the factors. We apply this approach to the state of Ohio and discuss the findings. Our framework provides a coherent approach for synthesizing information across multiple outcomes and age groups to better understand the spatial epidemiology of the opioid epidemic.

Identifying drivers of spatial variation in occupancy with limited replication camera trap data.

Occupancy models are widely used in camera trap studies to analyze species presence, abundance, and geographic distribution, among other important ecological quantities. These models account for imperfect detection using a latent variable to distinguish between true presence/absence and observed detection of a species. Under certain experimental setups, parameter estimation in a latent variable framework can be challenging. Several studies have issued guidelines on the number of independent replicated observations (surveys) needed for each unchanging occupancy field (season) to ensure reliable estimation. In this paper, we present a spatio-temporal occupancy model, and show through a simulation study that it can be fit to data obtained from a single survey per season, so long as the number of seasons is sufficiently large. We include an application using camera-trap data on the Thomson's gazelle in the Serengeti in Tanzania.