Branching Processes as Models of Progenitor Cell Populations and Estimation of the Offspring Distributions

Abstract

We consider two new models of reducible age-dependent branching processes with emigration in conjunction with estimation problems arising in cell biology. Methods of statistical inference are developed using the relevant embedded discrete branching structure. Based on observations of the branching process with emigration, estimators of the offspring probabilities are proposed for the hidden unobservable process without emigration, which is of prime interest to investigators. The problem under consideration is motivated by experimental data generated by time-lapse video recording of cultured cells, which provides abundant information on their individual evolutions and thus on the basic parameters of their life cycle in tissue culture. Some parameters, such as the mean and variance of the mitotic cycle time, can be estimated nonparametrically without resorting to any mathematical model of cell population kinetics. For other parameters, such as the offspring distribution, a model-based inference is needed. Age-dependent branching processes have proven to be useful models for that purpose. A special feature of the data generated by time-lapse experiments is the presence of censoring effects due to the migration of cells out of the field of observation. For the time-to-event observations, such as the mitotic cycle time, the effects of data censoring can be accounted for by standard methods of survival analysis. No methods are available to accommodate such effects in the statistical inference on the offspring distribution. Within the framework of branching processes, the loss of cells to follow-up can be modeled as a process of emigration. Incorporating the emigration process into a pertinent branching model of cell evolution provides the basis for the proposed estimation techniques. Statistical inference on the offspring distribution is illustrated with an application to the development of oligodendrocytes in cell culture.