Generalized Mixed Modeling in Massive Electronic Health Record Databases: What is a Healthy Serum Potassium?

Converting electronic health record (EHR) entries to useful clinical inferences requires one to address computational challenges due to the large number of repeated observations in individual patients. Unfortunately, the libraries of major statistical environments which implement Generalized Linear Mixed Models for such analyses have been shown to scale poorly in big datasets. The major computational bottleneck concerns the numerical evaluation of multivariable integrals, which even for the simplest EHR analyses may involve hundreds of thousands or millions of dimensions (one for each patient). The Laplace Approximation (LA) plays a major role in the development of the theory of GLMMs and it can approximate integrals in high dimensions with acceptable accuracy. We thus examined the scalability of Laplace based calculations for GLMMs. To do so we coded GLMMs in the R package TMB. TMB numerically optimizes complex likelihood expressions in a parallelizable manner by combining the LA with algorithmic differentiation (AD). We report on the feasibility of this approach to support clinical inferences in the HyperKalemia Benchmark Problem (HKBP). In the HKBP we associate potassium levels and their trajectories over time with survival in all patients in the Cerner Health Facts EHR database. Analyzing the HKBP requires the evaluation of an integral in over 10 million dimensions. The scale of this problem puts far beyond the reach of methodologies currently available. The major clinical inferences in this problem is the establishment of a population response curve that relates the potassium level with mortality, and an estimate of the variability of individual risk in the population. Based on our experience on the HKBP we conclude that the combination of the LA and AD offers a computationally efficient approach for the analysis of big repeated measures data with GLMMs.