A Mixture Model With Dependent Observations for the Analysis of CSFE–Labeling Experiments

Abstract

Recent advances in flow cytometry have resulted in the development of powerful bioassays to analyze the proliferation of cell populations. The carboxy-fluorescein diacetate succinimidyl ester (CFSE)-labeling experiment is one such assay that is widely used to study cell kinetics and as a standard tool for investigating lymphocyte proliferation. Several mathematical models have been proposed to describe cell proliferation during CFSE experiments. The statistical analysis of CFSE-labeling data has received little attention, but it poses a number of methodological issues. In this article we approach their analysis using a mixture model. The mixing proportions are specified through an age-dependent branching process that models the temporal organization of the cell population. Because the CFSE molecules are partitioned between daughter cells when their mother divides, the observations generated by this assay are dependent. The data structure can be compared with that of a partially observed random-effects model where the clusters cannot be identified. In this context, we propose three estimators. We prove their consistency and asymptotic normality, investigate their finite-sample properties in simulation studies, and contrast their relative merits for the analysis of CFSE-labeling data. We use the proposed methods to analyze the proliferation in vitro of CD4+ and CD8+ T lymphocytes. In particular, we compare their activation and proliferation rates, and also investigate the effect of two stimuli that activate resting lymphocytes: the nonspecific mitogen phytohemaglutanin (PHA) and ligation of both the T-cell receptor CD3 and the costimulatory receptor CD28 cell surface proteins with monoclonal antibodies.