Using TreeAge Pro 2009 (TreeAge Software, Williamstown, Massachusetts), we constructed a set of decision analytic computer simulation models, with probabilistic sensitivity analyses. The first type of model, the Vaccination Timing Model (depicted in and ) compared the administration of influenza vaccine to an older adult at different months of the year and the resulting incremental morbidity, mortality, and cost-effectiveness. The second type of model, the Monthly Vaccination versus No Vaccination Decision Model represented the decision of whether to vaccinate a patient in a given month (e.g., if you see an unvaccinated patient in March, should you vaccinate the patient) and the resulting incremental morbidity, mortality, and cost-effectiveness of each choice. We created a model for each month of the year from September to June.
Influenza Vaccination Timing Model Base Structure
Influenza Outcomes Tree Structure
The time frame for each of the models was one year, i.e., a single influenza season. For each model, the base case scenario assumed the societal perspective and accounted for direct and indirect costs of illness, and an additional scenario took the third-party payer perspective, considering only the direct costs of illness.
shows the different possible outcomes that each patient traveling through the model may have. After vaccination, a patient may develop local side effects, which would require one day of ibuprofen treatment or systemic side effects, which would require 3 days of ibuprofen treatment. We assumed that influenza vaccine would take at least 2 weeks to provide clinical protection. The patient's risk of subsequently contracting influenza is a function of how much time remains in the influenza season. Of the patients who develop influenza, the probability of requiring hospitalization depends on whether they were vaccinated and the effectiveness of the vaccine. Those who do not require hospitalization either just treat themselves with over-the-counter medications or visit an outpatient medical clinic, where 50% received prescriptions for anti-viral medications. Hospitalized patients have a probability of not surviving, dependent on whether they were vaccinated and the effectiveness of the vaccine. The model assumed that all older adult patients would first be hospitalized before they die from influenza. While in real life, some may pass away without being hospitalized, the majority would likely seek medical care; in fact, a percentage of older adults may undergo lengthy hospitalizations with multiple complications before succumbing (which would accrue additional costs not considered in our model). Excluding these costs may compensate for attributing hospitalizations to influenza victims who are never hospitalized.
To account for uncertainty and stochasticity, we used distributions for most of our data inputs and performed a probabilistic (Monte Carlo) sensitivity analysis, in which we simultaneously varied all parameters.
lists the various data inputs for our model (dividing them into probabilities, costs, and utilities) and the corresponding distributions and data sources used. We used beta distributions for all of our utility variables and normal distributions for all other variables. Where possible, data inputs came from published meta-analyses.
Data Inputs for Model Variables
Using the Centers for Disease Control and Prevention (CDC) monthly influenza surveillance data from 2000 to 2008 (), we created a risk distribution of influenza cases occurring each month.[6
] This distribution was stochastic to mimic variability from influenza season to season. So for each patient entering the model, the per month risk of developing influenza may be drawn from any year between 2000 and 2008. Determining the relationship between vaccine coverage and influenza activity among the overall adult population is challenging. Many other factors (e.g., vaccine coverage of children and strain matching) may play a role. Therefore, in addition to focusing on the individual rather than the overall population, we designed our simulation experiments so that they would randomly draw from one of the 2000-2007 influenza seasons. Such a time window served as a sample of years that would have enough variation in important factors such as vaccine availability, strain matching and coverage. Running millions of realizations helped minimize the effects of a single outlier influenza season.
Monthly Distribution of Influenza Cases, 2000-2008
All costs were in 2009 U.S. dollars. In the base case scenario, a 3% discount rate, the standard rate for time preference discounting, converted all costs from other years into 2009 dollars.[7
Our model measured effectiveness in quality adjusted life-years (QALY). Patients who did not develop vaccine side effects or influenza throughout our model time frame accrued 0.84 QALYs, based on the quality of life utility obtained by Gold et al
for persons 65 years or older with no health conditions.[10
] Vaccine side effects, influenza, and hospitalization each caused different decrements in QALY.[11
] The expected loss of QALYs from death came from the life expectancy in QALYs of the patient at that age. Life expectancy estimates came from the Human Mortality Database.[12
Sensitivity analyses determined the effects of varying different parameter values individually throughout the ranges listed in . Multi-dimensional sensitivity analyses were performed on selected parameters. In particular, we examined the effects of varying patient ages and levels of financial incentive ($1, $2.50, $5, $7.50, and $10 per patient) to get patients vaccinated earlier. Starting from a $0 incentive per patient, we systematically increased this incentive by $0.50 at a time until vaccination in October was no longer cost-effective. In other words, the goal was to find how high a per patient incentive could go for vaccination in October (versus later months) to remain cost-effective. In addition, we conducted probabilistic (Monte Carlo) sensitivity analyses.
Older Adult Population Model
To be conservative about the benefits of earlier vaccination, our base-case scenario model focused on the individual patient and did not consider the potential added benefits of getting a greater percentage of the overall older adult population vaccinated earlier. Earlier vaccine coverage of the population may provide herd immunity benefits, thereby decreasing the influenza attack rate. An additional scenario attempted to capture these effects. A search of the literature (including a 2006, Cochrane systematic review) found no clear correlation between influenza vaccination rates and influenza attack rates among the elderly.[13
] Therefore, without clear guidance on how to adjust the attack rate with earlier vaccination, we ran sensitivity analyses varying the effect that earlier vaccination would have on the influenza attack rate. In other words, this set of sensitivity analyses examined scenarios in which earlier vaccination would decrease the influenza attack rate by 1%, 5%, 10%, and 25%.