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

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

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

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

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Part 2 - data for multinomial partitioning when an end point occurs with prior prediction probabilities to account for uncertainty, data are pipe delimited

Participant diversity and publication growth.

<p>(A) Proportion of lead author affiliation disciplines across all 1,551 papers published in journals in the three major journal communities. “Math” here encompasses “math” and “stat” affiliations; “ecol” encompasses “eco,” “evo,” and “biol” affiliations; “vet” captures “vet,” “animal health,” and “animal science;” “Med” captures “med” and pharmacy affiliations. (B) Number of papers captured by our search through time. Blue = veterinary community; gold = ecology community; red = group 3. Numbers are the annual percent growth rate within each community. Data to generate this figure are contained in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002448#pbio.1002448.s001" target="_blank">S1 Data</a>.</p

Citation benefits of author diversity.

<p>Associations between author diversity and citation rate for papers in each journal community. Model estimates are derived from a Poisson mixed effects model with an offset term for years since publication, and coefficient estimates are reported in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002448#pbio.1002448.s018" target="_blank">S8 Table</a>. Predictions are calculated for papers published in 2010, with 25% of citations to other journal communities and 75% of citations to the paper’s own community. Data to generate this figure are contained in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002448#pbio.1002448.s001" target="_blank">S1 Data</a>.</p

Cross-disciplinary citations through time.

<p>(A) Citations from papers in ecology journals to papers in each journal community. (B) Citations from papers in veterinary journals to papers in each journal community. (C) Citations from papers in Group 3 journals to papers in each journal community. Shaded regions are 95% confidence intervals from a Poisson generalized additive model fit to each journal community's time series. Data to generate this figure are contained in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002448#pbio.1002448.s001" target="_blank">S1 Data</a>.</p

Model objectives from the three journal communities.

<p>(A) Study system: agricultural (domestic animals), human, hypothetical, plant, or wildlife. (B) Applied, basic science, or management objectives by community. “Applied science” was used to describe scenarios in which basic science questions were addressed using systems of management interest. (C) Predictive or descriptive modeling intent. Error bars depict 95% binomial confidence bounds. Data to generate this figure are contained in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002448#pbio.1002448.s002" target="_blank">S2 Data</a>.</p