Page 46 - 20dynamics of cancer

AGE OF CANCER INCIDENCE 31

-RGMHIRGI

(YVEXMSR ]IEVW

Figure 2.9 Age-specific incidence of tumor onset as a function of duration of
exposure to a carcinogen. The circles show the observed median duration, the
time until one-half of the experimental rats has esophageal tumors in response
to chronic exposure to N-nitrosodiethylamine (NDEA) in drinking water (Peto
et al. 1991). Each observed median corresponds to a group of rats treated with
a different dosage, as shown in Figure 2.10. For each observed median, I calcu-
lated the incidence line from Eq. (2.2). These calculated lines matched well the
observed age-specific incidences in each experimental group (Peto et al. 1991).
with time. Peto et al. (1991) showed mathematically that the constant b
is related to m, the median duration of carcinogen exposure to tumor
onset, as
b =− ln (0.5)m −n = 0.693m −n .
Later I will show how to derive this result. From the laboratory observa-
tions, Peto et al. (1991) estimated n = 7, so we can describe age-specific
incidence for this experiment as

I = 4.85m −7 6
t ,
and, on a log-log scale,

log (I) = log (4.85) − 7 log (m) + 6 log (t) . (2.2)
This equation and Figure 2.9 show that the median, m, sets the pattern
of incidence.
In the study by Peto et al. (1991), the observed relation between me-
dian duration and dosage followed the classical dose-response formula
given by Druckrey (1967),
n
r
k = d m , (2.3)