After licensure, the utilization of a vaccine increases until it reaches a steady state. Vaccination program costs also increase to a steady state (as would the numbers of adverse effects, if applicable). The rate at which a vaccine is adopted depends on provider and target population attitudes toward the new vaccine and other issues discussed in Chapter 6.
Predictions of the time to adoption for the various candidate vaccines are shown in Table 7.2. The major factor considered in estimating these times was the perception in the developing world of the seriousness of the disease threat. The times may be affected by such factors as governmental or donor purchase programs, or by the combination of new vaccines with vaccines currently delivered via the World Health Organization Expanded Program on Immunization (WHO-EPI). These factors were not considered in arriving at the times in Table 7.2, but the effects of adopting alternative values could be evaluated easily (see Appendix F).
The time between the probable age of vaccine administration and the probable age of disease occurrence without vaccination is termed the delay of vaccination benefits. This time must be determined separately for each vaccine (consider the difference between the vaccines for Hemophilus influenzae type b and hepatitis B virus) and is a component of the total time to the steady-state yield of vaccine benefits. Information used to determine the delay is shown in Table 7.1, and the derivation of the time to steady-state yield of benefits is shown in Table 7.2.
In the calculations presented later in this chapter, the present values of vaccine costs are calculated on the assumption that costs are incurred from the time at which steady-state vaccine use is achieved. The present values of health benefits and expected reduction in morbidity costs are calculated on the assumption that the benefits and reduced costs occur at the time of steady-state yield of vaccine benefits. Equations for deriving present values are given in Chapter 3.*
If desired, a more exact procedure can be used for these calculations—one that accounts for the presumably linear increase from zero at the time of licensure to the values at the steady state. This is accomplished by substituting in the discounting process (Chapter 3) an adjusted time, T*, for the time to adoption or for the time after licensure to a steady-state yield of benefits (time to adoption plus delay of vaccination benefits). The general equation defining T* is
T*=−1/r 1n[1/2 (1+e−rT)],
where T is the time to adoption or the time from licensure to steadystate yield of benefits, and r is the discount rate, in this analysis, the discount rate adopted is 0.05, so
T*=−20 1n[1/2 (1+e−0.05T)].