Page 233 - 20dynamics of cancer

218 CHAPTER 11

smooth = 0.5 smooth = 0.6
max = 1 max = 0.7 max = 1 max = 0.7
1 0.7
Fraction Tumorless 0.4 0.2

0.1
(a) (b) (c) (d)

−2
Incidence

−3
(e) (f) (g) (h)
4
3
LLA 2

1
0 (i) (j) (k) (l)
30 40 50 60 80 30 40 50 60 80 30 40 50 60 80 30 40 50 60 80
Age

Figure 11.3 Breast cancer rates for females who carry a mutation in BRCA1 or
BRCA2, shown as solid lines, versus those females who do not have a mutation,
shown as dashed lines. The circles in (a) and (c) mark the estimated fraction of
females in each class that have not yet developed tumors, taken from Figure 1B
of Struewing et al. (1997). In (b) and (d), I transformed the fraction tumorless,
f,as S = (max − f)/max, where max is the fraction of the carriers who have
fully elevated risk. Panels (a) and (b) used the smooth.spline function of the
R computing language (R Development Core Team 2004) to fit a smooth curve
to the observed points, with smoothing parameter set to 0.5; (c) and (d) force
a stiffer, less curved fit with a smoothing parameter of 0.6. The second row
shows incidence on a log 10 scale, obtained from −dln(S)/dt, where S is the
fraction tumorless in the curves of the top row. The bottom row shows ΔLLA,
the difference in the log-log slopes of incidence in the second row of plots.
for carriers and noncarriers. In all four panels, the noncarriers (dashed
curve) show the commonly observed pattern for sporadic breast cancer:
a diminishing slope of incidence with age, but little or no actual decrease
in the incidence rate before age 80. By contrast, the incidence declines
after midlife for the carriers (solid curves) in all of the panels except