Biomedical researchers are often interested in computing the correlation between RNA and protein abundance. However, correlations can be computed between rows of a data matrix or between columns, and the results are not the same. The belief that these two types of correlation are estimating the same phenomenon is a special case of a well-known logical error called the ecological fallacy. In this article, we review different uses of correlation found in the literature, explain the differences between row and column correlations and argue that one of them has an undesirable interpretation in most applications. Through simulation studies and theoretical derivations, we show that the commonly used Pearson's coefficient, computed from protein and transcript data from a single sample, is only loosely related to the biological correlation that most researchers will be interested in studying. Beyond our basic exploration of the ecological fallacy, we examine how correlations are affected by relative quantification proteomics data and common normalization procedures, finding that double normalization is capable of completely masking true correlative relationships. We conclude with guidelines for properly identifying and computing consistent correlation coefficients.

MOTIVATION: For cluster analysis, high-dimensional data are associated with instability, decreased classification accuracy and high-computational burden. The latter challenge can be eliminated as a serious concern. For applications where dimension reduction techniques are not implemented, we propose a temporary transformation which accelerates computations with no loss of information. The algorithm can be applied for any statistical procedure depending only on Euclidean distances and can be implemented sequentially to enable analyses of data that would otherwise exceed memory limitations. RESULTS: The method is easily implemented in common statistical software as a standard pre-processing step. The benefit of our algorithm grows with the dimensionality of the problem and the complexity of the analysis. Consequently, our simple algorithm not only decreases the computation time for routine analyses, it opens the door to performing calculations that may have otherwise been too burdensome to attempt. AVAILABILITY AND IMPLEMENTATION: R, Matlab and SAS/IML code for implementing lossless data reduction is freely available in the Appendix. CONTACT: [email protected].