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Correlation Coefficients for a Study with Repeated Measures.

ABSTRACT: Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlation calculation are compared: (1) Pearson correlation; (2) correlation of subject means; (3) partial correlation for subject effect; (4) partial correlation for visit effect; and (5) a mixed model approach. Pearson correlation coefficient is traditionally used in a cross-sectional study. Pearson correlation is close to the correlations computed from mixed-effects models that consider the correlation structure, but Pearson correlation may not be theoretically appropriate in a repeated-measure study as it ignores the correlation of the outcomes from multiple visits within the same subject. We compare these methods with regard to the average of correlation and the mean squared error. In general, correlation under the mixed-effects model with the compound symmetric structure is recommended as its correlation is close to the nominal level with small mean square error.

SUBMITTER: Shan G

PROVIDER: S-EPMC7136761 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Correlation Coefficients for a Study with Repeated Measures.

Shan Guogen G Zhang Hua H Jiang Tao T

Computational and mathematical methods in medicine 20200326

Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlation calculation are compared: (1) Pearson correlation; (2) correlation of subject means; (3) partial correlation for subject effect; (4) partial correlation for visit effect; and (5) a mixed model approach. Pearson correlation coefficient is traditionally used i ...[more]

PMID: 32300374

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Project description:Graph theory is a useful tool for deciphering structural and functional networks of the brain on various spatial and temporal scales. The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is affected by attentional and cognitive conditions, age, psychiatric disorders and so forth. However, it remains unclear how the clustering coefficient should be measured in a correlation-based network, which is among major representations of brain networks. In the present article, we propose clustering coefficients tailored to correlation matrices. The key idea is to use three-way partial correlation or partial mutual information to measure the strength of the association between the two neighboring nodes of a focal node relative to the amount of pseudo-correlation expected from indirect paths between the nodes. Our method avoids the difficulties of previous applications of clustering coefficient (and other) measures in defining correlational networks, i.e., thresholding on the correlation value, discarding of negative correlation values, the pseudo-correlation problem and full partial correlation matrices whose estimation is computationally difficult. For proof of concept, we apply the proposed clustering coefficient measures to functional magnetic resonance imaging data obtained from healthy participants of various ages and compare them with conventional clustering coefficients. We show that the clustering coefficients decline with the age. The proposed clustering coefficients are more strongly correlated with age than the conventional ones are. We also show that the local variants of the proposed clustering coefficients (i.e., abundance of triangles around a focal node) are useful in characterizing individual nodes. In contrast, the conventional local clustering coefficients were strongly correlated with and therefore may be confounded by the node's connectivity. The proposed methods are expected to help us to understand clustering and lack thereof in correlational brain networks, such as those derived from functional time series and across-participant correlation in neuroanatomical properties.

Project description:BackgroundWith the availability of the Affymetrix exon arrays a number of tools have been developed to enable the analysis. These however can be expensive or have several pre-installation requirements. This led us to develop an analysis workflow for analysing differential splicing using freely available software packages that are already being widely used for gene expression analysis. The workflow uses the packages in the standard installation of R and Bioconductor (BiocLite) to identify differential splicing. We use the splice index method with the LIMMA framework. The main drawback with this approach is that it relies on accurate estimates of gene expression from the probe-level data. Methods such as RMA and PLIER may misestimate when a large proportion of exons are spliced. We therefore present the novel concept of a gene correlation coefficient calculated using only the probeset expression pattern within a gene. We show that genes with lower correlation coefficients are likely to be differentially spliced.ResultsThe LIMMA approach was used to identify several tissue-specific transcripts and splicing events that are supported by previous experimental studies. Filtering the data is necessary, particularly removing exons and genes that are not expressed in all samples and cross-hybridising probesets, in order to reduce the false positive rate. The LIMMA approach ranked genes containing single or few differentially spliced exons much higher than genes containing several differentially spliced exons. On the other hand we found the gene correlation coefficient approach better for identifying genes with a large number of differentially spliced exons.ConclusionWe show that LIMMA can be used to identify differential exon splicing from Affymetrix exon array data. Though further work would be necessary to develop the use of correlation coefficients into a complete analysis approach, the preliminary results demonstrate their usefulness for identifying differentially spliced genes. The two approaches work complementary as they can potentially identify different subsets of genes (single/few spliced exons vs. large transcript structure differences).

Dataset Information

Correlation Coefficients for a Study with Repeated Measures.

Publications

Correlation Coefficients for a Study with Repeated Measures.

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