These are artificial datasets for illustration; and represent dividing up a T cell response into three categories. (A) Data for two individuals is shown. The two individuals have different overall magnitude of responses, but the response distributes identically into the categories. Hence, the pie charts that average the results (top) are identical whether they use absolute, unnormalized data (left) or relative, normalized data (right). (B) Here, 10 individuals are analyzed, one of whom is a sharp outlier from the other 9. The pie charts averaging the 10 individuals are very different when using absolute numbers (left) vs relative numbers (right). This is because the absolute representation weights each individual according to the magnitude of their response; thus, subject #10 is weighted almost 100-fold greater than the other subjects. The resulting pie chart looks very similar to the pie chart for subject #10, and not like the other nine. When averaging the normalized values (right), subject #10 is weighted equally to all others, and thereby contributes only 10% of the information. Hence, the average pie chart looks very similar to the majority of subjects.

PBMC were stimulated with (“Stimulated”) or without (“Background”) antigen; the proportion of T cells producing cytokine is shown as histograms. The top panel shows the results for the control, unstimulated cultures; small levels of background (up to 0.1% of T cells) are evident. The red line is an approximation of the distribution. The middle panel shows the results for the stimulated cultures. A low proportion of positives is evident, and represented by the blue line. To obtain an estimate of the true frequency of antigen-specific cells, the background value for each culture is subtracted from this measurement; the resulting distribution is shown at bottom. The major set of negative cultures is now centered on zero, with a symmetric spread representing measurement and experimental errors. A small positive threshold (green) is chosen based on an assumption that the negative cultures are symmetrically distributed and estimating the extent of that distribution from the values below zero (i.e., purple line); for further analysis or display of this distribution, those values can be set to zero. This does not introduce a systematic bias, and statistics will reflect values principally from true positive cultures.

The phenotype of all cytokine positive cells was determined; the fraction that falls into a Naïve, central memory (CM), transitional memory (TM), effector memory (EM), or terminal effector (TE) memory subset is shown in the bar chart and pie charts. Distributions are shown for the background (unstimulated) control, for all stimulated samples (stimulated with HIV envelope peptides, Env), for those samples with Env responses less than 3-fold above background, and for those with responses greater than 3-fold or 10-fold above background. Note that the phenotype for a response that is 3-fold above background would represent a mixture of cells that is 25% background and 75% antigen-specific. Bars show interquartile ranges for each measurement. p values were computed using the permutation test described in the text, comparing each distribution against the control.