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Corruption of the Pearson correlation coefficient by measurement error and its estimation, bias, and correction under different error models.

ABSTRACT: Correlation coefficients are abundantly used in the life sciences. Their use can be limited to simple exploratory analysis or to construct association networks for visualization but they are also basic ingredients for sophisticated multivariate data analysis methods. It is therefore important to have reliable estimates for correlation coefficients. In modern life sciences, comprehensive measurement techniques are used to measure metabolites, proteins, gene-expressions and other types of data. All these measurement techniques have errors. Whereas in the old days, with simple measurements, the errors were also simple, that is not the case anymore. Errors are heterogeneous, non-constant and not independent. This hampers the quality of the estimated correlation coefficients seriously. We will discuss the different types of errors as present in modern comprehensive life science data and show with theory, simulations and real-life data how these affect the correlation coefficients. We will briefly discuss ways to improve the estimation of such coefficients.

SUBMITTER: Saccenti E

PROVIDER: S-EPMC6965177 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature

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Corruption of the Pearson correlation coefficient by measurement error and its estimation, bias, and correction under different error models.

Saccenti Edoardo E Hendriks Margriet H W B MHWB Smilde Age K AK

Scientific reports 20200116 1

Correlation coefficients are abundantly used in the life sciences. Their use can be limited to simple exploratory analysis or to construct association networks for visualization but they are also basic ingredients for sophisticated multivariate data analysis methods. It is therefore important to have reliable estimates for correlation coefficients. In modern life sciences, comprehensive measurement techniques are used to measure metabolites, proteins, gene-expressions and other types of data. Al ...[more]

PMID: 31949233

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Project description:The revolution in fluorescence microscopy enables sub-diffraction-limit ("superresolution") localization of hundreds or thousands of copies of two differently labeled proteins in the same live cell. In typical experiments, fluorescence from the entire three-dimensional (3D) cell body is projected along the z-axis of the microscope to form a 2D image at the camera plane. For imaging of two different species, here denoted "red" and "green", a significant biological question is the extent to which the red and green spatial distributions are positively correlated, anti-correlated, or uncorrelated. A commonly used statistic for assessing the degree of linear correlation between two image matrices R and G is the Pearson Correlation Coefficient (PCC). PCC should vary from - 1 (perfect anti-correlation) to 0 (no linear correlation) to + 1 (perfect positive correlation). However, in the special case of spherocylindrical bacterial cells such as E. coli or B. subtilis, we show that the PCC fails both qualitatively and quantitatively. PCC returns the same + 1 value for 2D projections of distributions that are either perfectly correlated in 3D or completely uncorrelated in 3D. The PCC also systematically underestimates the degree of anti-correlation between the projections of two perfectly anti-correlated 3D distributions. The problem is that the projection of a random spatial distribution within the 3D spherocylinder is non-random in 2D, whereas PCC compares every matrix element of R or G with the constant mean value [Formula: see text] or [Formula: see text]. We propose a modified Pearson Correlation Coefficient (MPCC) that corrects this problem for spherocylindrical cell geometry by using the proper reference matrix for comparison with R and G. Correct behavior of MPCC is confirmed for a variety of numerical simulations and on experimental distributions of HU and RNA polymerase in live E. coli cells. The MPCC concept should be generalizable to other cell shapes.

Dataset Information

Corruption of the Pearson correlation coefficient by measurement error and its estimation, bias, and correction under different error models.

Publications

Corruption of the Pearson correlation coefficient by measurement error and its estimation, bias, and correction under different error models.

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