  Logistic regression (LR) is a widely used classification method for modeling
binary outcomes in many medical data classification tasks. Research that
collects and combines datasets from various data custodians and jurisdictions
can excessively benefit from the increased statistical power to support their
analyzing goals. However, combining data from these various sources creates
significant privacy concerns that need to be addressed. In this paper, we
proposed secret sharing-based privacy-preserving logistic regression protocols
using the Newton-Raphson method. Our proposed approaches are based on secure
Multi-Party Computation (MPC) with different security settings to analyze data
owned by several data holders. We conducted experiments on both synthetic data
and real-world datasets and compared the efficiency and accuracy of them with
those of an ordinary logistic regression model. Experimental results
demonstrate that the proposed protocols are highly efficient and accurate. This
study introduces iterative algorithms to simplify the federated training a
logistic regression model in a privacy-preserving manner. Our implementation
results show that our improved method can handle large datasets used in
securely training a logistic regression from multiple sources.
