Page 47 - 20dynamics of cancer

32 CHAPTER 2

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Figure 2.10 Esophageal tumor dose-response line. The circles show the same
observed median durations as in Figure 2.9. Here, each median duration is
matched to the dosage level for that experimental group of rats. The line shows
the excellent fit to the Druckrey formula expressed in Eq. (2.4), with r = 3, n = 7,
k = 0.036, and a slope of −r/n =−1/s =−1/2.33. Data from Peto et al. (1991).

where k is a constant measured in each data set; d is dosage given in this
experiment as mg/kg/day; r determines the rate of increase in incidence
with dosage at a fixed duration; m is the median duration; and n − 1is
the exponent on duration in Eq. (2.1) that fits the observed age-specific
s
incidences. The Druckrey formula is often given as k = dm , which is
equivalent to Eq. (2.3) with s = n/r and a different constant value, k.
Because median time to onset captures the patterns in the data, dose-
response experiments are usually summarized by plotting the medians
in response to varying dosage levels. We get the expected dose-response
relation by rearranging the Druckrey formula in Eq. (2.3) as

log (m) = (1/n) log (k) − (r/n) log (d) . (2.4)
Figure 2.10 shows the close experimental fit to this dose-response equa-
tion obtained by Peto et al. (1991). Figure 2.11 summarizes eight earlier
experiments that also showed a close fit to the Druckrey formula.

2.6 Sex Differences

Males and females have different patterns of cancer incidence. The
most obvious differences occur in the reproductive tissues. For example,
the breast and prostate account for a significant fraction of all cancers,
as shown in Figure 2.2.