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<p>The problem of estimating the growth rate of a birth and death processes based on the coalescence times of a sample of <i>n</i> individuals has been considered by several authors (Stadler in Journal of Theoretical Biology 261(1):58–66, 2009: Williams et al in Nature 602 (7895):162–168, 2022: Mitchell et al in Nature 606(7913):343–350, 2022: Johnson et al in Bioinformatics 39(9):btad561, 2023). This problem has applications, for example, to cancer research, when one is interested in determining the growth rate of a clone. Recently, Johnson et al Bioinformatics 39(9):btad561, 2023) 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 <i>n</i> is large. We use a similar approach to obtain an estimate of the growth rate that is not based on the assumption that <i>n</i> is large. We demonstrate, through simulations using the R package <Emphasis FontCategory="NonProportional">cloneRate</Emphasis>, that our estimator of the growth rate performs well in comparison with previous approaches when <i>n</i> is small.</p>

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Estimating the Growth Rate of a Birth and Death Process Using data From a Small Sample

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月2日

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  • Carola Sophia Heinzel,
  • Jason Schweinsberg

摘要

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 (Stadler in Journal of Theoretical Biology 261(1):58–66, 2009: Williams et al in Nature 602 (7895):162–168, 2022: Mitchell et al in Nature 606(7913):343–350, 2022: Johnson et al in Bioinformatics 39(9):btad561, 2023). This problem has applications, for example, to cancer research, when one is interested in determining the growth rate of a clone. Recently, Johnson et al Bioinformatics 39(9):btad561, 2023) 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 cloneRate, that our estimator of the growth rate performs well in comparison with previous approaches when n is small.