  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.
