Three‐marker phenotypic analysis of lymphocytes based on two‐color immunofluorescence using a multinomial model for flow cytometric counts and maximum likelihood estimation

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Abstract
The simultaneous flow cytometric study of multiple (≥ 3) markers on individual cells is restricted by technical reasons, e.g., the type of flow cytometer, and the availability of (monoclonal) antibodies (mAb) conjugated with the appropriate fluorochromes. However, a n‐way classification (n ≥ 3) may be derived from multiple 2‐way classifications. The 2‐way classifications are obtained by the use of only two fluorochromes, but each fluorochrome may be used for the simultaneous labelling of 2 or more mAb. We present a formal statistical model, based on an underlying multinomial distribution for the observed quadrant counts, by which data from such multiple 2‐way classifications can be analyzed. The model is restricted to 3‐marker phenotypic analyses, but can be extended to n‐way classifications (n > 3). Maximum likelihood estimates are obtained by the application of the EM algorithm. The model was tested on 20 samples of peripheral blood mononuclear cells to study the coexpression of CD45RA, CD45RO, and Leu 8 by lymphocyte subsets defined by the CD56 (MHC‐unrestricted cytotoxic cells) and CD3 (T cells) markers. Application of the model gave an excellent fit in all but one cases. In addition, the model reduced the effect of inter‐assay variation on the estimates and it provided an analysis of consistency over the data, which allows the detection of outliers due to staining errors.

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