Multi-Stage Models Of Cancer And Disease

Abstract Background Since Armitage and Doll's publication of “a multi-stage theory of carcinogenesis” in 1954, the multi-stage model has underpinned our conceptual understanding of cancer. In the last few years the model has been applied to other diseases, such as Amyotrophic Lateral Sclerosis (Motor Neurone Disease), providing new insight into how the disease can arise and progress. Methods The multi-stage model is simplified and generalised. The result is a simple mathematical toolkit to describe carcinogenesis or other multi-stage models of disease, with simple formulae corresponding to pictorial diagrams of the multi-stage process. Important practical issues are described regarding the fitting of data and the use of multi-stage models to interpret results. Results Relationships between established cancer models are clarified, and derivations are simplified. We provide examples and highlight pitfalls of fitting multistage models to data. It is explained how genetic markers and the multi-stage paradigm can provide new insights into mechanisms of disease. Limitations of the model are discussed in the context of recent cancer research. Conclusions A simple mathematical recipe can convert biologically-motivated models for each step in a disease’s progression, into a mathematical model. The framework provides a mathematical toolkit to study the failure of complex systems, biological or otherwise, simplifying the formulation and interpretation of multi-stage models. Key messages Multi-stage models are increasingly easy to use and understand. When combined with big data and genetic markers for stratification, they offer a new tool for epidemiological studies.