Electronic Journal of Statistics

Cox Markov models for estimating single cell growth

Federico Bassetti, Ilenia Epifani, and Lucia Ladelli

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Recent experimental techniques produce thousands of data of single cell growth, consequently stochastic models of growth can be validated on true data and used to understand the main mechanisms that control the cell cycle. A sequence of growing cells is usually modeled by a suitable Markov chain. In this framework, the most interesting goal is to infer the distribution of the doubling time (or of the added size) of a cell given its initial size and its elongation rate. In the literature, these distributions are described in terms of the corresponding conditional hazard function, referred as division hazard rate. In this work we propose a simple but effective way to estimate the division hazard by using extended Cox modeling. We investigate the convergence to the stationary distribution of the Markov chain describing the sequence of growing cells and we prove that, under reasonable conditions, the proposed estimators of the division hazard rates are asymptotically consistent. Finally, we apply our model to study some published datasets of E-Coli cells.

Article information

Electron. J. Statist., Volume 11, Number 2 (2017), 2931-2977.

Received: September 2016
First available in Project Euclid: 11 August 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces 62N02: Estimation 62P10: Applications to biology and medical sciences
Secondary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation

Asymptotic consistency cell size growth in bacteria Cox partial likelihood division hazard rate extended Cox model positive Harris recurrent Markov chains

Creative Commons Attribution 4.0 International License.


Bassetti, Federico; Epifani, Ilenia; Ladelli, Lucia. Cox Markov models for estimating single cell growth. Electron. J. Statist. 11 (2017), no. 2, 2931--2977. doi:10.1214/17-EJS1306. https://projecteuclid.org/euclid.ejs/1502416820

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