Page 23 - 20dynamics of cancer

8 CHAPTER 1

such fitting demonstrates only sufficient mathematical malleability to
be shaped to particular observations. A good framework and properly
formulated hypotheses express comparative predictions: how incidence
shifts in response to changes in genetics and changes in the cellular
mechanisms that control rates of progression. This book strongly em-
phasizes the importance of comparative hypotheses in the analysis of
incidence curves and the mechanisms that protect against failure.
I continue Chapter 5 with the observations of incidence to be ex-
plained. I follow with simple formulations of theories to introduce the
basic approach and to show the value of quantitative theories in the
analysis of cancer. I finish with technical definitions of incidence and
acceleration, the fundamental measures for rates of failure and how fail-
ure changes with age.
Chapters 6 and 7 provide full development of the quantitative theory
of incidence curves. Each section begins with a summary that explains in
plain language the main conceptual points and conclusions. After that
introduction, I provide mathematical development and a visual presen-
tation in graphs of the key predictions from the theory.
In Chapters 6 and 7, I include several original mathematical models
of incidence. I developed each new model to evaluate the existing data
on cancer incidence and to formulate appropriate hypotheses for future
study. These chapters provide a comprehensive theory of age-specific
failure, tailored to the problem of multistage progression in cell lin-
eages and in tissues, and accounting for inherited and somatic genetic
heterogeneity. I also relate the theory to classical models of aging given
by the Gompertz and Weibull formulations. Throughout, I emphasize
comparative predictions. Those comparative predictions can be used
to evaluate the differences in incidence curves between genotypes or
between alternative carcinogenic environments.
Chapter 8 uses the theory to evaluate shifts in incidence curves be-
tween individuals who inherit distinct predisposing genotypes. I begin
by placing two classical comparisons between inherited and noninher-
ited cancer within my quantitative framework. The studies of Ashley
(1969a) on colon cancer and Knudson (1971) on retinoblastoma made
the appropriate comparison within the multistage framework, demon-
strating that the inherited cases were born one stage advanced relative to
the noninherited cases. I show how to make such quantitative compar-
isons more simply and to evaluate such comparisons more rigorously,