Predicting prostate cancer recurrence via maximizing the concordance index

In order to effectively use machine learning algorithms, e.g., neural networks, for the analysis of survival data, the correct treatment of censored data is crucial. The concordance index (CI) is a typical metric for quantifying the predictive ability of a survival model. We propose a new algorithm that directly uses the CI as the objective function to train a model, which predicts whether an event will eventually occur or not. Directly optimizing the CI allows the model to make complete use of the information from both censored and non-censored observations. In particular, we approximate the CI via a differentiable function so that gradient-based methods can be used to train the model. We applied the new algorithm to predict the eventual recurrence of prostate cancer following radical prostatectomy. Compared with the traditional Cox proportional hazards model and several other algorithms based on neural networks and support vector machines, our algorithm achieves a significant improvement in being able to identify high-risk and low-risk groups of patients.

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