EDIT: I forgot to mention a paper on Chronic Myeloid Leukemia by Nowak et al. which possibly contradicts the point I'm trying to make. Thanks Heiko Enderling for pointing this out.
EDIT 2: Artem Kaznatcheev has written an excellent blog post arguing for the fact that the above mentioned paper does not contradict my argument.
The other day I was discussing the merits of mathematical oncology with some colleagues in the collaboratorium (a shared space at the IMO where scientific discussion blend with the smell of espresso) here at IMO. We came to the conclusion that our field of research still lacked that defining publication where the use of mathematical modelling was clearly tied to a clinical change benefiting patients. Or in other words, an instance where mathematical oncology has been proven to make a difference.
Other fields of mathematical biology have already had this pleasure. For example Ronald Ross developed a model of malaria dynamics in the 1910s (known as
the SIR-model), which allowed for a completely new understanding of
of malaria and opened up the field of epidemiology. A more recent example is the use of modelling in the
discovery of the high turnover rates of HIV-particles (http://www.tb.ethz.ch/education/model/HIV_module_1/PerelsonScience1996.pdf).
Given the fact that more and more researchers work in mathematical oncology, isn't it just a matter of time before that landmark publication appears? Actually I think the answer is no.
The reason for me being so pessimistic pertains to the relation between the complexity of the problem and the amount of knowledge that you can fit into a standard publication (journal paper, conference proceeding etc.). Some of you might object and say the way we communicate our results ought to be secondary to the subject at hand, but I would like to argue that the politics and funding structure of science imposes a certain mode of communication that in turn influence how we approach research questions. What biologist can stick to a specific research agenda, work on it for 15+ years, and then publish a monograph on the topic? (The answer to this question is obviously Darwin, whose meticulous work couldn't have been carried out today.)
This is not to say that mathematical modelling does not contribute to our understanding of cancer, but rather that the insights gained from it arrive in smaller chunks and are absorbed by the experimental and clinical community. These insights and novel concepts then shapes their thinking and inspires them to perform new experiments or look at existing data in new ways.
In support of this thesis I would like to cite two ideas that today are ubiquitous in cancer research: networks and intra-tumoral heterogeneity.
The idea that intra-cellular signalling forms a network with feedback loops, crosstalk and robust properties does not emanate from mathematical oncology per se, but rather from complex systems theory and statistical physics. Nevertheless it is now part of the vocabulary of cancer biologists and helps in moving the subject forward.
The concept of tumour evolution was coined by Nowell in 1976, and has been the subject of a large number of mathematical modelling papers. For a long time it was believed that this process was characterised by selective sweeps whereby a single clone would dominate the tumour cell population. However a number of theoretical studies suggested that spatial heterogeneity could give rise to a diversity of subclones, and also that tumour cells with similar phenotypes could harbour different genotypes, both processes contributing to intra-tumoral heterogeneity. When the technology arrived to measure genetic heterogeneity in cancers it was indeed shown that diversity can be large enough to classify different parts of a tumour into different subtypes.
Would these measurements have been made in the absence of theory supporting it? We can never know, but for one thing we can say that the theory facilitated the discovery.
In conclusion I think that mathematical oncology has an important role to play in advancing our knowledge of cancer, but I don't think it will happen through landmark discoveries, rather through piecemeal additions.