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arXiv · 2508.16110

Estimating the growth rate of a birth and death process using data from a small sample

Carola Sophia Heinzel·Jason Schweinsberg
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Abstract

The problem of estimating the growth rate of a birth and death processes based on the coalescence times of a sample of $n$ individuals has been considered by several authors (\cite{stadler2009incomplete, williams2022life, mitchell2022clonal, Johnson2023}). This problem has applications, for example, to cancer research, when one is interested in determining the growth rate of a clone. Recently, \cite{Johnson2023} proposed an analytical method for estimating the growth rate using the theory of coalescent point processes, which has comparable accuracy to more computationally intensive methods when the sample size $n$ is large. We use a similar approach to obtain an estimate of the growth rate that is not based on the assumption that $n$ is large. We demonstrate, through simulations using the R package \texttt{cloneRate}, that our estimator of the growth rate performs well in comparison with previous approaches when $n$ is small.

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Carola Sophia Heinzel, Jason Schweinsberg. 2025-08-22. Estimating the growth rate of a birth and death process using data from a small sample. https://arxiv.org/abs/2508.16110

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