Identifying interactions in omics data for clinical biomarker discovery using symbolic regression

Abstract

Motivation: The identification of predictive biomarker signatures from omics and multi-omics data for clinical applications is an active area of research. Recent developments in assay technologies and machine learning (ML) methods have led to significant improvements in predictive performance. However, most high-performing ML methods suffer from complex architectures and lack interpretability.

Results: We present the application of a novel symbolic-regression-based algorithm, the QLattice, on a selection of clinical omics datasets. This approach generates parsimonious high-performing models that can both predict disease outcomes and reveal putative disease mechanisms, demonstrating the importance of selecting maximally relevant and minimally redundant features in omics-based machine-learning applications. The simplicity and high-predictive power of these biomarker signatures make them attractive tools for high-stakes applications in areas such as primary care, clinical decision-making and patient stratification.

Availability and implementation: The QLattice is available as part of a python package (feyn), which is available at the Python Package Index (https://pypi.org/project/feyn/) and can be installed via pip. The documentation provides guides, tutorials and the API reference (https://docs.abzu.ai/). All code and data used to generate the models and plots discussed in this work can be found in https://github.com/abzu-ai/QLattice-clinical-omics.

Supplementary information: Supplementary material is available at Bioinformatics online.

Fig. 1.

Metrics of the best model (ranked by BIC criterion) for predicting Alzheimer’s disease. The model is robust as shown by the relatively small drop in performance from the training set (AUC 0.98) to the test set (AUC 0.92). Receiver operator characteristic (ROC) curves (top) and confusion matrices for training set (bottom left) and test set (bottom right)

Fig. 2.

Model signal path for AD. A prominent signal contribution from MAPT was found in all 10 models (green). The signal is expressed in terms of mutual information and displayed above the nodes in the model (see Cover and Thomas (2006)) (A color version of this figure appears in the online version of this article.)

Fig. 3.

Partial dependence plot for the AD model: marginal effect of MAPT on AD-risk

Fig. 4.

ROC AUC scores (top) for the selected three feature model for insulin response. Confusion matrices (bottom left: train, bottom right: test)

Fig. 5.

Decision boundaries of the selected model. We keep the feature C2CD2L fixed at the values corresponding to the 0.25, 0.50 and 0.75 quantiles

Fig. 6.

Distributions of the two classes for the variables PDK4 (top), PHF23 (bottom left) and the linear combination found in the second model of Table 2 (bottom right)

Fig. 7.

A representative model for predicting Hepatocellular Carcinoma. A prominent signal contribution from chr17_59473060_59483266 is found in all 10 models. The signal is expressed in terms of mutual information and displayed above the nodes in the model (Cover and Thomas, 2006)

Fig. 8.

Metrics of the best model (ranked by BIC criterion) for predicting Hepatocellular Carcinoma. The model is robust as shown by the performance of the training set (AUC 1.0) compared to the test set (AUC 1.0). ROC curves (top) and confusion matrices for training set (bottom left) and test set (bottom right)

Fig. 9.

Left: HCC. Pairplot for features in the selected model. Right: 2d response of the model predictions, with train data overlaid. The decision boundary separates the two outcome areas

Fig. 10.

Metrics of the best model of the first fold (ranked by BIC criterion) for predicting Breast Cancer outcomes. The model is not overfitted as shown by the performance of the training set (AUC 0.66) compared to the test set (AUC 0.66). ROC curves (top) and confusion matrices for training set (bottom left) and test set (bottom right)

Fig. 11.

Pairwise Pearson correlation (absolute value) heatmap of the gene expression features in the models shown in equation (1)

Fig. 12.

Decision boundary for three of the models at the head of each k-fold. The top right aread (green) indicate a higher probability of death, compared to the remaining area (purple) (A color version of this figure appears in the online version of this article.)

Fig. 13.

Metrics of the best model of the first fold (ranked by BIC criterion) for predicting Breast Cancer outcomes. The model shows some degree of overfitting as shown by the performance of the training set (AUC 0.75) compared to the test set (AUC 0.67). ROC curves (top) and confusion matrices for training set (bottom left) and test set (bottom right)