Empirical Bayesian Estimation of the Disease Transmission Probability in Multiple‐Vector‐Transfer Designs

Abstract

Plant disease is responsible for major losses in agriculture throughout the world. Diseases are often spread by insect organisms that transmit a bacterium, virus, or other pathogen. To assess disease epidemics, plant pathologists often use multiple-vector-transfers. In such contexts, groups of insect vectors are moved from an infected source to each of n test plants that will then be observed for developing symptoms of infection. The purpose of this paper is to present new estimators for p, the probability of pathogen transmission for an individual vector, motivated from an empirical Bayesian approach. We specifically investigate four such estimators, characterize their small-sample properties, and propose new credible intervals for p. These estimators remove the need to specify hyperparameters a priori and are shown to be easier to compute than the classical Bayes estimators proposed by Chaubey and Li (1995, Journal of Official Statistics 11, 1035-1046) and Chick (1996, Biometrics 52, 1055-1062). Furthermore, some of these estimators are shown to have better frequentist properties than the commonly used maximum likelihood estimator and to provide a smaller Bayes risk than the estimator proposed by Burrows (1987, Phytopathology 77, 363-365).

Robust procedures for experimental design in group testing considering misclassification

“…However, the maximum likelihood estimator of p is biased while using group testing (Swallow, 1985). There are better estimators than the maximum likelihood estimator, referring to Hepworth and Watson (2009) and Bilder and Tebbs (2005). Besides, we assume that sensitivity and specificity are not influenced by the prevalence or the group size.…”

Debiased Estimation of Proportions in Group Testing

“…In a large number of simulations, Burrows found the bias ofp to range from 1% to 5% of that ofp, and the MSE to be uniformly less than MSE(p). Bilder and Tebbs (2005) proposed an empirical Bayes estimator which also gave much smaller bias and MSE thanp, and almost as small asp. A more general bias adjustment, which was not specifically derived for group testing, was described by Gart (1991).…”

Evaluation of a Frequentist Hierarchical Model to Estimate Prevalence When Sampling from a Large Geographic Area Using Pool Screening

“…Note that $\hat{\beta }=\frac{\mathit{Mn}}{T}-n$ is the same estimator as obtained by Bilder and Tebbs (2005) in their empirical Bayes approach using the method of moments and taking α = 1 in their Beta prior. However, their approach is based on a completely different philosophy (i.e.…”