Combining Cox Regressions Across a Heterogeneous Distributed Research Network Facing Small and Zero Counts

TL;DR

This paper addresses bias in meta-analyses of Cox models in distributed healthcare data with small counts, proposing approximation methods that improve accuracy over standard techniques.

Contribution

It introduces novel approximation methods for Cox model meta-analysis that reduce bias in small and zero count scenarios in distributed data settings.

Findings

Proposed three flexible approximation methods for Cox model meta-analysis.

Demonstrated reduced bias with new methods in simulation studies.

Validated approaches with real-world healthcare data applications.

Abstract

Studies of the effects of medical interventions increasingly take place in distributed research settings using data from multiple clinical data sources including electronic health records and administrative claims. In such settings, privacy concerns typically prohibit sharing of individual patient data, and instead, analyses can only utilize summary statistics from the individual databases. In the specific but very common context of the Cox proportional hazards model, we show that standard meta analysis methods then lead to substantial bias when outcome counts are small. This bias derives primarily from the normal approximations that the methods utilize. Here we propose and evaluate methods that eschew normal approximations in favor of three more flexible approximations: a skew-normal, a one-dimensional grid, and a custom parametric function that mimics the behavior of the Cox likelihood function. In extensive simulation studies we demonstrate how these approximations impact bias in the context of both fixed-effects and (Bayesian) random-effects models. We then apply these approaches to three real-world studies of the comparative safety of antidepressants, each using data from four observational healthcare databases.