Fig. 1: Illustration of the Batch-Effect Reduction Trees (BERT) algorithm.

A Independent measurements are passed to the BERT algorithm, which leverages contemporary multi-core architectures for efficient, hierarchical data integration. B Omic data is typically afflicted with missing values. While the state-of-the-art HarmonizR method requires the neglect of large portions of numerical input data, BERT facilitates data integration with minimal loss of data. C Uneven distribution of covariate levels (e.g., sex, age certain biological conditions), can negatively affect data integration. BERT allows for the consideration of categorical covariate levels (top, covariates known for all samples) and user-defined references if covariates are not known for the entire dataset (bottom, covariate level unknown for non-starred samples). D Concept sketch: Batch effects typically mask biological conditions in the raw data (top). Data integration with BERT alleviates batch effects, making biological signals more prominent for downstream data analyses (e.g., hierarchical clustering).