Related Experiment Video
Updated: Oct 27, 2025
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
High performance implementation of the hierarchical likelihood for generalized linear mixed models: an application to
Cristian G Bologa1, Vernon Shane Pankratz1, Mark L Unruh1
1Department of Internal Medicine, University of New Mexico School of Medicine, MSC10 5550 1 University of New Mexico Albuquerque, Albuquerque, NM, 87131, USA.
Background:
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.
Methods:
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).
Results:
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.
Conclusions:
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.
More Related Videos
Related Concept Videos
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
01:12Analysis of Population Pharmacokinetic Data
01:15Model Approaches for Pharmacokinetic Data: Physiological Models
01:26Pharmacokinetic Models: Comparison and Selection Criterion
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
01:06Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
00:59Model-Independent Approaches for Pharmacokinetic Data: Noncompartmental Analysis
One important characteristic of noncompartmental analyses is that drug exposure increases proportionally with increasing doses. This...