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

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

Appendix D. A table of the weekly counts of House Finches, estimated encounter probabilities, estimated prevalence, and relative bias in apparent prevalence.

A table of the weekly counts of House Finches, estimated encounter probabilities, estimated prevalence, and relative bias in apparent prevalence

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

Appendix A. A general formula for corrected prevalence.

A general formula for corrected prevalence

Appendix B. The derivation of the approximate conditional variance for the reduced form prevalence estimator presented in the text.

The derivation of the approximate conditional variance for the reduced form prevalence estimator presented in the text

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

Appendix C. An evaluation of bias of an approach to prevalence estimation in a special case.

An evaluation of bias of an approach to prevalence estimation in a special case

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

Appendix E. Figures showing the bias in apparent prevalence as a function of a range of differences in health-state-specific detection probabilities.

Figures showing the bias in apparent prevalence as a function of a range of differences in health-state-specific detection probabilities