A stochastic simulation model to determine the sample size of repeated national surveys to document freedom from bovine herpesvirus 1 (BoHV-1) infection

Abstract

Background: International trade regulations require that countries document their livestock's sanitary status in general and freedom from specific infective agents in detail provided that import restrictions should be applied. The latter is generally achieved by large national serological surveys and risk assessments. The paper describes the basic structure and application of a generic stochastic model for risk-based sample size calculation of consecutive national surveys to document freedom from contagious disease agents in livestock.

Methods: In the model, disease spread during the time period between two consecutive surveys was considered, either from undetected infections within the domestic population or from imported infected animals. The @Risk model consists of the domestic spread in-between two national surveys; the infection of domestic herds from animals imported from countries with a sanitary status comparable to Switzerland or lower sanitary status and the summary sheet which summed up the numbers of resulting infected herds of all infection pathways to derive the pre-survey prevalence in the domestic population. Thereof the pre-survey probability of freedom from infection and required survey sample sizes were calculated. A scenario for detection of infected herds by general surveillance was included optionally.

Results: The model highlights the importance of residual domestic infection spread and characteristics of different import pathways. The sensitivity analysis revealed that number of infected, but undetected domestic herds and the multiplicative between-survey-spread factor were most correlated with the pre-survey probability of freedom from infection and the resulting sample size, respectively. Compared to the deterministic pre-cursor model, the stochastic model was therefore more sensitive to the previous survey's results. Undetected spread of infection in the domestic population between two surveys gained more importance than infection through animals of either import pathway.

Conclusion: The model estimated the pre-survey probability of freedom from infection accurately as was shown in the case of infectious bovine rhinotracheitis (IBR). With this model, a generic tool becomes available which can be adapted to changing conditions related to either importing or exporting countries.

Figure 1

Basic model structure and cattle import pathways. Basic structure of the stochastic simulation model to estimate the pre-survey probability of freedom from infection as applied to BoHV-1. Three main pathways of infectious agent introduction into the susceptible domestic population were considered. + = infected, - = uninfected, D = infection status of animal, T = diagnostic test status of animal, H = herd status

Figure 2

Cumulative probability distribution of pre-survey prevalence with increasing numbers of positive samples detected. Effect of increasing residual herd prevalence (HP) on the pre-survey prevalence estimates prior to the consecutive survey at a threshold HP of 0.2% (vertical black bar). Pre-survey herd prevalence was estimated using cumulative herd prevalence beta-distributions defined by a fixed sample size (N = 2400) and increasing numbers of positive samples

Figure 3

Comparative sample size of serological surveys derived from the pre-SPF. Comparative sample sizes for the follow-up survey derived from the model output pre-survey probability of infection freedom (pre-SPF). Standard sample sizes (SSS), risk-based sample sizes (RBS), with or without detection of newly infected herds, were used to define the herd prevalence (HP) of the previous survey. Ninety-five percent confidence intervals of pre-survey probability of infection freedom and hence resulting sample sizes, were obtained by exact binomial confidence intervals based on the proportion of iterations with values < 0.2 and < 0.1%, respectively, to the total number of iterations performed. Sample sizes were calculated with Survey Toolbox^® assuming a population of 50,000 herds, 99% herd sensitivity for diagnostic testing and a threshold HP of 0.2% and 0.1%, respectively.