Distributed Kaplan-Meier Analysis via the Influence Function with Application to COVID-19 and COVID-19 Vaccine Adverse Events

TL;DR

This paper introduces a distributed learning method for constructing Kaplan-Meier curves using the influence function, enabling multi-center survival analysis without sharing individual data, demonstrated on COVID-19 outcomes.

Contribution

The paper develops a novel distributed estimator for Kaplan-Meier curves that maintains statistical efficiency and privacy in multi-center studies, applied to COVID-19 data.

Findings

Higher incidence of blood clots after COVID-19 infection compared to vaccination.

Distributed estimator is unbiased and as efficient as pooled data methods.

Method enables privacy-preserving, timely survival analysis across multiple centers.

Abstract

During the COVID-19 pandemic, regulatory decision-making was hampered by a lack of timely and high-quality data on rare outcomes. Studying rare outcomes following infection and vaccination requires conducting multi-center observational studies, where sharing individual-level data is a privacy concern. In this paper, we conduct a multi-center observational study of thromboembolic events following COVID-19 and COVID-19 vaccination without sharing individual-level data. We accomplish this by developing a novel distributed learning method for constructing Kaplan-Meier (KM) curves and inverse propensity weighted KM curves with statistical inference. We sequentially update curves site-by-site using the KM influence function, which is a measure of the direction in which an observation should shift our estimate and so can be used to incorporate new observations without access to previous data. We show in simulations that our distributed estimator is unbiased and achieves equal efficiency to the combined data estimator. Applying our method to Beaumont Health, Spectrum Health, and Michigan Medicine data, we find a much higher covariate-adjusted incidence of blood clots after SARS-CoV-2 infection (3.13%, 95% CI: [2.93, 3.35]) compared to first COVID-19 vaccine (0.08%, 95% CI: [0.08, 0.09]). This suggests that the protection vaccines provide against COVID-19-related clots outweighs the risk of vaccine-related adverse events, and shows the potential of distributed survival analysis to provide actionable evidence for time-sensitive decision making.