Methodological approach for substantiating disease freedom in a heterogeneous small population. Application to ovine scrapie, a disease with a strong genetic susceptibility.

Demonstrating disease freedom is becoming important in different fields including animal disease control. Most methods consider sampling only from a homogeneous population in which each animal has the same probability of becoming infected. In this paper, we propose a new methodology to calculate the probability of detecting the disease if it is present in a heterogeneous population of small size with potentially different risk groups, differences in risk being defined using relative risks. To calculate this probability, for each possible arrangement of the infected animals in the different groups, the probability that all the animals tested are test-negative given this arrangement is multiplied by the probability that this arrangement occurs. The probability formula is developed using the assumption of a perfect test and hypergeometric sampling for finite small size populations. The methodology is applied to scrapie, a disease affecting small ruminants and characterized in sheep by a strong genetic susceptibility defining different risk groups. It illustrates that the genotypes of the tested animals influence heavily the confidence level of detecting scrapie. The results present the statistical power for substantiating disease freedom in a small heterogeneous population as a function of the design prevalence, the structure of the sample tested, the structure of the herd and the associated relative risks.