Page 184 - 20dynamics of cancer

CARCINOGENS 169

500

Incidence per 10 5 400 300

100 200

0
0 10 20 30 40
Dose (cigarettes/day)

Figure 9.1 Dose-response for cigarette smoking, standardized for age. The
filled circle and error bars mark the mean and 90% confidence interval at various
dosages. The solid line shows the quadratic fit given by Doll and Peto (1978)
2
5
with incidence per 10 equal to 9.36(1 + d/6) . The dashed curve shows my
5
calculation in which a nearly equivalent fit for incidence per 10 individuals can
5
be obtained with a higher power of dose, in this case 25(1 + d/46) . Redrawn
from Figure 1 of Doll and Peto (1978).
total incidence over the duration of exposure (see Background above
and Section 7.5). In empirical studies of dose-response, one typically
observes that CI increases approximately with the rth power of dose
r n
and the nth power of duration, CI(τ) ≈ cd t . Then for the fixed level
of cumulative incidence that occurs at the median duration to tumor
r
n
development, τ = m, we have CI(m)/c ≈ d m . Taking the logarithm
of both sides and solving for log(m) yields
log (m) ≈ (1/n) log (k) − (r/n) log (d) , (9.4)

where k = CI(m)/c is a constant estimated from data. This equation
is the expression of the classical Druckrey formula that I presented in
Eq. (2.4).