High‐Dimensional Variable Selection With Competing Events Using Cooperative Penalized Regression

Variable selection is an important step in the analysis of high-dimensional data, yet there are limited options for survival outcomes in the presence of competing risks. Commonly employed penalized Cox regression considers each event type separately through cause-specific models, neglecting possibly shared information between them. We adapt the feature-weighted elastic net (fwelnet), an elastic net generalization, to survival outcomes and competing risks. For two causes, our proposed algorithm fits two alternating cause-specific models, where each model receives the coefficient vector of the complementary model as prior information. We dub this "cooperative penalized regression," as it enables the modeling of competing risk data with cause-specific models while accounting for shared effects between causes. Coefficients that are shrunken toward zero in the model for the first cause will receive larger penalization weights in the model for the second cause and vice versa. Through multiple iterations, this process ensures stronger penalization of uninformative predictors in both models. We demonstrate our method's variable selection capabilities on simulated genomics data and apply it to bladder cancer microarray data. We evaluate selection performance using the positive predictive value for the correct selection of informative features and the false positive rate for the selection of uninformative variables. The benchmark compares results with cause-specific penalized Cox regression, random survival forests, and likelihood-boosted Cox regression. Results indicate that our approach is more effective at selecting informative features and removing uninformative features. In settings without shared effects, variable selection performance is similar to cause-specific penalized Cox regression.