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Converting electronic health record (EHR) entries to useful clinicalinferences requires one to address the poor scalability of existingimplementations of Generalized Linear Mixed Models (GLMM) for repeatedmeasures. The major computational bottleneck concerns the numerical evaluationof integrals, which even for the simplest EHR analyses may involve millions ofdimensions (one for each patient). The hierarchical likelihood (h-lik) approachto GLMMs is a framework for the estimation of GLMMs that is based on theLaplace Approximation (LA), which replaces integration with numericaloptimization, and thus scales very well with dimensionality. We present ahigh-performance implementation of the h-lik for GLMMs in the R package TMB.Using this approach, we examined the relation of serum potassium measurementsand survival in the Cerner Real World Data (CRWD) EHR database. Analyzing thisdata requires the evaluation of an integral in over 3 million dimensions. Wealso assessed the scalability and accuracy of LA in smaller samples of 1 and10% size of the full dataset that were analyzed via the a) original,interconnected Generalized Linear Models (iGLM), approach to h-lik, b) AdaptiveGaussian Hermite (AGH) and c) the gold standard of Markov Chain Monte Carlo(MCMC) for multivariate integration. Random effects estimates generated by theLA were within 10% of the values obtained by the iGLMs, AGH and MCMCtechniques. The H-lik approach was 4-30 times faster than AGH and nearly 800times faster than MCMC. We found that the combination of the LA and AD offers acomputationally efficient, numerically accurate approach for the analysis ofextremely large, real world repeated measures data via the h-lik approach toGLMMs. The clinical inference from our analysis may guide choices of threatmentthresholds for treating potassium disorders in the clinic.

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