In many areas of the world, Potato virus Y (PVY) is one of the most economically important disease problems in seed potatoes. In Taiwan, generation 2 (G2) class certified seed potatoes are required by law to be free of detectable levels of PVY. To meet this standard, it is necessary to perform accurate tests at a reasonable cost. We used a two-stage testing design involving group testing which was performed in Taiwan's Seed Improvement and Propagation Station to identify plants infected with PVY. At the first stage of this two-stage testing design, plants are tested in groups. The second stage involves no retesting for negative test groups and exhaustive testing of all constituent individual samples from positive test groups. In order to minimise costs while meeting government standards, it is imperative to estimate optimal group size. However, because of limited test accuracy, classification errors for diagnostic tests are inevitable; to get a more accurate estimate, it is necessary to adjust for these errors. Therefore, this paper describes an analysis of diagnostic test data in which specimens are grouped for batched testing to offset costs. The optimal batch size is determined by various cost parameters as well as test sensitivity, specificity and disease prevalence. Here, the Bayesian method is employed to deal with uncertainty in these parameters. Moreover, we developed a computer program to determine optimal group size for PVY tests such that the expected cost is minimised even when using imperfect diagnostic tests of pooled samples. Results from this research show that, compared with error free testing, when the presence of diagnostic testing errors is taken into account, the optimal group size becomes smaller. Higher diagnostic testing costs, lower costs of false negatives or smaller prevalence can all lead to a larger optimal group size. Regarding the effects of sensitivity and specificity, optimal group size increases as sensitivity increases; however, specificity has little effect on determining optimal group size. From our simulated study, it is apparent that the Bayesian method can truly update the prior information to more closely approximate the intrinsic characteristics of the parameters of interest. We believe that the results of this study will be useful in the implementation of seed potato certification programmes, particularly those which require zero tolerance for quarantine diseases in certified tubers

Viral diseases that can reduce yield and tuber quality are major concerns for potato growers. To produce healthy potato tubers and prevent yield reduction, a certification scheme for foundation class seed potato propagation has been established at the Seed Improvement and Propagation Station in Taiwan. The certification scheme uses an ELISA technique to index specific virus diseases such as Potato virus Y (PVY), Potato leafroll virus (PLRV), Potato virus X (PVX), Potato virus A (PVA), and Potato virus S (PVS). In order to produce foundation class potato tubers, the Dorfman group testing procedure is adopted. The Dorfman testing procedure utilizes a two-stage sampling scheme. The first stage comprises making measurements on all groups. The second stage involves no retesting for negative testing groups and exhaustive testing of all constituent individual samples of positive testing groups. In the seed potato certification scheme in Taiwan, field investigations have usually used groups of 20 plants. However, because of the limitations of available financial resources, the effect of group size on cost is an important consideration. Thus, selection of group size for design considerations is a critical issue. In order to solve the problem, we present the expected cost model as a nonlinear integer programming problem and determine the optimal group size such that the expected cost is minimized. The result demonstrates that the optimal sample size for group testing is 13 plants per group and that the cost, using this optimal group size, is not greatly different from the cost when using 20 plants per group. Thus, 20 plants per group is reasonable for the group testing procedure with regard to cost considerations. The result of this research could be useful in the execution of the seed potato certification program