Abstract
Background: It is important to identify when two exposures impact a molecular marker (e.g., a gene's expression) in similar ways, for example, to learn that a new drug has a similar effect to an existing drug. Currently, statistically robust approaches for making comparisons of equivalence of effect sizes obtained from two independently run treatment vs. control comparisons have not been developed. Results: Here, we propose two approaches for evaluating the question of equivalence between effect sizes of two independent studies: a bootstrap test of the Equivalent Change Index (ECI), which we previously developed, and performing Two One-Sided t-Tests (TOST) on the difference in log-fold changes directly. The ECI of a gene is computed by taking the ratio of the effect size estimates obtained from the two different studies, weighted by the maximum of the two p-values and giving it a sign indicating if the effects are in the same or opposite directions, whereas TOST is a test of whether the difference in log-fold changes lies outside a region of equivalence. We used a series of simulation studies to compare the two tests on the basis of sensitivity, specificity, balanced accuracy, and F1-score. We found that TOST is not efficient for identifying equivalently changed gene expression values (F1-score = 0) because it is too conservative, while the ECI bootstrap test shows good performance (F1-score = 0.95). Furthermore, applying the ECI bootstrap test and TOST to publicly available microarray expression data from pancreatic cancer showed that, while TOST was not able to identify any equivalently or inversely changed genes, the ECI bootstrap test identified genes associated with pancreatic cancer. Additionally, when investigating publicly available RNAseq data of smoking vs. vaping, no equivalently changed genes were identified by TOST, but ECI bootstrap test identified genes associated with smoking. Conclusion: A bootstrap test of the ECI is a promising new statistical approach for determining if two diverse studies show similarity in the differential expression of genes and can help to identify genes which are similarly influenced by a specific treatment or exposure. The R package for the ECI bootstrap test is available at https://github.com/Hecate08/ECIbootstrap.