MOTIVATION: Random forest is a popular machine learning approach for the analysis of high-dimensional data because it is flexible and provides variable importance measures for the selection of relevant features. However, the complex relationships between the features are usually not considered for the selection and thus also neglected for the characterization of the analysed samples. RESULTS: Here we propose two novel approaches that focus on the mutual impact of features in random forests. Mutual forest impact (MFI) is a relation parameter that evaluates the mutual association of the features to the outcome and, hence, goes beyond the analysis of correlation coefficients. Mutual impurity reduction (MIR) is an importance measure that combines this relation parameter with the importance of the individual features. MIR and MFI are implemented together with testing procedures that generate P-values for the selection of related and important features. Applications to one experimental and various simulated datasets and the comparison to other methods for feature selection and relation analysis show that MFI and MIR are very promising to shed light on the complex relationships between features and outcome. In addition, they are not affected by common biases, e.g. that features with many possible splits or high minor allele frequencies are preferred. AVAILABILITY AND IMPLEMENTATION: The approaches are implemented in Version 0.3.3 of the R package RFSurrogates that is available at github.com/AGSeifert/RFSurrogates and the data are available at doi.org/10.25592/uhhfdm.12620.

MOTIVATION: High-throughput technologies allow comprehensive characterization of individuals on many molecular levels. However, training computational models to predict disease status based on omics data is challenging. A promising solution is the integration of external knowledge about structural and functional relationships into the modeling process. We compared four published random forest-based approaches using two simulation studies and nine experimental datasets. RESULTS: The self-sufficient prediction error approach should be applied when large numbers of relevant pathways are expected. The competing methods hunting and learner of functional enrichment should be used when low numbers of relevant pathways are expected or the most strongly associated pathways are of interest. The hybrid approach synthetic features is not recommended because of its high false discovery rate. AVAILABILITY AND IMPLEMENTATION: An R package providing functions for data analysis and simulation is available at GitHub (https://github.com/szymczak-lab/PathwayGuidedRF). An accompanying R data package (https://github.com/szymczak-lab/DataPathwayGuidedRF) stores the processed and quality controlled experimental datasets downloaded from Gene Expression Omnibus (GEO). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Machine learning methods and in particular random forests are promising approaches for prediction based on high dimensional omics data sets. They provide variable importance measures to rank predictors according to their predictive power. If building a prediction model is the main goal of a study, often a minimal set of variables with good prediction performance is selected. However, if the objective is the identification of involved variables to find active networks and pathways, approaches that aim to select all relevant variables should be preferred. We evaluated several variable selection procedures based on simulated data as well as publicly available experimental methylation and gene expression data. Our comparison included the Boruta algorithm, the Vita method, recurrent relative variable importance, a permutation approach and its parametric variant (Altmann) as well as recursive feature elimination (RFE). In our simulation studies, Boruta was the most powerful approach, followed closely by the Vita method. Both approaches demonstrated similar stability in variable selection, while Vita was the most robust approach under a pure null model without any predictor variables related to the outcome. In the analysis of the different experimental data sets, Vita demonstrated slightly better stability in variable selection and was less computationally intensive than Boruta. In conclusion, we recommend the Boruta and Vita approaches for the analysis of high-dimensional data sets. Vita is considerably faster than Boruta and thus more suitable for large data sets, but only Boruta can also be applied in low-dimensional settings.

MOTIVATION: It has been shown that the machine learning approach random forest can be successfully applied to omics data, such as gene expression data, for classification or regression and to select variables that are important for prediction. However, the complex relationships between predictor variables, in particular between causal predictor variables, make the interpretation of currently applied variable selection techniques difficult. RESULTS: Here we propose a new variable selection approach called surrogate minimal depth (SMD) that incorporates surrogate variables into the concept of minimal depth (MD) variable importance. Applying SMD, we show that simulated correlation patterns can be reconstructed and that the increased consideration of variable relationships improves variable selection. When compared with existing state-of-the-art methods and MD, SMD has higher empirical power to identify causal variables while the resulting variable lists are equally stable. In conclusion, SMD is a promising approach to get more insight into the complex interplay of predictor variables and outcome in a high-dimensional data setting. AVAILABILITY AND IMPLEMENTATION: https://github.com/StephanSeifert/SurrogateMinimalDepth. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.