The probability of failing in detecting an infectious disease at entry points into a country

In a group of N individuals, carrying an infection with prevalence π , the exact probability P of failing in detecting the infection is evaluated when a diagnostic test of sensitivity s and specificity s′ is carried out on a sample of n individuals extracted without replacement from the group. Furthermore, the minimal number of individuals that must be tested if the probability P has to be lower than a fixed value is determined as a function of π . If all n tests result negative, confidence intervals for π are given both in the frequentistic and Bayesian approach. These results are applied to recent data for severe acute respiratory syndrome (SARS). The conclusion is that entry screening with a diagnostic test is rarely an efficacious tool for preventing importation of a disease into a country. Copyright © 2005 John Wiley & Sons, Ltd.