Page 164 - 20dynamics of cancer

GENETICS OF PROGRESSION 149

6
8
5 4
Incidence 3 2 X 10 -5 4

1 R
2
0 (a) (b)

0.5 1.5 4.5 0.5 1.5 2.5
Age Age

Figure 8.2 Age-specific incidence of retinoblastoma. (a) Bilateral (solid line)
6
and unilateral (dashed line) cases of retinoblastoma per 10 population, shown
on a log 10 scale. Description of the data in Figure 2.6. (b) Ratio, R, of unilateral
(I U ) to bilateral (I B ) incidence at each age multiplied by 10 −5 , using the data
in the previous panel. From Frank (2005).
be the probability that nonmutant individuals acquire an extra muta-
tion somatically: approximately the mutation rate per cell division mul-
tiplied by the number of cell divisions (Frank 2005). The data shown in
Figure 8.2 provide a good match to that prediction when using common
assumptions about somatic mutation and cell division.
I now develop a simpler, more general comparative prediction for the
difference in incidence between sporadic and inherited cases. In almost
all multistage theories, an inherited mutation advances progression and
therefore decreases the acceleration of cancer. So, multistage theory
predicts that the acceleration of sporadic cases is greater than the ac-
celeration of inherited cases. If we assume that a mutation advances
progression by one step, then the theory predicts that the acceleration
of inherited cases declines by about one when compared to the acceler-
ation of sporadic cases.
I developed the general theory for comparing accelerations in Sec-
tions 7.2 and 7.3. The main features of the theory follow from basic
definitions. The ratio of sporadic to inherited incidence is
I S
R = .
I I
The slope of R on a log-log scale is
d log (R) d log (I S ) d log (I I )
= − .
d log (t) d log (t) d log (t)