Page 237 - 20dynamics of cancer

222 CHAPTER 11

To study the curves in relation to the number of rate-limiting steps, n,
n
we can use the form applied by Knudson (1971), ln(S) =−k 1 t , where
k is a constant, or, differentiating ln(S) with respect to t, we can use in-
cidence, I(t) = k 2 t n−1 . I discussed in earlier chapters the theory behind
these equations.
If I were to analyze the data in Figure 11.4b, I would highlight two is-
sues before starting. First, there are only four individuals in the variant
homozygote (G/G) sample. One will not get a reliable estimate of a rate
(incidence) from four observations. Second, the median age of onset
is nearly identical for the wild type (T/T) and the heterozygote (T/G).
Median age of onset often provides a good measure for the rate of pro-
gression as, for example, in the classical Druckrey analysis of chemical
carcinogens (see Section 2.5). With nearly identical medians for those
two genotypes, I would not be inclined to put much weight on any es-
timated differences in the slopes of the incidence curves, unless I had
reason to believe that one genotype had both more rate-limiting steps
and a faster transition rate between steps than the other genotype. In
this study, those assumptions would over-interpret the data.
Given these issues with regard to the data analysis of Figure 11.4b, I
would be content to note that the direction of shift in the homozygote
variant (G/G) is consistent with enhanced progression.
I have emphasized data interpretation because the work of Bond et al.
(2004) is just the sort of study that will become increasingly common
and important as genomic technology improves. I agree with the au-
thors that the analysis of inherited variants comes down to understand-
ing how those variants affect age of onset. Further, the quantitative as-
pects of rates could, in principle, provide insight into the mechanisms
by which variants influence the complex process of progression. With
the inevitably larger samples that will soon be available, it should be pos-
sible to accomplish such analyses with much greater ease and power.

INTERACTION BETWEEN VARIANTS AT DIFFERENT SITES

Variants at different nucleotide sites may interact to influence pro-
gression. Studies to date have generally not had sufficient resolution
and sample sizes to demonstrate the joint effects of different variants
on age-incidence patterns in human populations. The work of Bond et al.