DC-COX: Data collaboration Cox proportional hazards model for privacy-preserving survival analysis on multiple parties.

The demand for the privacy-preserving survival analysis of medical data integrated from multiple institutions or countries has been increased. However, sharing the original medical data is difficult because of privacy concerns, and even if it could be achieved, we have to pay huge costs for cross-institutional or cross-border communications. To tackle these difficulties of privacy-preserving survival analysis on multiple parties, this study proposes a novel data collaboration Cox proportional hazards (DC-COX) model based on a data collaboration framework for horizontally and vertically partitioned data. By integrating dimensionality-reduced intermediate representations instead of the original data, DC-COX obtains a privacy-preserving survival analysis without iterative cross-institutional communications or huge computational costs. DC-COX enables each local party to obtain an approximation of the maximum likelihood model parameter, the corresponding statistic, such as the p-value, and survival curves for subgroups. Based on a bootstrap technique, we introduce a dimensionality reduction method to improve the efficiency of DC-COX. Numerical experiments demonstrate that DC-COX can compute a model parameter and the corresponding statistics with higher performance than the local party analysis. Particularly, DC-COX demonstrates outstanding performance in essential feature selection based on the p-value compared with the existing methods including the federated learning-based method.