Joint Concordance Index

Abstract

Existing metrics in competing risks survival analysis such as concordance and accuracy do not evaluate a model’s ability to jointly predict the event type and the event time. To address these limitations, we propose a new metric, which we call the joint concordance. The joint concordance measures a model’s ability to predict the overall risk profile, i.e., risk of death from different event types. We develop a consistent estimator for the new metric that accounts for the censoring bias. We use the new metric to develop a variable importance ranking approach. Using the real and synthetic data experiments, we show that models selected using the existing metrics are worse than those selected using joint concordance at jointly predicting the event type and event time. We show that the existing approaches for variable importance ranking often fail to recognize the importance of the event-specific risk factors, whereas, the proposed approach does not, since it compares risk factors based on their contribution to the prediction of the different event-types. To summarize, joint concordance is helpful for model comparisons and variable importance ranking and has the potential to impact applications such as risk-stratification and treatment planning in multimorbid populations.