Padé approximant meets federated learning: A nearly lossless, one-shot algorithm for evidence synthesis in distributed research networks with rare outcomes.

OBJECTIVE: We developed and evaluated a novel one-shot distributed algorithm for evidence synthesis in distributed research networks with rare outcomes. MATERIALS AND METHODS: Fed-Padé, motivated by a classic mathematical tool, Padé approximants, reconstructs the multi-site data likelihood via Padé approximant whose key parameters can be computed distributively. Thanks to the simplicity of [2,2] Padé approximant, Fed-Padé requests an extremely simple task and low communication cost for data partners. Specifically, each data partner only needs to compute and share the log-likelihood and its first 4 gradients evaluated at an initial estimator. We evaluated the performance of our algorithm with extensive simulation studies and four observational healthcare databases. RESULTS: Our simulation studies revealed that a [2,2]-Padé approximant can well reconstruct the multi-site likelihood so that Fed-Padé produces nearly identical estimates to the pooled analysis. Across all simulation scenarios considered, the median of relative bias and rate of instability of our Fed-Padé are both <0.1%, whereas meta-analysis estimates have bias up to 50% and instability up to 75%. Furthermore, the confidence intervals derived from the Fed-Padé algorithm showed better coverage of the truth than confidence intervals based on the meta-analysis. In real data analysis, the Fed-Padé has a relative bias of <1% for all three comparisons for risks of acute liver injury and decreased libido, whereas the meta-analysis estimates have a substantially higher bias (around 10%). CONCLUSION: The Fed-Padé algorithm is nearly lossless, stable, communication-efficient, and easy to implement for models with rare outcomes. It provides an extremely suitable and convenient approach for synthesizing evidence in distributed research networks with rare outcomes.