Generalized Concordance for Competing Risks
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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 generalized concordance. The different components of the generalized concordance correspond to the probabilities that a model makes an error in the event-type prediction only, or the discrimination only or both. We develop a consistent estimator for the new metric that accounts for the censoring bias. Using the real and synthetic data experiments, we show that models selected using the existing metrics are worse than those selected using generalized concordance at jointly predicting the event type and event time. We use the new metric to develop a variable importance ranking approach, which we call the stepwise competing risks regression. The purpose of this approach is to identify the factors that are important for predicting both the event type and the event time. We use real and synthetic datasets to show that the existing approaches for variable importance ranking often fail to recognize the importance of the event-specific risk factors, whereas, our approach does not.
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