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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.<\/jats:p>","DOI":"10.1007\/s10928-024-09931-w","type":"journal-article","created":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T16:01:58Z","timestamp":1720108918000},"page":"797-808","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mixed effect estimation in deep compartment models: Variational methods outperform first-order approximations"],"prefix":"10.1007","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0719-0831","authenticated-orcid":false,"given":"Alexander","family":"Janssen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank C.","family":"Bennis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marjon H.","family":"Cnossen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ron A. 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R.A.A.M. has received grants from governmental and societal research institutes such as NWO, ZonMW, Dutch Kidney Foundation and Innovation Fund and unrestricted investigator research grants from Baxter\/Baxalta\/ Shire\/Takeda, Bayer, CSL Behring, Sobi and CelltrionHC. He has served as advisor for Bayer, CSL Behring, Merck Sharp & Dohme and Baxter\/Baxalta\/Shire\/Takeda. All grants and fees paid to the institution.  A.J. and F.C.B. have no conflicts of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}