Federated Learning with Incomplete Data: When to Use Complete Cases and When to Weight

TL;DR

This paper presents a federated learning framework for handling missing data, providing guidelines on when to use complete case analysis versus weighting, and introduces a calibrated weighting method for improved estimates.

Contribution

It develops a novel federated missing data framework, including a calibrated weight estimation approach that ensures consistency under certain model specifications.

Findings

The complete case estimator is preferred under specific conditions.

The calibrated weighting approach remains consistent if at least one model is correct.

A sandwich variance estimator accounts for weight estimation uncertainty.

Abstract

Privacy constraints have driven the rise of federated learning (FL), which enables multi-site analyses without sharing individual participant data. We develop a framework for FL with missing data, identifying conditions under which the complete case (CC) estimator is preferred over the inverse probability weighting (IPW) estimator. For settings where the CC estimator fails, we introduce a calibrated weight estimation approach that combines candidate weighting models across sites and remains consistent if at least one is correctly specified. Consistency conditions are stated at the site level, ensuring that the federated estimator inherits validity from local properties. We derive a sandwich variance estimator that accounts for uncertainty in weight estimation, and illustrate the framework by evaluating risk factors for 90-day mortality among patients with pleural infections treated with intrapleural enzyme therapy.