Statistical Models and Bioterrorism

Abstract

In the fall of 2001 an outbreak of inhalational anthrax occurred in the United States that was the result of bioterrorism. Letters contaminated with anthrax spores were sent through the postal system. In response to the outbreak, public health officials treated over 10,000 persons with antibiotic prophylaxis in the hopes of preventing further morbidity and mortality. No persons receiving the antibiotics subsequently developed disease. The question arises as to how many cases of disease may actually have been prevented by the public health intervention of antibiotic prophylaxis. A statistical model is developed to answer this question by relating to the incubation period distribution the dates of disease onset, dates of initiation of antibiotic prophylaxis, and dates of exposure to the anthrax spores. An important complication is that the date of exposure to the anthrax spores was unknown for a cluster of cases in Florida because the contaminated letter was never found. A general likelihood function for a multicommon source outbreak is developed where the dates of exposure to the source (e.g., anthrax spores) may or may not be known. Estimates of the incubation period distribution are derived from an outbreak in Sverdlovsk, Russia. The methods are applied to the 2001 U.S. outbreak. The sensitivity of the estimates to the assumed incubation period is investigated. Properties of the estimators, particularly when the outbreak sizes are small, are evaluated by simulation. In the absence of antibiotic prophylaxis, the outbreak could have been about twice as large but unlikely would have been more than 50 cases. The results underscore the importance of early detection of outbreaks together with targeted and effective public health control measures.