Modeling the plasma concentration – time profile in a single
rising dose study using the fractional polynomials approach.
Abstract
Preclinical toxicology studies identify a safe exposure range (NOAEL) to a novel
chemical or biological entity. When going into man, it is important not to exceed this
boundary. Therefore, an accurate prediction of the area under the curve (AUC) is crucial
in a dose rising study. The estimation of the AUC can be obtained using a compartmental
PK model or using an empirical approach, i.e., trapezoidal method.
Our gaol is to explore the behaviour of a third method by modelling the plasma
concentration – time curve using a fractional polynomials approach. Fractional
Polynomials widen the class of ordinary polynomials and offer more flexibility within the
linear framework. Since the number of polynomials in infinite, the possible exponents in
the model are limited to a prespecified set. In order to improve the quality of the
estimators, we do not restrict to a single model but we will select a prefixed number of
model, each of which will give an estimate and the final estimator will be obtained by
model averaging. The weight of each term will be determined by the posterior probability
of the model.
Given the dose escalation paradigm of our case study, a Bayesian approach was chosen to
fit our models. The accuracy and precision of the three different methods is compared
and presented.
References.

Aerts Marc, Faes Christel, Geys Helena and Molenberghs Geert,
Model averaging using fractionnal polynomials to estimate a safe level of
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Sabanes Bove, D; Held, L,
Bayesian fractional polynomial, Statistic andComputing 2010,
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Aerts Marc, Boelaert Frank, Faes Christel, Greys Helena, Hens Niel,
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