Goodness-of-fit testing for the stationary density of a size-structured PDE

TL;DR

This paper develops a goodness-of-fit test for the stationary size and age distributions in cell population models, aiming to detect whether cell division is symmetric or asymmetric, with applications to biological data analysis.

Contribution

It introduces a novel statistical test for assessing symmetry in cell division models based on stationary distributions, validated through simulations and real data.

Findings

Test effectively distinguishes symmetric and asymmetric division.

Simulation results demonstrate high accuracy of the test.

Application to real data shows practical utility.

Abstract

We consider two division models for structured cell populations, where cells can grow, age and divide. These models have been introduced in the literature under the denomination of `mitosis' and `adder' models. In the recent years, there has been an increasing interest in biology to understand whether the cells divide equally or not, as this can be related to important mechanisms in cellular aging or recovery. We are therefore interested in testing the null hypothesis $H_0$ where the division of a mother cell results into two daughters of equal size, against the alternative hypothesis $H_1$ where the division is asymmetric and ruled by a kernel that is absolutely continuous with respect to the Lebesgue measure. The sample consists of i.i.d. observations of cell sizes and ages drawn from the population, and the division is not directly observed. The hypotheses of the test are reformulated as hypotheses on the stationary size and age distributions of the models, which we assume are also the distributions of the observations. We propose a goodness-of-fit test that we study numerically on simulated data before applying it on real data.