Estimation of half-life periods in nonlinear data with fractional polynomials

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.