A Bayesian approach to assess the accuracy of a diagnostic test based on plant disease measurement

The proportion of diseased plant organs measured before chemical treatment is often used to make an assessment of the need for crop protection in agricultural plots, but such diagnostic tests are not perfect and sometimes lead to incorrect decisions. The area under the receiver operating characteristic (ROC) curve is a popular index of the overall performance of a test. It can be interpreted as the probability that the test value for a randomly chosen diseased subject will exceed that of a randomly chosen disease-free subject. In this paper, we present a Gaussian/Binomial model to assess the accuracy of diagnostic test based on a measured proportion of diseased plant organs. The model parameters were estimated from a real dataset and the model was used to analyse the accuracy of a diagnostic test based on a measured proportion of oilseed rape flowers contaminated by Sclerotinia sclerotiorum. The results showed that the accuracy of the test depends on the number of collected flowers, but that it is not necessary to collect more than 40 flowers per plot. A simulation study showed that the bias of the estimator of the area under the ROC curve was near zero for all size of dataset and that its mean-square error decreased in function of the number of experimental plots used in the ROC analysis. A major interest of our approach is that it allows one to study the effect of the sample size of the organs on the accuracy of the test. It can also be used to estimate the probability of disease occurrence, and to determine a decision threshold according to the sensitivity and specificity values.