Bayesian inference in a hidden stochastic two-compartment model for feline hematopoiesis

In this paper, we describe a hidden two-compartment stochastic process used to model the kinetics of feline hematopoietic stem cells (HSCs) in continuous time. Because of the experimental design and data collection scheme, the inferential task presents numerous challenges. While the hematopoietic process evolves in continuous time, the observations are collected only at discrete irregular times and are a probabilistic function of the state of the process. In addition, the animals go through an experimental procedure such that their reserve of HSCs is severely depleted at the start of the observation period. This impedes any approximation of the hematopoietic process with a continuous state-space process (normal approximation of the transition probabilities would be inaccurate when the state of the process, i.e. the number of stem cells, is small). We implement a Markov chain Monte Carlo algorithm that allows us to estimate the posterior distribution of the parameters of the hematopoietic process while maintaining its state-space discrete (i.e. without using any approximation). We show the performance of the algorithm on simulated data. Finally, we apply the algorithm to data on multiple experimental cats and provide estimates of the rates of the fates of feline HSCs. The obtained estimates are in agreement with the estimates obtained with different methods published in the medical literature. However, the proposed approach makes a more efficient use of the data and hence the parameter estimates are much more accurate than the one obtained with the methods previously proposed.