Non-linear mixed-effects modeling software
{{Short description|Special case of regression analysis}}
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 BLUE estimator impossible. Nonlinear mixed effects models are therefore estimated according to Maximum Likelihood principles.{{cite book |last1=Davidian |first1=Marie |last2=Giltinan |first2=David M. |title=Nonlinear Models for Repeated Measurement Data |date=1995 |publisher=CRC Press |isbn=978-0-412-98341-2 |chapter=Preface |chapter-url=https://books.google.com/books?id=0eSIBPAL4qsC&pg=PR13 |pages=xiii–xv }} Specific estimation methods are applied, such as linearization methods as first-order (FO), first-order conditional (FOCE) or the laplacian (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.{{cite journal |last1=Tsiros |first1=Periklis |last2=Bois |first2=Frederic Y. |last3=Dokoumetzidis |first3=Aristides |last4=Tsiliki |first4=Georgia |last5=Sarimveis |first5=Haralambos |title=Population pharmacokinetic reanalysis of a Diazepam PBPK model: a comparison of Stan and GNU MCSim |journal=Journal of Pharmacokinetics and Pharmacodynamics |date=April 2019 |volume=46 |issue=2 |pages=173–192 |doi=10.1007/s10928-019-09630-x |pmid=30949914 }} 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.{{Cite web |title=nlme function - RDocumentation |url=https://www.rdocumentation.org/packages/nlme/versions/3.1-157/topics/nlme |access-date=2022-05-09 |website=www.rdocumentation.org}}
- MATLAB provides multiple estimation methods in their nlmefit system.{{Cite web |title=Nonlinear mixed-effects estimation - MATLAB nlmefit - MathWorks Benelux |url=https://nl.mathworks.com/help/stats/nlmefit.html |access-date=2022-05-09 |website=nl.mathworks.com}}
SPSS at the moment does not support non-linear mixed effects methods.{{Cite web |date=2020-04-16 |title=Does IBM SPSS Statistics offer nonlinear mixed models? |url=https://www.ibm.com/support/pages/does-ibm-spss-statistics-offer-nonlinear-mixed-models |access-date=2022-05-09 |website=www.ibm.com |language=en}}
= Software dedicated to a single estimation method =
Software dedicated to pharmacometrics
The field of pharmacometrics relies heavily on nonlinear mixed effects approaches and therefore uses specialized software approaches.{{cite book |isbn=978-0-12-812736-0 |title=Encyclopedia of Pharmacy Practice and Clinical Pharmacy |chapter=Pharmacometrics and its Application in Clinical Practice |date=2019 |pages=227–238 |publisher=Elsevier |editor1-first=Zaheer-Ud-Din |editor1-last=Babar |first1=Muhammad |last1=Usman |first2=Huma |last2=Rasheed |doi=10.1016/B978-0-12-812735-3.00132-1 |doi-broken-date=29 May 2025 }} As with general-purpose software, implementations of both single or multiple estimation methods are available. This type of software relies heavily on ODE solvers.
= Software with multiple estimation methods =
- NONMEM is the most widely used software in the field of pharmacometics.
- Phoenix implements multiple estimation methods in a graphical user interface.{{Cite web |title=Pharmacokinetic Software |url=https://www.pharmpk.com/soft.html |access-date=2022-05-09 |website=www.pharmpk.com}}
- Pumas implements multiple estimation methods in the julia language.
- nlmixr/nlmixr2 is a suite interfaced in R that implements FOCE and SAEM.{{Cite book |last=Wang |first=Matthew Fidler, Teun M. Post, Richard Hooijmaijers, Rik Schoemaker, Mirjam N. Trame, Justin Wilkins, Yuan Xiong and Wenping |url=https://nlmixrdevelopment.github.io/nlmixr_bookdown/index.html |title=nlmixr: an R package for population PKPD modeling}}
- ADAPT and S-ADAPT implement multiple estimation methods in a graphical or scripting interface, respectively.
= Software dedicated to a single estimation method =
= Related software =
- Efficiency of ODE solvers impacts quality of estimation. Popular solvers are Runge-Kutta based methods, various stiff solvers and switching solvers such as LSODA of the LAPACK suite.
- A specialized form of pharmacokinetics modeling, physiology-based pharmacokinetic (PBPK) modeling can in some cases also be seen as a nonlinear mixed-effects implementation, see also the software section of that lemma.
- Optimal design software such as PopED can be used in conjunction with estimation.