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Background: Set enrichment methods are commonly used to analyze high-dimensional molecular data and gain biological insight into molecular or clinical phenotypes. One important category of analysis methods employs an enrichment score, which is created from ranked univariate correlations between phenotype and each molecular attribute. Estimates of the significance of the associations are determined via a null distribution generated from phenotype permutation. We investigate some statistical properties of this method and demonstrate how alternative assessments of enrichment can be used to increase the statistical power of such analyses to detect associations between phenotype and biological processes and pathways. Results: For this category of set enrichment analysis, the null distribution is largely independent of the number of samples with available molecular data. Hence, providing the sample cohort is not too small, we show that increased statistical power to identify associations between biological processes and phenotype can be achieved by splitting the cohort into two halves and using the average of the enrichment scores evaluated for each half as an alternative test statistic. Further, we demonstrate that this principle can be extended by averaging over multiple random splits of the cohort into halves. This enables the calculation of an enrichment statistic and associated p value of arbitrary precision, independent of the exact random splits used. Conclusions: It is possible to increase the statistical power of gene set enrichment analyses that employ enrichment scores created from running sums of univariate phenotype-attribute correlations and phenotype-permutation generated null distributions. This increase can be achieved by using alternative test statistics that average enrichment scores calculated for splits of the dataset. Apart from the special case of a close balance between up- and down-regulated genes within a gene set, statistical power can be improved, or at least maintained, by this method down to small sample sizes, where accurate assessment of univariate phenotype-gene correlations becomes unfeasible.
Roder, J., Linstid, B., & Oliveira, C. (2019). Improving the power of gene set enrichment analyses. BMC Bioinformatics, 20(1). https://doi.org/10.1186/s12859-019-2850-1