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Non-linear mixed-effects modeling software

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Nonlinear mixed effects models are a special case of regression analysis for which a range of different software solutions are available. The statistical properties of nonlinear mixed-effects models make direct estimation by a Gauss–Markov theorem impossible. Nonlinear mixed effects models are therefore estimated according to Maximum Likelihood principles.[1]. Specific estimation methods are applied, such as linearization methods as first-order (FO), first-order conditional (FOCE) or the lapplacian (LAPL), approximation methods such as iterative-two stage (ITS), importance sampling (IMP), stochastic approximation estimation (SAEM) or direct sampling. A special case is use of non-parametric approaches. Furthermore, estimation in limited or full Bayesian frameworks is performed using the Metropolis-Hastings or the NUTS algorithms.[2] Some software solutions focus on a single estimation method, others cover a range of estimation methods and/or with interfaces for specific use cases.

General-purpose software

General (use case agnostic) nonlinear mixed effects estimation software can be covering multiple estimation methods or focus on a single.

Software with multiple estimation methods

  • SAS is a package that is used in the wide statistical community and supports multiple estimation methods from PROC NLMIX
  • Multiple estimation methods are available in the R open source software system, such as nlme[3]
  • MATLAB provides multiple estimation methods in their nlmefit system[4]

SPSS at the moment does not support non-linear mixed effects methods.[5]

Software dedicated to a single estimation method

  • WinBUGS is an implementation of the Metropolis-Hastings method for Bayesian analysis
  • Stan is open source software that implements the NUTS algorithm

Software dedicated to pharmacometrics

The field of pharmacometrics relies heavily on nonlinear mixed effects approaches and therefore uses specialized software approaches. [6] As with general-purpose software, implementations of both single or multiple estimation methods are available.

Software with multiple estimation methods

  • NONMEM is the most widely used software in the field of pharmacometics

References

  1. ^ Davidian, Marie; Giltinan, David M. (1995-06-01). Nonlinear Models for Repeated Measurement Data. CRC Press. ISBN 978-0-412-98341-2.
  2. ^ Tsiros, Periklis; Bois, Frederic Y.; Dokoumetzidis, Aristides; Tsiliki, Georgia; Sarimveis, Haralambos (2019-04-01). "Population pharmacokinetic reanalysis of a Diazepam PBPK model: a comparison of Stan and GNU MCSim". Journal of Pharmacokinetics and Pharmacodynamics. 46 (2): 173–192. doi:10.1007/s10928-019-09630-x. ISSN 1573-8744.
  3. ^ "nlme function - RDocumentation". www.rdocumentation.org. Retrieved 2022-05-09.
  4. ^ "Nonlinear mixed-effects estimation - MATLAB nlmefit - MathWorks Benelux". nl.mathworks.com. Retrieved 2022-05-09.
  5. ^ "Does IBM SPSS Statistics offer nonlinear mixed models?". www.ibm.com. 2020-04-16. Retrieved 2022-05-09.
  6. ^ "Pharmacometrics - an overview | ScienceDirect Topics". www.sciencedirect.com. Retrieved 2022-05-09.
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