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

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