Geodesic
Nonlinear mixed effect modeling in recognition of underlying population dynamics
Mathematica Applicanda, Tome 48 (2020) no. 1, pp. 87-97.

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Nonlinear mixed effect modeling (NMEM) is a useful method allowing to fit parameters of the assumed model to the repeated data. In this paper we present results of some theoretical experiment designed to study the effectiveness of NMEM in recognition of the underlying population dynamics. In this experiment we used the logistic equation with fixed parameters to sample population data assuming log-normal distribution of the parameters. Two set of data have been created, each of them containing ten time-measurements of the size for one hundred virtual populations. Then we used NMEM to fit parameters of three most recognizable in tumor dynamics models: logistic, Gompertz and Greenspan model. It occurs that NMEM properly recognized the model structure, that is the fit of Gompertz model is worse (in terms of mean square error) comparing to the others. However, the difference between the fits for the logistic and Greenspan models is not very significant. Moreover, visually all the fits look equally good.
DOI : 10.14708/ma.v48i1.7042
Classification : 62P10, 92D25
Mots-clés : fitting model parameters, underlying population dynamics, nonlinear mixed effect modeling, logistic model, Gompertz model, Greenspan model 
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Urszula Foryś. Nonlinear mixed effect modeling in recognition of underlying population dynamics. Mathematica Applicanda, Tome 48 (2020) no. 1, pp.  87-97. doi : 10.14708/ma.v48i1.7042. http://geodesic.mathdoc.fr/articles/10.14708/ma.v48i1.7042/

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