Probability binning comparison: a metric for quantitating univariate distribution differences.

BACKGROUND: Comparing distributions of data is an important goal in many applications. For example, determining whether two samples (e.g., a control and test sample) are statistically significantly different is useful to detect a response, or to provide feedback regarding instrument stability by detecting when collected data varies significantly over time. METHODS: We apply a variant of the chi-squared statistic to comparing univariate distributions. In this variant, a control distribution is divided such that an equal number of events fall into each of the divisions, or bins. This approach is thereby a mini-max algorithm, in that it minimizes the maximum expected variance for the control distribution. The control-derived bins are then applied to test sample distributions, and a normalized chi-squared value is computed. We term this algorithm Probability Binning. RESULTS: Using a Monte-Carlo simulation, we determined the distribution of chi-squared values obtained by comparing sets of events derived from the same distribution. Based on this distribution, we derive a conversion of any given chi-squared value into a metric that is analogous to a t-score, i.e., it can be used to estimate the probability that a test distribution is different from a control distribution. We demonstrate that this metric scales with the difference between two distributions, and can be used to rank samples according to similarity to a control. Finally, we demonstrate the applicability of this metric to ranking immunophenotyping distributions to suggest that it indeed can be used to objectively determine the relative distance of distributions compared to a single control. CONCLUSION: Probability Binning, as shown here, provides a useful metric for determining the probability that two or more flow cytometric data distributions are different. This metric can also be used to rank distributions to identify which are most similar or dissimilar. In addition, the algorithm can be used to quantitate contamination of even highly-overlapping populations. Finally, as demonstrated in an accompanying paper, Probability Binning can be used to gate on events that represent significantly different subsets from a control sample. Published 2001 Wiley-Liss, Inc.

Probability binning comparison: a metric for quantitating multivariate distribution differences.

BACKGROUND: While several algorithms for the comparison of univariate distributions arising from flow cytometric analyses have been developed and studied for many years, algorithms for comparing multivariate distributions remain elusive. Such algorithms could be useful for comparing differences between samples based on several independent measurements, rather than differences based on any single measurement. It is conceivable that distributions could be completely distinct in multivariate space, but unresolvable in any combination of univariate histograms. Multivariate comparisons could also be useful for providing feedback about instrument stability, when only subtle changes in measurements are occurring. METHODS: We apply a variant of Probability Binning, described in the accompanying article, to multidimensional data. In this approach, hyper-rectangles of n dimensions (where n is the number of measurements being compared) comprise the bins used for the chi-squared statistic. These hyper-dimensional bins are constructed such that the control sample has the same number of events in each bin; the bins are then applied to the test samples for chi-squared calculations. RESULTS: Using a Monte-Carlo simulation, we determined the distribution of chi-squared values obtained by comparing sets of events from the same distribution; this distribution of chi-squared values was identical as for the univariate algorithm. Hence, the same formulae can be used to construct a metric, analogous to a t-score, that estimates the probability with which distributions are distinct. As for univariate comparisons, this metric scales with the difference between two distributions, and can be used to rank samples according to similarity to a control. We apply the algorithm to multivariate immunophenotyping data, and demonstrate that it can be used to discriminate distinct samples and to rank samples according to a biologically-meaningful difference. CONCLUSION: Probability binning, as shown here, provides a useful metric for determining the probability with which two or more multivariate distributions represent distinct sets of data. The metric can be used to identify the similarity or dissimilarity of samples. Finally, as demonstrated in the accompanying paper, the algorithm can be used to gate on events in one sample that are different from a control sample, even if those events cannot be distinguished on the basis of any combination of univariate or bivariate displays. Published 2001 Wiley-Liss, Inc.

Expression of Ly-6, a marker for highly malignant murine tumor cells, is regulated by growth conditions and stress.

Ly-6E.1 is highly expressed in murine tumor cells with a high malignancy phenotype and may serve as a marker for such a phenotype. In this study, we examined the effects of various growth conditions and stress on the expression levels of Ly-6E.1 by tumor cells. Previous preliminary results have shown that murine DA3 mammary tumor cells expressing high levels of Ly-6E.1 (Ly-6(hi)) are more highly tumorigenic than the same tumor cells expressing low levels of this membrane protein (Ly-6(lo)). In this study, we demonstrate that mice bearing Ly-6(hi) DA3 tumors have a significantly higher burden of spontaneous pulmonary metastasis than mice bearing Ly-6(lo) DA3 tumors. Furthermore, the survival time of the former mice was significantly shorter than that of the latter ones. We further show that certain other members of the Ly-6 gene family such as Ly-6C.1 and Ly-6G.1 are coregulated with Ly-6E.1. This was shown to occur with respect to both DA3 cells as well as A3 tumor cells which are of fibroblast origin. However, these 2 cells differ with respect to regulation of Sca-2 (TSA1, another member of the Ly-6 family) expression on these cells. Levels of Sca-2 on A3 cells appear to be coregulated with Ly-6E.1 (i.e., Ly-6(hi) A3 cells express high levels of Sca-2 and Ly-6(lo) A3 cells express low levels of Sca-2). These 2 Ly-6 proteins were, however, not coregulated on DA3 cells. Both Ly-6(hi) as well as Ly-6(lo) DA3 cells express equal levels of Sca-2. Levels of Thy-1, another glycosylphosphatidylinositol (GPI)-anchored protein expressed by A3 tumor cells, were equally expressed by both Ly-6(hi) and Ly-6(lo) A3 tumor cells. Levels of Ly-6 (but not those of CD44) on A3 tumor cells were upregulated on cells from dense cultures but were not influenced by the position of the cells in the cell cycle. Stress conditions such as serum starvation or heat shock upregulated the expression of Ly-6 by the 2 types of tumor cells but did not induce apoptosis in these cells. The kinetics of the stress-dependent upregulation of Ly-6 expression differed, however, between the epithelial and fibroblastic tumor cells.