Objective:
We developed and evaluated a privacy-preserving One-shot Distributed Algorithm for Cox model to analyze multi-center time-to-event data without sharing patient-level information across sites, while accounting for heterogeneity across sites by allowing site-specific baseline hazard functions and feature distributions.
Materials and Methods:
We constructed a surrogate likelihood function to approximate the Cox log partial likelihood function which is stratified by site, using patient-level data from a single site and aggregated information from other sites. The ODAC estimator was obtained by maximizing the surrogate likelihood function. We evaluated and compare the performance of ODACH with meta-analysis by extensive numerical studies.
Results:
The simulation study showed that ODACH provided estimates close to the pooled estimator, which is obtained by directly analyzing patient-level data from all sites via a stratified Cox model. The relative bias was <1% across all scenarios. As a comparison, the meta-analysis estimator, which was obtained by the inverse variance weighted average of the site-specific estimates, had substantial bias when the event rate is <5%, with the relative bias reaching 12% when the event rate is 1%.
Conclusions:
ODACH is a privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data, which allows the baseline hazard functions as well as the distribution of covariate variables to vary across sites. It provides estimates that is close to the pooled estimator and substantially outperforms the meta-analysis estimator when the event is rare. It is thus extremely suitable for studying rare events with heterogeneous baseline hazards across sites in a distributed manner.
Re. “Effect of Low Skeletal Muscle Mass on Post-operative Survival of Patients With Abdominal Aortic Aneurysm: A Prognostic Factor Review and Meta-Analysis of Time to Event Data”
