Parameter Estimation for Nonlinear Mixed Effects Models Implemented in Mathematica

• In many applications within biology and medicine, measurements are gathered from several entities in the same experiment. This could for example be patients exposed to a treatment or cells measured after stimuli. To characterize the variability in response between entities, the nonlinear mixed effects (NLME) model is a suitable statistical model. An NLME model enables quantification of both within- and between subject variability. The parameter estimation in NLME models is not straightforward, due to the intractable expression of the likelihood function. In this work we present a Mathematica package for parameter estimation in NLME models where the longitudinal model is defined by differential equations. The parameter estimation problem is solved by the first-order conditional estimation (FOCE) method with exact gradients. The package is demonstrated using data from a simulated drug concentration model.

Ämnesord

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinska och farmaceutiska grundvetenskaper -- Farmaceutiska vetenskaper (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Basic Medicine -- Pharmaceutical Sciences (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

Mixed effects models

Stochastic differential equations

Ordinary differential equations

Parameter estimation

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