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Rare Event Analysis: The Fundamental Things Apply as Cells Go By

Many of the tasks in modern cytometry are examples of rare event analysis. Examples are looking for primitive stem cells, leukemic cells or cancer cells in blood or bone marrow, for fetal cells in maternal blood, or for transfected cells present at low frequency in a culture. In comparing different samples, it is frequently necessary to determine the statistical significance of small differences between large numbers. Some people seem to think that counting hundreds of thousands or millions of cells lets them beat the Poisson statistics; what’s important, however, is the number of cells of interest you count, not the total. Suppose, for example, that you find your cells of interest present at a frequency of 0.04% positives in one sample of 200,000 cells and 0.15% in another. Simple arithmetic tells you that 0.01% of 200,000 is 20cells, so the first sample has 80 cells of interest and the second has 300. The Poisson standard deviations for the numbers of cells of interest counted would be about 9 for the 80 cells in the first sample and about 18 for the 300 cells in the second. The two values are thus separated by several standard deviations, which is to say that there is a statistically significant difference between them. However, the statistics provide no information as to the source of the difference. If the cells came from the same pot, one would suspect instrumental factors related to data collection and/or analysis, unless there is reason to believe that a process such as differential settling of the rare cell type would change the composition of a sample aliquot with time. A mild degree of paranoia is probably an asset when dealing with rare event analysis.


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