Abstract: Multistage models were developed in the 1950s as a mathematical model for the accumulation of genetic mutations that can lead to cancer. More recently they have been applied to a range of neurodegenerative diseases including Amyotrophic Lateral Sclerosis (ALS), Parkinson’s, and Alzheimer's. These studies have been followed by a comprehensive survey of diseases in UK Biobank, that was motivated by the discovery that somatic mutations may be involved in many more diseases than just cancer. The study used two simple multistage models to describe the age-dependent incidence of 400 common diseases affecting men and women [1]. By providing a simple statistical correction to account for the limited age-range in cohort studies such as UK Biobank, it was found that approximately 60% of the diseases studied were consistent with a multistage disease process [1]. The parametric age-dependent model allowed late-onset diseases that are increasingly inevitable with age, to be distinguished from more sporadic diseases with a low risk that increases slowly with age. From a statistical perspective, the sporadic diseases might in principle be avoided over a lifetime, but the late-onset diseases appeared to become increasingly inevitable with increasing age.
 

The multistage model can allow mechanistic insights to be obtained by studying differences between stratified data [1]. Differences between plots can be interpreted as changes in the rates of underlying processes, changes to the number of rate-limiting steps needed for disease, or different underlying causes of disease. More recently [2], the model has inspired a simple statistical test for whether two diseases share a first step that is necessary for both diseases. It is widely believed that there are shared underlying pathways that can lead to several disease types (a shared “pathogenesis”). If true, this may help to explain clusters of disease types and the growing burden of multimorbidity (multiple diseases concurrently within an individual). This hypothesis can now start to be tested using data of disease incidence. Overall, the approach provides new biologically-motivated tools for using observational data to study diseases and to characterise disease risk.
 

[1] “Sporadic, late-onset, and multistage diseases”, A.J. Webster, R. Clarke, PNAS Nexus, Volume 1, Issue 3, pgac095, https://doi.org/10.1093/pnasnexus/pgac095, (2022).

[2] “A simple multistage theory for multimorbidity”, A.J. Webster, arXiv:2501.18742, (2025).

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Dr. Anthony Webster, Department of Statistics, Oxford University.

Contact Gilbert MacKenzie, Chair, RSSNI