Flow cytometry is a technology that rapidly measures antigen-based markers associated to cells in a cell population. Although analysis of flow cytometry data has traditionally considered one or two markers at a time, there has been increasing interest in multidimensional analysis. However, flow cytometers are limited in the number of markers they can jointly observe, which is typically a fraction of the number of markers of interest. For this reason, practitioners often perform multiple assays based on different, overlapping combinations of markers. In this paper, we address the challenge of imputing the high dimensional jointly distributed values of marker attributes based on overlapping marginal observations. We show that simple nearest neighbor based imputation can lead to spurious subpopulations in the imputed data, and introduce an alternative approach based on nearest neighbor imputation restricted to a cells subpopulation. This requires us to perform clustering with missing data, which we address with a mixture model approach and novel EM algorithm. Since mixture model fitting may be ill-posed, we also develop techniques to initialize the EM algorithm using domain knowledge. We demonstrate our approach on real flow cytometry data.
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