Page 103 - 20dynamics of cancer

88 CHAPTER 5

Several mathematical methods test the quality of a fit. But techni-
cal fixes do not overcome the main difficulty: mathematical models fail
to capture the full complexity of multidimensional problems such as
cancer. If a model does become sufficiently complex, one has so many
parameters that fitting almost anything is accomplished too easily.
Although a good fit means little, a lack of fit also provides little insight:
lack of fit means only that one does not have exactly the right model.
However, one rarely has exactly the right model. So, by lack of fit, one
may end up rejecting a theory that in fact captures much of the essential
nature of a process but misses one aspect.
Finally, another common approach considers the realism of parame-
ter estimates obtained from the data. For example, when fitting a model,
how close do the estimated mutation rates match values thought to be
realistic? However, parameter estimates can only be compared to real-
istic values when one has a complete model. In incomplete models, the
parameter estimates change to make up for processes not included in
the model. So the realism of parameter estimates provides a test only
when fitting a complete model that captures the full complexity of a
process. But for cancer and for most interesting biological phenomena,
we do not have complete models and probably never will have complete
models.
Models do have great value in spite of the difficulties of drawing con-
clusions by fitting to the data. The key is to develop and test theories in
a comparative way.

COMPARISON
A comparison is simple to formulate, understand, and test. Consider
the following prediction: as the number of steps in progression declines,
the slope of the incidence curve decreases. To test this, one has to mea-
sure a relative change in the number of steps and a relative change in the
slope of the incidence curve. This test can be accomplished by compar-
ing the incidence curves between genotypes, where one genotype has a
mutation that abrogates a suspected rate-limiting step in progression.
A comparative prediction allows tests of causal hypotheses. If I un-
derstand what causes cancer, then I can predict how incidence curves
change as I change the underlying parameters of cancer dynamics.
The limited role of mathematics and quantitative studies in much of
biology follows from a fatal attraction to fitting complex models. Simple