Abstract
BackgroundThe synthesis of information across microarray studies has been performed by combining statistical results of individual studies (as in a mosaic), or by combining data from multiple studies into a large pool to be analyzed as a single data set (as in a melting pot of data). Specific issues relating to data heterogeneity across microarray studies, such as differences within and between labs or differences among experimental conditions, could lead to equivocal results in a melting pot approach.ResultsWe applied statistical theory to determine the specific effect of different means and heteroskedasticity across 19 groups of microarray data on the sign and magnitude of gene-to-gene Pearson correlation coefficients obtained from the pool of 19 groups. We quantified the biases of the pooled coefficients and compared them to the biases of correlations estimated by an effect-size model. Mean differences across the 19 groups were the main factor determining the magnitude and sign of the pooled coefficients, which showed largest values of bias as they approached ±1. Only heteroskedasticity across the pool of 19 groups resulted in less efficient estimations of correlations than did a classical meta-analysis approach of combining correlation coefficients. These results were corroborated by simulation studies involving either mean differences or heteroskedasticity across a pool of N > 2 groups.ConclusionsThe combination of statistical results is best suited for synthesizing the correlation between expression profiles of a gene pair across several microarray studies.
Highlights
The synthesis of information across microarray studies has been performed by combining statistical results of individual studies, or by combining data from multiple studies into a large pool to be analyzed as a single data set
By applying the asymptotic theory developed by Hassler and Thadewald [9] to the Pearson correlation coefficients obtained from the large expression matrix, we showed that differences in means across 19 heterogeneous groups of data is the main factor determining the magnitude and sign of coefficients of 124,750 gene pairs
We found a strong linear relationship between the Pearson correlation coefficients obtained from the large matrix of residuals and the coefficients resulting from averaging correlation estimates within groups
Summary
The synthesis of information across microarray studies has been performed by combining statistical results of individual studies (as in a mosaic), or by combining data from multiple studies into a large pool to be analyzed as a single data set (as in a melting pot of data). Blyth [8] gives an example involving the analysis of 2x2 contingency tables across two groups, and Hassler and Thadewald [9] illustrate Simpson’s paradox when correlation coefficients are estimated from a pool of two groups versus within each group In both cases, the paradox can be explained as results are further investigated in light of the specific statistical properties of each group of data. An early example of an ecological fallacy can be found in Gehlke and Biehl [11], whose study of grouping effects in census tract data showed that the magnitude of correlation coefficients of two variables tend to increase as the level of census tract aggregation increases. This problem was later referred to as the “modifiable areal unit problem” and further studied by Openshaw and Taylor [12]
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