Using Auxiliary Information to Improve Wildlife Disease Surveillance When Infected Animals Are Not Detected: A Bayesian Approach

<div><p>There are numerous situations in which it is important to determine whether a particular disease of interest is present in a free-ranging wildlife population. However adequate disease surveillance can be labor-intensive and expensive and thus there is substantial motivation to conduct it as efficiently as possible. Surveillance is often based on the assumption of a simple random sample, but this can almost always be improved upon if there is auxiliary information available about disease risk factors. We present a Bayesian approach to disease surveillance when auxiliary risk information is available which will usually allow for substantial improvements over simple random sampling. Others have employed risk weights in surveillance, but this can result in overly optimistic statements regarding freedom from disease due to not accounting for the uncertainty in the auxiliary information; our approach remedies this. We compare our Bayesian approach to a published example of risk weights applied to chronic wasting disease in deer in Colorado, and we also present calculations to examine when uncertainty in the auxiliary information has a serious impact on the risk weights approach. Our approach allows “apples-to-apples” comparisons of surveillance efficiencies between units where heterogeneous samples were collected.</p></div

Estimates of nominal CWD surveillance weights for 8 classes of mule deer from Colorado (data from WM[15]) using a binomial complementary log-log regression model with Bayesian and maximum likelihood approaches, as well as a Poisson regression model.

<p><i>Notes</i>: The <i>Harvest-adult-M</i> category is used as the reference class in these analyses, as in WM <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089843#pone.0089843-Walsh1" target="_blank">[15]</a>. We provide both the count of CWD positive animals (<i>C</i>) and the total number sampled (<i>N</i>) from WM <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089843#pone.0089843-Walsh1" target="_blank">[15]</a>.</p

Factors controlling the departure of real and nominal weights.

<p>The red curves correspond to a prevalence ratio of 10, and the black curves correspond to a prevalence ratio of 2. For each fixed prevalence ratio, two sample sizes (plotting symbol  = 1) and (plotting symbol  = 2) are shown. For a fixed prevalence ratio and sample size, one can vary the number of positives in class 0 (<i>C₀</i>), and compute the corresponding number of positives in class 1 (<i>C₁</i>). The x-axis is <i>C₀</i>. One can then compute the nominal and real weights from <i>C₀</i>, <i>C₁</i>, <i>N₀</i>, and <i>N₁</i>. The primary determinate for departures between the real and nominal weights appears to be the number of positives in the sample (x-axis), and not the total sample size (1 versus 2 plotting symbol). The apparent prevalence ratio (red versus black) appears to play a minor secondary role.</p

Nominal weights as a function of the prevalence ratio and prevalence <i>π₀</i>.

<p>Nominal weights are shown for 5 fixed prevalence ratios: 10, 5, 2, 1, and 0.5, which are in ascending order in the figure. The x-axis is the denominator prevalence <i>π₀</i>. Nominal weights increase rapidly as the numerator prevalence <i>π₁</i> approaches 1; as the numerator class becomes more like a “perfect sentinel”.</p

Nominal and real surveillance weights calculated using data from WM[15].

<p>For real weights, a sample equivalent to reference class animals was needed to obtain the target goal, which is for the posterior probability .</p><p><i>Notes</i>: Values for nominal weights are the Bayesian posterior means of the hazard ratios. Real weights were obtained by posterior credible bound matching, described in the text.</p

Spatial and Temporal Patterns in Concentrations of Perfluorinated Compounds in Bald Eagle Nestlings in the Upper Midwestern United States

Perfluorinated chemicals (PFCs) are of concern due to their widespread use, persistence in the environment, tendency to accumulate in animal tissues, and growing evidence of toxicity. Between 2006 and 2011 we collected blood plasma from 261 bald eagle nestlings in six study areas from the upper Midwestern United States. Samples were assessed for levels of 16 different PFCs. We used regression analysis in a Bayesian framework to evaluate spatial and temporal trends for these analytes. We found levels as high as 7370 ng/mL for the sum of all 16 PFCs (∑PFCs). Perfluorooctanesulfonate (PFOS) and perfluorodecanesulfonate (PFDS) were the most abundant analytes, making up 67% and 23% of the PFC burden, respectively. Levels of ∑PFC, PFOS, and PFDS were highest in more urban and industrial areas, moderate on Lake Superior, and low on the remote upper St. Croix River watershed. We found evidence of declines in ∑PFCs and seven analytes, including PFOS, PFDS, and perfluorooctanoic acid (PFOA); no trend in two analytes; and increases in two analytes. We argue that PFDS, a long-chained PFC with potential for high bioaccumulation and toxicity, should be considered for future animal and human studies

Supplement 1. Annotated WinBUGS source code containing the models described in this paper.

File List s1.txt-- annotated WinBUGS code Description Code for running the occupancy models described in the paper is included in this Supplement. This code can be modified by users to fit their individual needs. The R2WINBUGS function in R can be used for running this code. </blockquote

Appendix A. List of species common names, scientific names, American Ornithologists' Union codes, and total number of detections for a dry coniferous forest in Washington State, USA.

List of species common names, scientific names, American Ornithologists' Union codes, and total number of detections for a dry coniferous forest in Washington State, USA

Appendix B. Estimates of alpha (the treatment effect) with random effects (i.e., the borrowing of information from other species) and without random effects.

Estimates of alpha (the treatment effect) with random effects (i.e., the borrowing of information from other species) and without random effects

Sampling locations of sea ducks in the North Atlantic region.

<p>Sampling locations of sea ducks in the North Atlantic region.</p