dPQL: A lossless distributed algorithm for generalized linear mixed model with application to privacy-preserving hospital profiling

Objective: To develop a lossless distributed algorithm for generalized linear mixed model (GLMM) with application to privacy-preserving hospital profiling. Materials and Methods: The GLMM is often fitted to implement hospital profiling, using clinical or administrative claims data. Due to individual patient data (IPD) privacy regulations and the computational complexity of GLMM, a distributed algorithm for hospital profiling is needed. We develop a novel distributed penalized quasi-likelihood (dPQL) algorithm to fit GLMM when only aggregated data, rather than IPD, can be shared across hospitals. We also show that the standardized mortality rates, which are often reported as the results of hospital profiling, can also be calculated distributively without sharing IPD. We demonstrate the applicability of the proposed dPQL algorithm by ranking 929 hospitals for coronavirus disease 2019 (COVID-19) mortality or referral to hospice that have been previously studied. Results: The proposed dPQL algorithm is mathematically proven to be lossless, that is, it obtains identical results as if IPD were pooled from all hospitals. In the example of hospital profiling regarding COVID-19 mortality, the dPQL algorithm reached convergence with only 5 iterations, and the estimation of fixed effects, random effects, and mortality rates were identical to that of the PQL from pooled data. Conclusion: The dPQL algorithm is lossless, privacy-preserving and fast-converging for fitting GLMM. It provides an extremely suitable and convenient distributed approach for hospital profiling.