Perchlorate Distribution, Excretion, and Depuration in Prairie Voles and Deer Mice

A study on perchlorate distribution was conducted in male adult prairie voles (Microtus ochrogaster). Excretion via urine was the major pathway for perchlorate fate in the body, with the highest concentrations of perchlorate detected in urine after exposure to perchlorate through drinking water [250 μg/ml Mg(ClO₄)₂], and an average of 34% and 88% of perchlorate intake recovered in urine in the 4- and 8-h exposure groups, respectively. Perchlorate mass in kidney, thyroid, blood, and urine were related to perchlorate intake (254.5–2687.7 μg). Perchlorate excretion and depuration patterns via urine were tested further using male adult deer mice (Peromyscus maniculatus). Animals were exposed to perchlorate through dosed drinking water (0, 17, 165, and 1600 ng/ml). Perchlorate concentrations in urine showed a significant difference among the three dosed groups during a 28-day exposure period. However, no difference was found in urine among the three dosages in terms of mass percentage of perchlorate intake from water at each sampling time over the 28-day exposure period. Both concentrations of perchlorate and mass percentage in urine reached a steady state after 1 day in all treatments. On average 46%, 46%, and 61% of perchlorate intake from water was recovered in urine over the exposure period in high, medium, and low dose groups, respectively. Including perchlorate consumption from rodent chow (1.44 ng/g), less than 46% of perchlorate intake was recovered in urine in the high and medium dose groups, and <61% in the low dose group. Three parameter first-order decay models fit the depuration curve very well, with r?>?0.99 in both the low and high dose groups; half-lives of perchlorate in deer mice were estimated as 9.12 and 7.25 h in the low and high dose groups, respectively. Endogenous generation of perchlorate and/or some degree of retention or metabolism of perchlorate may occur in deer mice, based in part on the uncompleted mass balance in the excretion and depuration experiments. The data reported herein should provide additional insight for perchlorate fate determination in animals and humans and valuable information for perchlorate risk assessment in the environment, especially wildlife.     

Predicting perchlorate exposure in milk from concentrations in dairy feed

Perchlorate has been detected in U.S. milk samples from many different states. Applying data from a recently reported 9-week experiment in which 16 Holstein dairy cows were administered perchlorate allowed us to derive an equation for the dose-response relationship between perchlorate concentrations in feed/drinking water and its appearance in milk. Examination of background concentrations of perchlorate in the total mixed ration (TMR) fed in addition to the variable dose supplied to treated cows as a ruminal infusate revealed that cows receive significant and variable exposure to perchlorate from the TMR. Weekly examination of the TMR disclosed that a change in ingredients midway through the experiment caused a significant (78%) change in TMR perchlorate concentration. Analyses of the ingredients comprising the TMR revealed that 41.9% of the perchlorate came from corn silage, 22.9% came from alfalfa hay and 11.7% was supplied by sudan grass. Finally, USDA Food and Nutrition Survey data on fluid milk consumption were used to predict potential human exposure from milk that contained concentrations of perchlorate observed in our previous dosing study. The study suggests that reducing perchlorate concentration in dairy feed may reduce perchlorate concentrations in milk as well as the potential to reduce human exposure to perchlorate in milk.     

Risk Assessment for Toxicity Experiments with Discrete and Continuous Outcomes: A Bayesian Nonparametric Approach

We present a Bayesian nonparametric modeling approach to inference and risk assessment for developmental toxicity studies. The primary objective of these studies is to determine the relationship between the level of exposure to a toxic chemical and the probability of a physiological or biochemical response. We consider a general data setting involving clustered categorical responses on the number of prenatal deaths, the number of live pups, and the number of live malformed pups from each laboratory animal, as well as continuous outcomes (e.g., body weight) on each of the live pups. We utilize mixture modeling to provide flexibility in the functional form of both the multivariate response distribution and the various dose–response curves of interest. The nonparametric model is built from a structured mixture kernel and a dose-dependent Dirichlet process prior for the mixing distribution. The modeling framework enables general inference for the implied dose–response relationships and for dose-dependent correlations between the different endpoints, features which provide practical advances relative to traditional parametric models for developmental toxicology. We use data from a toxicity experiment that investigated the toxic effects of an organic solvent (diethylene glycol dimethyl ether) to demonstrate the range of inferences obtained from the nonparametric mixture model, including comparison with a parametric hierarchical model.Supplementary materials accompanying this paper appear on-line.     

A study on perchlorate exposure and absorption in beef cattle

Perchlorate exposure and potential effects were evaluated in large mammals by monitoring heifer calves placed on a site with access to streamwater fed by a perchlorate-contaminated groundwater spring ( approximately 25 ng/mL). Blood was collected from the two calves on the site (and two control calves from an uncontaminated site) approximately every 2 weeks for analysis of perchlorate residues and thyroid hormones. During the 14 week study, perchlorate was detected (detection limit = 13.7 ng/mL) in blood plasma twice (15 ng/mL and 22 ng/mL) in one of the heifer calves drinking perchlorate-contaminated water on consecutive sampling periods 4 and 6 weeks after the beginning of perchlorate exposure. Constant exposure to 25 ppb perchlorate in drinking water had no effect on circulating thyroid hormones (T(3) and T(4)) in the heifer calves.     

Hierarchical Nonlinear Spatio-temporal Agent-Based Models for Collective Animal Movement

Modeling complex collective animal movement presents distinct challenges. In particular, modeling the interactions between animals and the nonlinear behaviors associated with these interactions, while accounting for uncertainty in data, model, and parameters, requires a flexible modeling framework. To address these challenges, we propose a general hierarchical framework for modeling collective movement behavior with multiple stages. Each of these stages can be thought of as processes that are flexible enough to model a variety of complex behaviors. For example, self-propelled particle (SPP) models (e.g., Vicsek et al. in Phys Rev Lett 75:1226–1229, 1995) represent collective behavior and are often applied in the physics and biology literature. To date, the study and application of these models has almost exclusively focused on simulation studies, with less attention given to rigorously quantifying the uncertainty. Here, we demonstrate our general framework with a hierarchical version of the SPP model applied to collective animal movement. This structure allows us to make inference on potential covariates (e.g., habitat) that describe the behavior of agents and rigorously quantify uncertainty. Further, this framework allows for the discrete time prediction of animal locations in the presence of missing observations. Due to the computational challenges associated with the proposed model, we develop an approximate Bayesian computation algorithm for estimation. We illustrate the hierarchical SPP methodology with a simulation study and by modeling the movement of guppies.Supplementary materials accompanying this paper appear online.     

The simultaneous analysis of mixed discrete and continuous outcomes using nonlinear threshold models

Mixed discrete and continuous outcomes are commonly measured on each experimental unit in dose-response studies in toxicology. The dose-response relationships for these outcomes often have dose thresholds and nonlinear patterns. In addition, the endpoints are typically correlated, and a statistical analysis that incorporates the association may result in improved precision. We propose an extension of the generalized estimating equation (GEE) methodology to simultaneously analyze binary, count, and continuous outcomes with nonlinear threshold models that incorporates the intra-subject correlation. The methodology uses a quasi-likelihood framework and a working correlation matrix, and is appropriate when the marginal expectation of each outcome is of primary interest and the correlation between endpoints is a nuisance parameter. Because the derivatives of threshold models are not continuous at each point of the parameter space, we describe the necessary modifications that result in asymptotically normal and consistent estimators. Using dose-response data from a neurotoxicity experiment, the methodology is illustrated by analyzing five outcomes of mixed type with nonlinear threshold models. In this example, the incorporation of the intra-subject correlation resulted in decreased standard errors for the threshold parameters.     

A Bayesian hierarchical model for risk assessment of methylmercury

This article uses a Bayesian hierarchical model to quantify the adverse health effects associated with in-utero exposure to methylmercury. By allowing for study-to-studyas well as outcome-to-outcome variability, the approach provides a useful meta-analytic tool for multi-outcome, multi-study environmental risk assessments. The analysis presented here expands on the findings of a National Academy of Sciences (NAS) committee, charged with advising the United States Environmental Protection Agency (EPA) on an appropriate approach to conducting a risk assessment for methylmercury. The NAS committee, for which the senior author (Ryan) was a committee member, reviewed the findings from several conflicting studies and reported the results from a Bayesian hierarchical model that synthesized information across several studies and for several outcomes. Although the NAS committee did not suggest that the hierarchical model be used as the actual basis for a methylmercury risk assessment, the results from the model were used to justify and support the final recommendation that the risk analysis be based on data from a study conducted in the Faroe Islands, which had found a positive association between in-utero exposure to methylmercury and impaired neurological development. We considera variety of statistical issues, but particularly sensitivity to model specification.     

A Bayesian Approach to Estimating Agricultural Yield Based on Multiple Repeated Surveys

Forecasting the end-of-year crop yield is critical for agricultural decision-making and inherently difficult. Historically, a panel of commodity specialists known as the Agricultural Statistics Board convene regularly to set estimates based on expert review of a combination of survey data and administrative/auxiliary information. To make this process less subjective and more repeatable, we develop a Bayesian hierarchical model that produces superior yield forecasts/estimates, while quantifying different sources of uncertainty. The proposed hierarchical model naturally combines information from multiple monthly surveys measured on different temporal supports, including a field measurement survey and two farmer interview surveys. The dependence between the monthly updated surveys and the serial dependence of the annual yield are incorporated at different levels of the hierarchy. The effectiveness of our approach is demonstrated through an application from the US Department of Agriculture. Empirical results indicate that the hierarchical model produces superior forecasts to both the panel of experts and the composite estimator developed by Keller and Olkin (Technical Report, National Agricultural Statistics Service, 2002), while providing an accurate measure of uncertainty.     

Accumulation and perchlorate exposure potential of lettuce produced in the Lower Colorado River region

The Colorado River is contaminated with perchlorate concentrations of 1.5-8 microg/L, an anion linked to thyroid dysfunction. Over 90% of the lettuce (Lactuca sativa L.) consumed during the winter months in the United States is produced in the Lower Colorado River region. Studies were conducted in this region to survey the potential for lettuce perchlorate accumulation and estimate potential human exposure to perchlorate from lettuce. Total uptake of perchlorate in the above-ground plant of iceberg lettuce was approximately 5 g/ha. Exposure estimates ranged from 0.45 to 1.8 microg/day depending on lettuce types and trimming. For all lettuce types, hypothetical exposures were less than 4% of the reference dose recommended by the National Academy of Sciences. Results show the relative iodide uptake inhibition potential because of lettuce nitrate was 2 orders of magnitude greater than that associated with the corresponding trace levels of perchlorate. These data support the conclusion that potential perchlorate exposures from lettuce irrigated with Colorado River water are negligible relative to acute or long-term harmful amounts.     

A Hierarchical Model for Serially-Dependent Extremes: A Study of Heat Waves in the Western US

Heat waves take a major toll on human populations, with negative impacts on the economy, agriculture, and human health. As a result, there is great interest in studying the changes over time in the probability and magnitude of heat waves. In this paper we propose a hierarchical Bayesian model for serially-dependent extreme temperatures. We assume the marginal temperature distribution follows the generalized Pareto distribution (GPD) above a location-specific threshold, and capture dependence between subsequent days using a transformed max-stable process. Our model allows both the parameters in the marginal GPD and the temporal dependence function to change over time. This allows Bayesian inference on the change in likelihood of a heat wave. We apply this methodology to daily high temperatures in nine cities in the western US for 1979–2010. Our analysis reveals increases in the probability of a heat wave in several US cities. This article has supplementary material online.     

A Bayesian Model for Presence-Only Semicontinuous Data,With Application to Prediction of Abundance of <Emphasis Type="Italic">Taxus Baccata</Emphasis> in Two Italian Regions

In studies about the potential distribution of ecological niches, only the presence of the species of interest is usually recorded. Pseudo-absences are sampled from the study area in order to avoid biased estimates and predictions. For cases in which, instead of the mere presence, a continuous abundance index is recorded, we derive a two-part model for semicontinuous (i.e., positive with excess zeros) data which explicitly takes into account uncertainty about the sampled zeros. Our model is a direct extension of the one of Ward et al. (Biometrics 65, 554–563, 2009). It is fit in a Bayesian framework, which has many advantages over the maximum likelihood approach of Ward et al. (2009), the most important of which is that the prevalence of the species does not need to be known in advance. We illustrate our approach with real data arising from an original study aiming at the prediction of the potential distribution of the Taxus baccata in two central Italian regions. Supplemental materials giving detailed proofs of propositions, tables and code are available online.     

A unified capture-recapture framework

This article develops a hierarchical framework for capture-recapture data that separates the capture process from the demographic processes of interest, such as birth and survival. This allows users to parameterize in terms of meaningful demographic parameters. The framework is very flexible with many of the current capture-recapture models included as special cases. The hierarchical nature of the model allows natural expression of relationships, both between parameters and between parameters and the realization of random variables, such as population size. Previously, many of these relationships, such as density dependence have been unable to be explored using capture-recapture data. Density dependence, where survival and birth rates depend on the population size, is an interesting special case. We fit a density-dependent model to male Gonodontis bidentata data and report evidence of negative density dependence in percapita birth rates and weak evidence of negative density dependence in survival.     

Tissue distribution, elimination, and metabolism of sodium [36Cl]perchlorate in lactating goats

Perchlorate has contaminated water sources throughout the United States but particularly in the arid Southwest, an area containing large numbers of people and few water sources. Recent studies have demonstrated that perchlorate is present in alfalfa and that perchlorate is secreted into the milk of cows. Studies in lactating cows have indicated that only a small portion of a perchlorate dose could be accounted for by elimination in milk, feces, or urine. It was hypothesized that the remainder of the perchlorate dose was excreted as chloride ion. The purpose of this study was to determine the fate and disposition of (36)Cl-perchlorate in lactating dairy goats. Two goats (60 kg) were each orally administered 3.5 mg (16.5 muCi) of (36)Cl-perchlorate, a dose selected to approximate environmental perchlorate exposure but that would allow for adequate detection of radioactive residues after a 72 h withdrawal period. Blood, milk, urine, and feces were collected incrementally until slaughter at 72 h. Total radioactive residue (TRR) and perchlorate concentrations were measured using radiochemical techniques and liquid chromatography mass spectrometry (LC-MS-MS). Peak blood levels of TRR occurred at 12 h ( approximately 195 ppb) postdose; peak levels of parent perchlorate, however, occurred after only 2 h, suggesting that perchlorate metabolism occurred rapidly in the rumen. The serum half-life of perchlorate was estimated to be 2.3 h. After 24 h, perchlorate was not detectable in blood serum but TRR remained elevated (160 ppb) through 72 h. Milk perchlorate levels peaked at 12 h (155 ppb) and were no longer detectable by 36 h, even though TRRs were readily detected through 72 h. Perchlorate was not detectable in skeletal muscle or liver at slaughter (72 h). Chlorite and chlorate were not detected in any matrix. The only radioactive residues observed were perchlorate and chloride ion. Bioavailability of perchlorate was poor in lactating goats, but the perchlorate that was absorbed intact was rapidly eliminated in milk and urine.     

Bayesian 2-Stage Space-Time Mixture Modeling With Spatial Misalignment of the Exposure in Small Area Health Data

We develop a new Bayesian two-stage space-time mixture model to investigate the effects of air pollution on asthma. The two-stage mixture model proposed allows for the identification of temporal latent structure as well as the estimation of the effects of covariates on health outcomes. In the paper, we also consider spatial misalignment of exposure and health data. A simulation study is conducted to assess the performance of the 2-stage mixture model. We apply our statistical framework to a county-level ambulatory care asthma data set in the US state of Georgia for the years 1999?C2008.     

D-optimal designs for mixed discrete and continuous outcomes analyzed using nonlinear models

Many dose-response experiments in toxicology and other biological sciences are designed to measure multiple outcomes. Unfortunately, most of these studies are powered or designed for a single response, and the inference on the under-powered endpoints is limited. As additional design challenges, the outcomes may have different regions and shapes of activity or have different response types. As a new application to the traditional D-optimality criterion, we have developed optimal designs for mixed discrete and continuous outcomes that are analyzed with nonlinear models. These designs use a numerical algorithm to choose the location of the dose groups and proportion of total sample size allocated to each group that minimize the generalized variance of a model-based covariance matrix that incorporates the correlation between outcomes. Using this methodology, we designed a dose-response experiment with binary, count, and continuous outcomes to evaluate neurotoxicity. In this example, the optimal designs placed dose groups at the predicted dose thresholds and throughout the active range. The designs were generally robust to different correlation structures. In addition, when the expected correlation was moderate or large, we observed a substantial gain in efficiency compared to optimal designs created for each outcome separately.     

Evaluating the relationship between ecological and habitat conditions using hierarchical models

Understanding the relationship between an index of biological community state and habitat is important for policy makers and environmental managers. A common approach to modeling this relationship is to use regression. However, this simple method becomes complicated when the data are clustered and have both within-cluster and between-cluster spatial correlation. This article proposes a Bayesian hierarchical model that incorporates both types of spatial correlation. This model yields both an understanding of the within-cluster relationships as well as an overall relationship between these variables. We apply this method to evaluate the relationship between the index of biotic integrity (a common measure of fish condition) and the qualitative habitat evaluation index (a common measure of habitat quality). This method allows us to show that there is a relationship between the biological community state and habitat and that this relationship varies across river basins, while accounting for the within- and between-spatial correlations.     

Hierarchical models of animal abundance and occurrence

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.     

Using Copulas to Introduce Dependence in Dose-Response Modeling of Multiple Binary Endpoints

We propose a method for introducing dependence in the dose-response modeling of multiple dichotomous endpoints. The method uses a copula to define a joint multivariate distribution that is consistent with predetermined marginal distributions representing the individual dose-response functions for each endpoint. Use of copulas allows the marginal dose-response functions for each dose-endpoint combination to be unrestricted in form. An application of particular relevance to risk assessment is the dose-response modeling of multiple types of tumors in test animals exposed to a carcinogen, allowing for tumors at different sites in the same animal to be statistically dependent. In addition, the method can be used to address the possibility that different tissues/organs are subject to different internal doses and possibly different active moieties. These applications are illustrated with rodent cancer bioassay data from two example compounds.     

Spatial Hierarchical Modeling of Precipitation Extremes From a Regional Climate Model

The goal of this work is to characterize the extreme precipitation simulated by a regional climate model (RCM) over its spatial domain. For this purpose, we develop a Bayesian hierarchical model. Since extreme value analyses typically only use data considered to be extreme, the hierarchical approach is particularly useful as it sensibly pools the limited data from neighboring locations. We simultaneously model the data from both a control and future run of the RCM which allows for easy inference about projected change. Additionally, this hierarchical model is the first to spatially model the shape parameter which characterizes the nature of the distribution’s tail. Our hierarchical model shows that for the winter season, the RCM indicates a general increase in 100-year precipitation return levels for most of the study region. For the summer season, the RCM surprisingly indicates a significant decrease in the 100-year precipitation return level.     

An Approximate Method for Population Toxicokinetic Analysis With Aggregated Data

Standard statistical models for analyzing inter-individual variability in clinical pharmacokinetics (nonlinear mixed effects; hierarchical Bayesian) require individual data. However, for environmental or occupational toxicants only aggregated data are usually available, so toxicokinetic analyses typically ignore population variability. We propose a hierarchical Bayesian approach to estimate inter-individual variability from the observed mean and variance at each time point, using a bivariate normal (or lognormal) approximation to their joint likelihood. Through analysis of both simulated data and real toxicokinetic data from 1,3-butadiene exposures, we conclude that given information on the form of the individual-level model, useful information on inter-individual variability may be obtainable from aggregated data, but that additional sensitivity and identifiability checks are recommended.