Mixed effect estimation in deep compartment models: Variational methods outperform first-order approximations

Abstract

This work focusses on extending the deep compartment model (DCM) framework to the estimation of mixed-effects. By introducing random effects, model predictions can be personalized based on drug measurements, enabling the testing of different treatment schedules on an individual basis. The performance of classical first-order (FO and FOCE) and machine learning based variational inference (VI) algorithms were compared in a simulation study. In VI, posterior distributions of the random variables are approximated using variational distributions whose parameters can be directly optimized. We found that variational approximations estimated using the path derivative gradient estimator version of VI were highly accurate. Models fit on the simulated data set using the FO and VI objective functions gave similar results, with accurate predictions of both the population parameters and covariate effects. Contrastingly, models fit using FOCE depicted erratic behaviour during optimization, and resulting parameter estimates were inaccurate. Finally, we compared the performance of the methods on two real-world data sets of haemophilia A patients who received standard half-life factor VIII concentrates during prophylactic and perioperative settings. Again, models fit using FO and VI depicted similar results, although some models fit using FO presented divergent results. Again, models fit using FOCE were unstable. In conclusion, we show that mixed-effects estimation using the DCM is feasible. VI performs conditional estimation, which might lead to more accurate results in more complex models compared to the FO method.