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bioRxiv · 10.1101/2025.01.13.632690

A fast numerical integration scheme for clonal expansion processes on graphs

Paterson, C. G. B.·Gao, M.·Hellier, J.·Luebeck, G.·Wedge, D. C.·Bozic, I.
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Abstract

Compound birth-death processes are widely used to model the age-incidence curves of many cancers [1]. There are efficient schemes for directly computing the relevant probability distributions in the context of linear multi-stage clonal expansion (MSCE) models [2]. However, these schemes have not been generalised to models on arbitrary graphs, forcing the use of either full stochastic simulations or mean-field approximations, which can become inaccurate at late times or old ages [3, 4]. Here, we present a numerical integration scheme for directly computing survival probabilities of a first-order birth-death process on an arbitrary directed graph, without the use of stochastic simulations. As a concrete application, we show that this new numerical method can be used to infer the parameters of an example graphical model from simulated data.

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Paterson, C. G. B., Gao, M., Hellier, J., Luebeck, G., Wedge, D. C., Bozic, I.. 2025-01-15. A fast numerical integration scheme for clonal expansion processes on graphs. https://doi.org/10.1101/2025.01.13.632690

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