# Determination of Eleven Veterinary Drugs in Chicken Meat and Liver
## 3 Results and Discussion
### Feed Additives
The main discrete models used in the PNCRC are based on the Hypergeometric and Binomial Distribution Models. The Hypergeometric Model aims to describe the number of successes (for example, a sample violating the MRL of a given residue displayed at the PNCRC) in a sequence of \"N\" extractions from a finite population of small size, without replacement. In this case, the effect of sampling without replacement significantly impacts in the coming probabilities of a new successful sample. For this situation, the sample distribution must be based on the Hypergeometric Distribution. In populations of larger sizes (N > 5000 units, for instance), the effect of sampling without replacement is negligible. Thus, the Binomial Distribution can be used to determine an appropriate number of samples to be used, as the number of samples for a high confidence coefficient defined previously, will be constant for populations over 5000 evaluated units [25]. PNCRC for poultry, swine, and cattle (and other species) fall into this category, given the number of animals normally slaughtered along one year. For adoption of the Binomial Distribution Model, initially a certain residue/contaminant is quantified in a particular number of samples and, subsequently, each sample is classified as a Binary Variable as: 0 = does not violate the MRL for market \"X\" or 1 = violates the MRLs for the same \"X\" market. Thus, each sample behaves like a success and failure test, characterized as a classic Bernoulli distribution model, where the sum of \"N\" Bernoulli results in the Binomial Probability Distribution. Thus, the Binomial model is more likely to be suitable for PNCRC because the populations of interest (cattle, poultry, swine, etc.) consist of thousands of individuals and/or units. When non-compliance results are detected (for example, MRL violations of a given residue \"X\"), it is possible to obtain an estimate of likely prevalence of each residue in the general population. However, when no non-compliant results are found or the behavior of residue \"X\" is unknown, as is the case for some residues not yet assessed by the PNCRC, any claims about prevalence should be stated with a defined confidence coefficient, so that the prevalence of non-compliant results does not exceed a specified percentage. In this case, a prevalence of 1% is usually adopted when the behavior of residue \"X\" is unknown. The number of samples needed to provide a high coefficient of confidence to detect at least one non-compliant result is around 300 samples [25]. For a 95% probability of detecting a violation, if it occurs in 1% of the population, the survey should be done in 299 units of that population, a number that is rounded to 300, for practical purposes as recommended by MAPA [26]. That means that 300 samples per evaluated compound are a reasonable amount to be dealt with when referring to chemical residues in poultry farming. This minimum amount is important for the establishment of plans/protocols that are being implemented for the first time and whenever necessary, the sampling plan can be revised. Therefore, considering our satisfactory results and that more evaluations of each compound are carried out annually, making the Brazilian protocol increasingly robust, it is possible to increase the non-compliance limit from 1.0% to 1.5% for the substances allowed in national poultry farming (that means all residues evaluated in 300 samples according to the third column in Table 1). In this situation, the sampling calculated by the binomial model to guarantee (with 95% confidence) that there would be at least one sample above the MRL would be 199 per year, rounded up to 204 samples for convenience, representing 17 monthly samples. Therefore, instead of 300 samples analyzed annually, this number can be reduced to 204 samples per year. For substances not allowed in Brazilian poultry farming (for instance, those described in item 2.3), sampling must be maintained according to the ongoing protocol (60 samples/year).