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

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).