Statistical inference in partially observed stochastic compartmental models with application to cell lineage tracking of in vivo hematopoiesis

Single-cell lineage tracking strategies enabled by recent experimental technologies have produced significant insights into cell fate decisions, but lack the quantitative framework necessary for rigorous statistical analysis of mechanistic models of cell division and differentiation. In this paper, we develop such a framework with corresponding moment-based parameter estimation techniques for continuous-time stochastic compartmental models that provide a probabilistic description of how cells divide and differentiate. We apply this method to hematopoiesis, the complex mechanism of blood cell production. Viewing compartmental models of cell division and differentiation as multi-type branching processes, we derive closed-form expressions for higher moments in a general class of such models. These analytical results allow us to efficiently estimate parameters of compartmental models of hematopoiesis that are much richer than the models used in previous statistical studies. To our knowledge, the method provides the first rate inference procedure for fitting such models to time series data generated from cellular barcoding experiments. After testing the methodology in simulation studies, we apply our estimator to hematopoietic lineage tracking data from rhesus macaques. Our analysis provides a more complete understanding of cell fate decisions during hematopoiesis in non-human primates, which may be more relevant to human biology and clinical strategies than previous findings in murine studies. The methodology is transferrable to a large class of compartmental models and multi-type branching models, commonly used in studies of cancer progression, epidemiology, and many other fields.