Case Study: Economic Evaluation of a Smallpox Attack Composite page for printing

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The Context
The concern that a rogue nation or a terrorist group might mount an attack with the use of a biologic weapon has motivated multiple studies on the consequences of bioterrorism attacks and optimal response strategies.
We develop the case study based on a published paper to illustrate the outcomes associated with two possible smallpox related alternative scenarios, which are listed below.
Scenario 1: Airport Attack
Equipped with portable nebulizers, the terrorists go to the 10 largest U.S. airports during busy periods and distribute smallpox virus in domestic terminals. They infect 5,000–200,000 persons who are present in the terminals during those times.
Scenario 2: Hoax
An activist mails a threatening letter containing monkeypox to a clinic in a city of 500,000 persons. Field tests are positive for poxvirus, and health officials vaccinate 25 health-care workers and patients at the clinic. Fortunately, no infections occur.
Methods
U.S. population at large
Prospective
Societal
The Model: Data and Assumptions
A mathematical model is constructed to describe the smallpox outbreaks in the population of interest, based on the probabilistic development of infection among persons initially infected. The preparedness and response strategies below were modeled.
Vaccination of contacts and isolation
Postattack vaccination of health-care workers
Postattack vaccination of health-care workers and public
Previous vaccination of health-care workers
Previous vaccination of health-care workers and postattack vaccination of public
Previous vaccination of health-care workers and public
The following consecutive stages of smallpox are experienced by each person:
  • incubation,
  • fever,
  • rash,
  • scab formation, and
  • recovery.
The duration of each stage, the rate of death, and the rate of transmission are determined probabilistically.
The mean durations of the stages of smallpox infection are derived from the literature. The death rates for the unvaccinated persons, persons vaccinated in the remote past, and persons infected after recent vaccination are determined based on the natural history of smallpox.
The vaccine effectiveness among persons vaccinated once (as would occur with vaccination of contacts) and repeatedly vaccinated, as well as rates of serious complications and mortality caused by complications, are identified from the literature.
Assumptions
Our assumptions are:
  • 98% of heath-care worker contacts, 80% of other close contacts, and 50% of distant contacts will be identified.
  • 60% of 290 million U.S. residents will be vaccinated in pre- or postattack vaccination of the public.
  • Vaccination of health-care workers means that 90% of 10.1 million health-care workers will be vaccinated.
The number and timing of new cases were simulated by multiplying a randomly selected value for infectiousness by the daily rate of new infections. The daily rate of new infections is determined by the relevant specified value for the reproductive rate.
The reproductive rate (the average number of next-generation cases of smallpox arising from the current generation of cases) varies with the pattern of spread. The patterns of spread are identified as:
  • hospital,
  • community, and
  • hospital and community.
Among the model parameters are
  • the reproductive rate before the implementation of control measures,
  • the reproductive rate after the implementation of control measures,
  • the number of days the control measures are implemented.
These parameters vary for the different response strategies mentioned above.
The outbreaks are simulated for a specified number of days or until they die out.
The Decision Rule
The goal for the decision rule for selecting the optimal strategy is to maximize net benefits (more gains than losses).
For:
Net benefit > 0
Net gains > Net losses
( Probability of attack x Lives saved given an attack ) > ( Probability of no attack x Lives lost given no attack )
We can use this formula to determine the policy threshold, which is the probability of attack beyond which the expected number of lives saved with the response strategy in case of an attack exceeds the expected number of deaths from the strategy in the absence of attack. From the definition of complementary probabilities, we have
Probability of no attack = ( 1 Probability of attack )
Substituting in the formula above, we have
( Probability of attack x Lives saved given an attack ) > [ ( 1 Probability of attack ) x Lives lost given no attack ]
By factoring and rearrangement, the policy threshold is
Probability of attack > [ Lives lost given no attack / ( Lives lost given no attack + Lives saved given an attack ) ]
Results
The Number of Vaccinations for Each Strategy
The number of vaccinations administered for each response strategy for both scenarios is reported in the table below.
Approximate Number of Vaccinations According to the Control Strategy
Control strategy * Hoax Airport
  (in thousands)
Vaccination of contacts and isolation 0 680
Postattack vaccination of health-care workers 9 9,700
Postattack vaccination of health-care workers and public 0 177,000
Previous vaccination of health-care workers 9,100 9,600
Previous vaccination of health-care workers and postattack vaccination of public 9,100 177,000
Previous vaccination of health-care workers and public 177,000 177,000
* Vaccination of contacts and isolation are part of all control strategies.
For example, the strategy of vaccinating and isolating contacts (ST 1) results in
  • 0 vaccinations in the hoax scenario, and
  • 680,000 vaccinations in the airport attack scenario.
Outcomes
The expected number of deaths for each response strategy is presented in the table below.
Expected Deaths as a Result of Smallpox and Vaccination
Control strategy * Hoax Airport
ST 1: Vaccination of contacts and isolation  
  Deaths from smallpox 0 2,733
  Deaths from vaccination 0 2
  Total number of deaths 0 2,735
ST 2: Postattack vaccination of health-care workers  
  Deaths from smallpox 0 2,731
  Deaths from vaccination 0 26
  Total number of deaths 0 2,757
ST 3: Postattack vaccination of health-care workers and public  
  Deaths from smallpox 0 2,631
  Deaths from vaccination 0 482
  Total number of deaths 0 3,113
ST 4: Previous vaccination of health-care workers  
  Deaths from smallpox 0 2,192
  Deaths from vaccination 25 26
  Total number of deaths 25 2,218
ST 5: Previous vaccination of health-care workers and postattack vaccination of public  
  Deaths from smallpox 0 2,114
  Deaths from vaccination 25 482
  Total number of deaths 25 2,596
ST 6: Previous vaccination of health-care workers and public  
  Deaths from smallpox 0 641
  Deaths from vaccination 482 482
  Total number of deaths 482 1,123
* Vaccination of contacts and isolation are part of all control strategies.
From the outcomes in the table above, we can draw the following conclusions:
  • The strategy of vaccinating and isolating contacts (ST 1) results in
    • 0 deaths in the hoax scenario, and
    • 2,735 deaths in the airport attack scenario.
  • Control strategies involving vaccination of the public (ST 3, ST 5, and ST 6) result in considerable number of deaths as a result of vaccination complications (e.g., 482 deaths for the airport attack scenario).
  • Previous vaccination of health-care workers (ST 4) results in 2,218 deaths in the case of the airport attack scenario.
  • Adopting ST 5 (a strategy that is broader in scope than ST 4 because it includes postattack vaccination of the public) results in 2,596 deaths, which is higher than the number of deaths for ST 4.
  • However, if the strategy adopted involved previous vaccination of the public (ST 6), the total number of deaths is 1,123 in the airport attack (despite the increase in the number of deaths from vaccination).
  • Therefore, the preferable strategies resulting in the lowest numbers of deaths are the previous vaccination of health-care workers only (ST 4) and the broader strategy of previous vaccination of health-care workers and the public (ST 5).
  • The optimal policy, which minimizes the number of deaths, depends on the probability of attack, as shown in the graph below.
    Optimal Policy Varies with the Probability of Attack
    This chart shows how the policy for previous vaccination varies with the probability of attack. If the probability is less that 0.05, no vaccinations should be performed. If the probability is between 0.05 and .23, health-care workers should be vaccinated. If the probability is greater than .23, then both health-care workers and the public should be vaccinated.
    This graph shows:
    • Previous vaccination of health-care workers is expected to save lives if the probability of attack is above 0.05.
    • Previous vaccination of the public is expected to save lives at a probability of >0.23. Therefore, previous vaccination of health-care workers is expected to save lives at a lower threshold probability of an attack.
Sensitivity Analysis
Federal decisionmakers should consider the risks and benefits for the whole nation, whereas local officials should balance local benefits and risks. Simulations indicate that the thresholds for local policymakers are lower than those for national policymakers because the expected number of vaccine complications within a given region is limited.
Variations in the time required to recognize the outbreak and the initial reproductive rate affect the policy threshold the most, compared with the impact of other assumptions. Changes in assumptions have smaller effects on thresholds for previous vaccination of the public.
Conclusions
The major determinant of benefits of various bioterrorism preparedness and response strategies is the probability of an attack.
The benefits in terms of expected lives saved must be compared with the expected loss of lives as a result of infection spread and vaccination.
The benefits of the strategy of previous vaccination of health-care workers outweigh the expected losses at substantially lower attack probabilities than those of the strategy of previous vaccination of the public.
Therefore,
  • the optimal preparedness and response policy at lower probabilities of attack is the vaccination of health-care workers and
  • vaccination of the public is preferable only if the probability of an attack is high.
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