# Verticox+: vertically distributed Cox proportional hazards model with improved privacy guarantees

## TL;DR

Verticox+ is an improved privacy-preserving version of the Verticox model for federated learning in survival analysis.

## Contribution

Verticox+ introduces a privacy-preserving protocol to handle scenarios where survival outcomes are not locally known.

## Key findings

- Verticox+ achieves equivalent performance to the original Verticox model.
- The new protocol preserves privacy without requiring survival outcomes to be shared.
- The computational and communication costs are analyzed and discussed.

## Abstract

Federated learning allows us to run machine learning algorithms on decentralized data when data sharing is not permitted due to privacy concerns. Various models have been adapted to use in a federated setting. Among these models is Verticox, a federated implementation of Cox proportional hazards models, which can be used in a vertically partitioned setting. However, Verticox assumes that the survival outcome is known locally by all parties involved in the federated setting. Realistically speaking, this is not the case in most settings and thus would require the outcome to be shared. However, sharing the survival outcome would in many cases be a breach of privacy which federated learning aims to prevent. Our extension to Verticox, dubbed Verticox+, solves this problem by incorporating a privacy preserving 2-party scalar product protocol at different stages. This allows it to be used in scenarios where the survival outcome is not known at each party. In this article, we demonstrate that our algorithm achieves equivalent performance to the original Verticox implementation. We discuss the changes to the computational complexity and communication cost caused by our additions.