1. Statistical analysis A maximum likelihood function L(p i ) consisting of binomial frequency functions was set up and used in estimating the 4 prevalence values in estimation a) and c) (equation given below). In the case of sequential estimation, a), the conditional maximum likelihood function was applied. Firstly, the parameter which was most well-determined was estimated, secondly the parameter which was second best determined was estimated and so on. The order of estimation happened to be: p I, p II, p III and p IV. In the case of simultaneously estimation, b), we did not use the maximum likelihood function in estimating the parameters; we used a linear model to describe an approximate relations between the pool-prevalence and the 4 level-specific prevalences, the equation is given below. The covariance values and the standard deviations of the parameter estimates were found from the inverse Hessian matrix. j is the index for each pool-combination. a) b) c) The same as a) but with no conditions Abstract Estimation of different prevalence values (p I, p II, p III and p IV ) from pooled samples is carried out by setting up a maximum likelihood function and subsequently optimizing this function. The estimation of the prevalence values has been performed in 3 different ways: a) sequential estimation of the 4 prevalences from a conditional maximum likelihood function, b) simultaneously estimation based on an approximation, and c) simultaneously estimation from the maximum likelihood function. When the prevalence estimates are very little correlated the sequential estimation a) is close to the ‘true’ value in estimation c). When the prevalence values are very small (close to 1%) then the simultaneously estimation b) based on an approximation is close to the ‘true’ value in estimation c). The prevalence estimates from a) the sequential estimation, differ somewhat from the simultaneously estimations b) and c). The largest correlation between the parameter estimates is found between p II and p IV and has a magnitude of -0.29. The standard deviations estimated by b) the simultaneously estimation based on an approximation, are somewhat smaller than the standard deviations from a) and c). Introduction A risk assessment on Salmonella DT104 in slaughter pigs was conducted in 2003. For this risk assessment, Salmonella prevalence values of carcasses originating from different herd groups (level I, II, III and IV) had to be obtained. Due to the sampling procedure (surveillances data) the samples were pooled independently of original herd levels. The purpose of this estimation was to obtain estimates of level-specific prevalences (one for each level) from pooled samples and to compare the 3 different estimation methods. Estimating 4 different Salmonella prevalence values of pig carcasses from pooled samples Helle Mølgaard Sommer and Jens Strodl Andersen Institute for Food and Veterinary Research (DFVF), Denmark, hms@fdir.dk Results The results showed that the prevalence value from level I, p I is significant different from the prevalence value from level II, p II. Non of the other prevalence values are significant different from each other, most likely due to too few pools where samples from level III and IV entered into (179 and 151 respectively). In comparison, the number of pools where samples from level I and II entered into was more than 7,000 and 2,000 respectively. In the figure the profile likelihood for the four different levels is show in the interval 2 times standard deviation of the prevalence estimates. The results of the different estimation methods a), b) and c) showed little difference between the three estimations due to relative low correlation between the prevalence estimates and prevalence estimates less than 3%. Data The data used in the estimation of the four prevalence values is surveillance data. According to the serologic Salmonella surveillance implemented in Denmark, slaughter pig herds are divided into three infection levels (I, II and III). For this project, we defined a fourth level of pig herds outside the surveillance program producing less than< 200 finishers per year. The data was pooled in 5, in order to save the amount of samples that were analyzed for being either Salmonella positive or negative. The pooled samples consisted of 5 swab samples taken from 5 different pig carcasses at the end of the slaughter line. The pooled samples were analyzed for the presence of Salmonella. (Salmonella data was used as surrogate for Salmonella DT104). If one or more of the individual swab samples are positive then the pooled sample is positive. For each pooled sample, the levels of the 5 individual swab samples were known. In a pooled sample, the 5 swab samples come from one or more different levels. For example, a pool-combination could be samples from levels I, I, I, II, IV. In total, more than 7,000 pooled samples, with different combinations of levels, were available. ? ? ? ? ? Level I II I I IV Pooled sample Salmonella positive Salmonella negative Estimation methoda) sequentialb) approximatec) full, simultan. p I (SD) 0.97% (0.06%)0.96% (0.06%)0.97% (0.06%) p II (SD) 2.11% (0.89%)2.20% (0.75%)2.39% (0.93%) p III (SD) 2.50% (1.84%)1.54% (1.14%)1.85% (1.55%) p IV (SD) 2.57% (2.11%)2.26% (1.59%)2.36% (2.14%) Profile likelihood in the interval: 2 x SD, for each of the 4 prevalence estimates Software: S-Plus 6.2 For estimation method a) and c) : routine nlminb, optimizer quasi-Newton and for method b) : glm link=identity Prevalence estimates plus their standard deviation (SD) for estimation method a), b) and c).