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

TL;DR

This paper introduces a new estimator for the growth rate of birth and death processes from small samples, improving accuracy without large-sample assumptions, with applications in cancer research.

Contribution

It develops a novel estimation method that does not rely on large sample assumptions, enhancing accuracy for small sample sizes in coalescent-based growth rate estimation.

Findings

Estimator performs well with small samples

Comparable accuracy to large-sample methods

Validated through simulations using R package cloneRate

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.