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HISTORY OF THEORIES 65

rate, u, increases linearly with dose, d, then for n steps in carcinogenesis,
n
the incidence is proportional to d . In those cases known to Armitage
and Doll, incidence increased only with a low power of dose but a high
power of time. Thus, they rejected the multicell theory.
Against Armitage and Doll’s quick rejection of multicell theory, Whit-
temore and Keller (1978) pointed out that if a particular carcinogen af-
fected only a few of the various stages in progression, for example only
m< n of the stages, then multicell theory predicts that incidence would
m
increase as d . So, Armitage and Doll’s argument did not really rule
out the multicell theory. Later molecular evidence tends to favor se-
quential changes to a cell lineage rather than changes to many different
cells. However, recent work on genetic changes in stromal cells and
analyses of the tissue environment (see below) will probably lead to the
conclusion that changes to the surrounding cells and tissue can also be
important in some cases.
The next step in the history, from a chronological point of view, con-
cerns the role of cell proliferation and clonal expansion. However, I
delay that topic until a later section. Instead, I take up what I consider
to be the next major insight: how to test theories of progression.

4.2 A Way to Test Multistage Models

Various forms of multistage theory can be fit to the data. But the fact
that a particular model can be fit to the data by itself provides only weak
support for the model. The problem is that models are often too pliable,
too easily fit to different forms of data. Because many different models
can be nicely fit to the same data, fitting models to data provides very
little insight. For testing multistage hypotheses, the key breakthrough
came with Knudson’s (1971) comparison of incidence between inherited
and noninherited forms of retinoblastoma. In this section, I present the
background to Knudson’s work, what he accomplished in his studies,
and some of the historical aspects of his work (Knudson 1977).
In the 1960s, the importance of somatic mutations and the nature of
stages in progression continued to be debated (Foulds 1969). Several
authors developed the idea that cancer arises by the accumulation of
genetic mutations to cell lineages. Burch (1963) noted that if a sequence
of mutations drives progression, then some individuals may inherit one
mutation and obtain the rest after birth by somatic mutation. Burch