High performance implementation of the hierarchical likelihood for generalized linear mixed models: an application to estimate the potassium reference range in massive electronic health records datasets

Abstract Background Converting electronic health record (EHR) entries to useful clinical inferences requires one address the poor scalability of existing implementations Generalized Linear Mixed Models (GLMM) for repeated measures. The major computational bottleneck concerns numerical evaluation multivariable integrals, which even simplest EHR analyses may involve millions dimensions (one each patient). hierarchical likelihood (h-lik) approach GLMMs is a methodologically rigorous framework estimation that based on Laplace Approximation (LA), replaces integration with optimization, and thus scales very well dimensionality. Methods We present high-performance, direct implementation h-lik in R package TMB. Using this approach, we examined relation serum potassium measurements survival Cerner Real World Data (CRWD) database. Analyzing data an integral over 3 million dimensions, putting problem beyond reach conventional approaches. also assessed accuracy LA smaller samples 1 10% size full dataset were analyzed via a) original, interconnected (iGLM), h-lik, b) Adaptive Gaussian Hermite (AGH) c) gold standard multivariate Markov Chain Monte Carlo (MCMC). Results Random effects estimates generated by within values obtained iGLMs, AGH MCMC techniques. H-lik was 4–30 times faster than nearly 800 MCMC. are establishment non-linear relationship between level risk mortality, as individual care facility sources variations mortality CRWD. Conclusions found offers computationally efficient, numerically accurate analysis extremely large, real world measures GLMMs. inference from our guide choices treatment thresholds treating disorders clinic.