Accurate training of the Cox proportional hazards model on vertically-partitioned data while preserving privacy.

BACKGROUND: Analysing distributed medical data is challenging because of data sensitivity and various regulations to access and combine data. Some privacy-preserving methods are known for analyzing horizontally-partitioned data, where different organisations have similar data on disjoint sets of people. Technically more challenging is the case of vertically-partitioned data, dealing with data on overlapping sets of people. We use an emerging technology based on cryptographic techniques called secure multi-party computation (MPC), and apply it to perform privacy-preserving survival analysis on vertically-distributed data by means of the Cox proportional hazards (CPH) model. Both MPC and CPH are explained. METHODS: We use a Newton-Raphson solver to securely train the CPH model with MPC, jointly with all data holders, without revealing any sensitive data. In order to securely compute the log-partial likelihood in each iteration, we run into several technical challenges to preserve the efficiency and security of our solution. To tackle these technical challenges, we generalize a cryptographic protocol for securely computing the inverse of the Hessian matrix and develop a new method for securely computing exponentiations. A theoretical complexity estimate is given to get insight into the computational and communication effort that is needed. RESULTS: Our secure solution is implemented in a setting with three different machines, each presenting a different data holder, which can communicate through the internet. The MPyC platform is used for implementing this privacy-preserving solution to obtain the CPH model. We test the accuracy and computation time of our methods on three standard benchmark survival datasets. We identify future work to make our solution more efficient. CONCLUSIONS: Our secure solution is comparable with the standard, non-secure solver in terms of accuracy and convergence speed. The computation time is considerably larger, although the theoretical complexity is still cubic in the number of covariates and quadratic in the number of subjects. We conclude that this is a promising way of performing parametric survival analysis on vertically-distributed medical data, while realising high level of security and privacy.

Privacy-preserving dataset combination and Lasso regression for healthcare predictions.

BACKGROUND: Recent developments in machine learning have shown its potential impact for clinical use such as risk prediction, prognosis, and treatment selection. However, relevant data are often scattered across different stakeholders and their use is regulated, e.g. by GDPR or HIPAA. As a concrete use-case, hospital Erasmus MC and health insurance company Achmea have data on individuals in the city of Rotterdam, which would in theory enable them to train a regression model in order to identify high-impact lifestyle factors for heart failure. However, privacy and confidentiality concerns make it unfeasible to exchange these data. METHODS: This article describes a solution where vertically-partitioned synthetic data of Achmea and of Erasmus MC are combined using Secure Multi-Party Computation. First, a secure inner join protocol takes place to securely determine the identifiers of the patients that are represented in both datasets. Then, a secure Lasso Regression model is trained on the securely combined data. The involved parties thus obtain the prediction model but no further information on the input data of the other parties. RESULTS: We implement our secure solution and describe its performance and scalability: we can train a prediction model on two datasets with 5000 records each and a total of 30 features in less than one hour, with a minimal difference from the results of standard (non-secure) methods. CONCLUSIONS: This article shows that it is possible to combine datasets and train a Lasso regression model on this combination in a secure way. Such a solution thus further expands the potential of privacy-preserving data analysis in the medical domain.