Computation and Measurement of Risk - Mathematics and Statistics for the Environment - page 209

Given the proven causal relationship between cigarette smoking and lung cancer, and assuming that
the groups were comparable in all other ways, once could say that about 88% of the lung cancer
among smokers of 1 to 14 cigarettes per day might be attributable to their smoking. The remaining
12% of the lung cancer cases in this group would have occurred anyway.

8.7.2 v aCCine e FFiCaCy or v aCCine e FFeCtiveness
Vaccine efficacy and vaccine effectiveness measure the proportionate reduction in cases among
vaccinated persons. Vaccine efficacy is used when a study is carried out under ideal conditions—
for example, during a clinical trial. Vaccine effectiveness is used when a study is carried out under
typical field (that is, less than perfectly controlled) conditions. Vaccine efficacy/effectiveness (VE)
is measured by calculating the risk of disease among vaccinated and unvaccinated persons and
determining the percentage reduction in risk of disease among vaccinated persons relative to unvac-
cinated persons. The greater the percentage reduction of illness in the vaccinated group, the greater
the vaccine efficacy/effectiveness. The basic formula is written as

Risk among unvaccinatedgroup − risk among va ccinatedgroup

Risk among unvaccinatedgroup

or

1 - Risk ratio

In the first formula, the numerator (risk among unvaccinated - risk among vaccinated) is sometimes
called the risk difference or excess risk .
Vaccine efficacy/effectiveness is interpreted as the proportionate reduction in disease among
the vaccinated group, so a VE of 90% indicates a 90% reduction in disease occurrence among the
vaccinated group, or a 90% reduction from the number of cases you would expect if they have not
been vaccinated.

■ EXAMPLE 8.25
Problem: Calculate the vaccine effectiveness from the Varicella data in Table 8.10.

Solution:

VE = (42.9 - 11.8)/42.9 = 31.1/42.9 = 72%

Alternatively,

VE = 1 - RR = 1 - 0.28 = 72%

So, the vaccinated group experienced 72% fewer Varicella cases than they would have if they had
not been vaccinated.

REFERENCES AND RECOMMENDED READING
Arias, E., Anderson, R.N., Kung, H-F., Murphy, SI., and Kochanek, K.D. (2003). Deaths: final data for 2001.
National Vital Statistics Reports , 52(3), 1-116.
CDC. (1999). Summary of notifiable diseases—United States, 1998. MMWR , 47(53), 1-93.
CDC. (2001). Summary of notifiable diseases—United States, 1999. MMWR 48(53), 1-104.
CDC. (2003). Summary of notifiable disease—United States, 2001. MMWR , 50(53), 1-108.
CDC. (2004). Reported Tuberculosis in the United States, 2003 . U.S. Centers for Disease Control and
Prevention, Atlanta, GA.