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

• Published in: BMC medical research methodology Vol. 21; no. 1; pp. 151 - 24
• Main Authors: Bologa, Cristian G, Pankratz, Vernon Shane, Unruh, Mark L, Roumelioti, Maria Eleni, Shah, Vallabh, Shaffi, Saeed Kamran, Arzhan, Soraya, Cook, John, Argyropoulos, Christos
• Format: Journal Article
• Language: English
• Published: England BioMed Central 24-07-2021; BMC
• Subjects: Adaptive Gaussian Hermite quadrature; Approximation; Bayes Theorem; Big Data; Biomarkers; Clinical medicine; Datasets; Deep learning; Dyskalemias; Electronic Health Records; Generalized linear mixed models; Health care; Health facilities; Humans; Hyperkalemia; Hypokalemia; Laplace approximation; Linear Models; Markov chain Monte Carlo; Markov Chains; Medical research; Monte Carlo Method; Mortality; Nephrology; Patients; Potassium; Reference Values; Research methodology; Technical Advance; Vital signs; Work stations; United States > US; Dyskalemias; Generalized linear mixed models; Adaptive Gaussian Hermite quadrature; Electronic health records; Markov chain Monte Carlo; Laplace approximation
• ISSN: 1471-2288; 1471-2288
• DOI: 10.1186/s12874-021-01318-6

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 multivariable 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 methodologically rigorous 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, direct implementation of the h-lik for GLMMs in the R package TMB. Using this approach, we examined the relation of repeated 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, putting this problem beyond the reach of conventional approaches. 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 for multivariate integration Markov Chain Monte Carlo (MCMC).
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. The major clinical inferences in this problem are the establishment of the non-linear relationship between the potassium level and the risk of mortality, as well as estimates of the individual and health care facility sources of variations for mortality risk in CRWD.
We found that the direct implementation of the h-lik 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 treatment thresholds for treating potassium disorders in the clinic.