OSCAR: Optimal subset cardinality regression using the L0-pseudonorm with applications to prognostic modelling of prostate cancer

Abstract

In many real-world applications, such as those based on patient electronic health records, prognostic prediction of patient survival is based on heterogeneous sets of clinical laboratory measurements. To address the trade-off between the predictive accuracy of a prognostic model and the costs related to its clinical implementation, we propose an optimized L0-pseudonorm approach to learn sparse solutions in multivariable regression. The model sparsity is maintained by restricting the number of nonzero coefficients in the model with a cardinality constraint, which makes the optimization problem NP-hard. In addition, we generalize the cardinality constraint for grouped feature selection, hence making it possible to identify key sets of predictors that may be measured together in a kit in clinical practice. We demonstrate the operation of our cardinality constraint-based feature subset selection method, named OSCAR, in the context of prognostic modelling of prostate cancer, where it enabled one to determine the key explanatory predictors at different levels of model sparsity, and to explore how the model sparsity affects the model accuracy and implementation cost.

A Community Challenge to Predict Clinical Outcomes After Immune Checkpoint Blockade in Non-Small Cell Lung Cancer

“…A single linear regression model using a novel Optimal Subset CArdinality Regression (oscar) L0-quasinorm regularization was generated using the R package available at https://github.com/Syksy/oscar/releases/tag/v0.6.1. 47,48 The model is a linear product of the data matrix X and regularized beta coefficients b. Gene expression signature (CUSTOM FOPANEL) was estimated using a custom gene panel analyzed with GSVA (with the parameter mx.diff = TRUE). Other variables included in the model were sex, histology (squamous vs not), smoking history, ECOG performance status (0 vs not), TMB, and PD-L1.…”