On the use of the Kolmogorov-Smirnov statistical test for immunofluorescence histogram comparison

The problem considered is the quantitative comparison of immunofluorescence frequency distributions in order to detect their differences of biological significance, i.e., to evaluate the potential positivity of a cell sample with respect to negative control cells. The Kolmogorov-Smirnov (KS) statistical test, proposed in the literature for this purpose, is examined and discussed through its application to a set of experimental measurements. It is shown that even differences due to the stain procedure or to instrumental biases may be considered significant by the test implemented in the standard form.

In order to ensure valid results, it is necessary to take into account the various sources of variation in the specific experimental context. A procedure is proposed that uses the KS statistics as a reference for determining an appropriate estimate of the overall variability in the control data. This estimate is derived from the comparisons of the cumulative distributions associated with repeated measurements of the negative cell sample.

The KS-related index thus defined provides a tool for assessing the potential positivity of a cell sample, since it allows to distinguish between statistical and biological significance of the difference between the histogram to be tested and the set of control data. In particular, if a cell sample is not included in the control variability, either a positive cell subpopulation is present, or all cells are positive. Instead, for a sample included in the control variability, the difference will be not biologically meaningful, even if statistically significant. Moreover, when a purely positive control sample is also available, it is possible to derive a measure of the precision at which a true biological positivity can be detected. Finally, since the index is not absolute, but relative to the features of the instrumentation, of the antibodies and of the fluorochromes used, it represents a quantitative measure of the stability and reproducibility of the measurement process and could be used for quality control of flow cytometric experiments in immunofluorescence.