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

Hospital profiling provides a quantitative comparison of health care providers for their quality of care regarding certain clinical outcomes. To implement hospital profiling, the generalized linear mixed model (GLMM) is usually used to fit clinical or administrative claims data, adjusting for the effects of covariates. For better generalizability, data across multiple hospitals, databases or networks are desired. However, due to the privacy regulation and the computation complexity of GLMM, a convenient distributed algorithm for hospital profiling is needed. In this paper, we develop a novel distributed Penalized Quasi Likelihood algorithm (dPQL) to fit GLMM, when only aggregated data, rather than the individual patient data are available across hospitals. The dPQL algorithm is based on a newly-developed distributed linear mixed model (DLMM) algorithm. This proposed dPQL algorithm is lossless, i.e. it obtains identical results as if the individual patient data are pooled from all hospitals. We demonstrate the usage of the dPQL algorithms by ranking 929 hospitals for COVID-19 mortality or referral to hospice in Asch, et al. 2020.