Joint modeling of mixed outcomes using a rank-based sparse neural network.

Objective: In the past few decades, high-throughput profiling has been extensively conducted, leading to significant advancements in cancer research, survival analysis, and other biomedical studies. While many methods have been developed to identify important features and construct predictive models, biomedical research often faces challenges due to insufficient information caused by high dimensionality and small sample sizes, which frequently lead to unsatisfactory identification and prediction accuracy.

Methods: In this paper, we propose a rank-based sparse neural network that efficiently leverages information from mixed outcomes, particularly incorporating survival data. The proposed method accounts for unknown relationships between outcomes and high-dimensional covariates, whereas many traditional methods are built on a parametric framework. A novel loss function is derived to address the gradient imbalance issue and accommodate mixed outcomes. A sparse layer is developed to implement the penalization method, enabling the identification of important variables.

Results: We conducted extensive simulation studies, showing that the proposed method is effective and broadly applicable. The analysis of skin cutaneous melanoma (SKCM) demonstrates the competitive performance of our proposed method.

Conclusion: The proposed method effectively models mixed outcomes (including survival data) and selects important features, which is beneficial for biomedical studies like cancer and genomic research.