title: Estimation of half-life periods in nonlinear data with fractional polynomials.
abstract: Regression models are frequently used to model the functional relationship between an interesting outcome parameter and one or more potentially relevant explanatory variables. Objectives can be to set up as a prognostic model, for example, or an estimation model for a certain parameter of interest. Determining half-life periods can be viewed as a particular application of such an estimation model. However, specific to these modelling problems is that time-dependent active agent concentrations can be nonlinear. Concurrently, a major limitation to common regression approaches is the assumed linear relation of the investigated variables. Therefore, a more flexible approach is required to handle the problem of finding a model which fits the data adequately. One possibility is the use of fractional polynomials. The application of this modelling approach in a univariate setting is proposed in order to have an appropriate data model which subsequently serves as an estimation model for half-life periods. This estimation model includes Ridders' method which is based on a regula falsi approach, a standard methodology of numerical analysis. The suggested procedure is applied to real data examples of antibiotic tissue concentrations in visceral surgery, nephropharmacology and clinical pharmacology and is furthermore compared to simple approaches of modelling nonlinear data.
authors.affiliation: Institute of Epidemiology and Medical Biometry, Ulm University, Germany benjamin.mayer@uni-ulm.de.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Mayer
authors.affiliation: Nephrology Division, Department of Internal Medicine 1, Ulm University Hospital, Germany.
authors.forename: Frieder
authors.initials: F
authors.lastname: Keller
authors.affiliation: Institute of Pharmacology of Natural Products and Clinical Pharmacology, Ulm University, Germany.
authors.forename: Tatiana
authors.initials: T
authors.lastname: Syrovets
authors.affiliation: Department of General and Visceral Surgery, Ulm University Hospital, Germany.
authors.forename: Mathias
authors.initials: M
authors.lastname: Wittau
mesh_terms: D000465:Algorithms; D006207:Half-Life; D006801:Humans; D016014:Linear Models; D017711:Nonlinear Dynamics; D010601:Pharmacology, Clinical / Q000379:methods*; D011379:Prognosis; D014018:Tissue Distribution
keywords: Ridders’ method; fractional polynomials; half-life period; nonlinear; pharmacokinetics; regula falsi; tissue and plasma concentrations