Construction of an optimal destructive sampling design for noncompartmental AUC estimation

Optimising time samples for determining area under the curve of pharmacokinetic data using non-compartmental analysis

Objectives

The selection of sample times for a pharmacokinetic study is important when trapezoidal integration (e.g. non-compartmental analysis) is used to determine the area under the concentration–time curve (AUC). The aim of this study was to develop an algorithm that determines optimal times that provide the most accurate AUC by minimising trapezoidal integration error.

Methods

The algorithm required initial single individual or mean pooled concentration data but did not specifically require a prior pharmacokinetic model. Optimal sample intervals were determined by minimising trapezoidal error using a genetic algorithm followed by a quasi-Newton method. The method was evaluated against simulated and clinical datasets to determine the method's ability to estimate the AUC.

Key findings

The sample times produced by the algorithm were able to accurately estimate the AUC of pharmacokinetic profiles, with the relative AUC having 90% confidence intervals of 0.919–1.05 for profiles with two-compartment kinetics. When comparing the algorithm with rich sampling (e.g. phase I trial), the algorithm provided equivalent or superior sample times with fewer observations.

Conclusions

The creation of the algorithm and its companion web application allows users with limited pharmacometric or programming training can obtain optimal sampling times for pharmacokinetic studies.

Pharmacokinetic parameters estimation using adaptive Bayesian P-splines models

In preclinical and clinical experiments, pharmacokinetic (PK) studies are designed to analyse the evolution of drug concentration in plasma over time i.e. the PK profile. Some PK parameters are estimated in order to summarize the complete drug's kinetic profile: area under the curve (AUC), maximal concentration (C(max)), time at which the maximal concentration occurs (t(max)) and half-life time (t(1/2)).Several methods have been proposed to estimate these PK parameters. A first method relies on interpolating between observed concentrations. The interpolation method is often chosen linear. This method is simple and fast. Another method relies on compartmental modelling. In this case, nonlinear methods are used to estimate parameters of a chosen compartmental model. This method provides generally good results. However, if the data are sparse and noisy, two difficulties can arise with this method. The first one is related to the choice of the suitable compartmental model given the small number of data available in preclinical experiment for instance. Second, nonlinear methods can fail to converge. Much work has been done recently to circumvent these problems (J. Pharmacokinet. Pharmacodyn. 2007; 34:229-249, Stat. Comput., to appear, Biometrical J., to appear, ESAIM P&S 2004; 8:115-131).In this paper, we propose a Bayesian nonparametric model based on P-splines. This method provides good PK parameters estimation, whatever be the number of available observations and the level of noise in the data. Simulations show that the proposed method provides better PK parameters estimations than the interpolation method, both in terms of bias and precision. The Bayesian nonparametric method provides also better AUC and t(1/2) estimations than a correctly specified compartmental model, whereas this last method performs better in t(max) and C(max) estimations.We extend the basic model to a hierarchical one that treats the case where we have concentrations from different subjects. We are then able to get individual PK parameter estimations. Finally, with Bayesian methods, we can get easily some uncertainty measures by obtaining credibility sets for each PK parameter.

Assessing the clinical benefits of erythropoietic agents using area under the hemoglobin change curve

INTRODUCTION

In assessing erythropoietic agents for chemotherapy-induced anemia, traditional single time-point end points (e.g., hematopoietic response [HR]) fail to reflect clinical benefits over the entire therapy course. Area under the hemoglobin change curve (Hb AUC) is introduced as an alternative measure, and its reliability, clinical significance, and superiority are assessed.

METHODS

Using data from a phase IV open-label epoetin alfa (EPO) trial, we tested Hb AUC reliability by comparing its values derived from primary patient data with those derived from aggregated data. Clinical significance of the Hb AUC was investigated in three phase IV EPO trials by examining the linear relationship between Hb AUC quartiles and established clinical end points. The superiority of the Hb AUC over HR in its association with blood transfusion was tested through logistic regressions and area under the receiver operating characteristic (ROC) curve analysis.

RESULTS

The Hb AUC values derived from patient and aggregated data were similar. Strong and statistically significant linear trends of decreasing transfusion requirements, increasing quality-of-life improvements, and decreasing time to HR were found across Hb AUC quartiles. The Hb AUC rendered the HR variable insignificant when both were present in the same model. Area under the ROC curve analysis supported the superior performance of the Hb AUC.

CONCLUSIONS

We found that the Hb AUC is an objective, reliable, clinically meaningful, and comprehensive summary statistic that may be used to quantify clinical benefits for patients receiving erythropoietic agents. Further prospective validation of the Hb AUC metric is recommended.

Gaussian quadrature as a numerical integration method for estimating area under the curve

This paper presents a numerical integration method for estimating the area under the curve (AUC) over the infinite time interval. This method is based on the Gauss-Laguerre quadrature and produces AUC estimates over the infinite time interval without extrapolation in a usual sense. By contrast, in traditional schemes, piecewise interpolation is used to obtain the area up to the final sampling point, and the remaining portion is extrapolated using nonlinear regression. In this case, there is no theoretical consistency between the quadrature and extrapolation. The inconsistency may cause certain problems. For example, the optimal sampling criterion for the former is not necessarily optimal for the latter. Such inconsistency does not arise in the method of this work. The sampling points are placed near the zeros of Laguerre polynomials so as to directly estimate the AUC over the infinite time interval. The sampling design requires no particular prior information. This is also advantageous over the previous strategy, which worked by minimizing the variance of estimated AUC under the assumptions of particular pharmacokinetic and variance functions. The original Gaussian quadrature is believed to be inappropriate for numerical integration of data because of several restrictions. In this paper, it is shown that, using a simple strategy for managing errors due to these restrictions, the method produces an estimate of AUC with practically sufficient precision. The efficacy of this method is finally shown by numerical simulations in which the bias and variance of its estimate were compared with those of the previous methods such as the trapezoidal, log-trapezoidal, Lagrange, and parabolas-through-the-origin methods.

Variability of the model-independent AUC: the one sample per individual case

A theory is developed for estimation of a population value of AUC along with its standard deviation, in the case, when only one concentration-time (C-t) sample is available for each individual. This theory is based on model-independent pharmacokinetics. Integration methods are classified due to their applicability to the presented approach. The main goal of this work is to establish a statistical hypothesis-testing procedure which would make single C-t samples usable for bioequivalence studies. An application of the theory to a number of integration methods currently in use is analyzed in detail. A real data illustration is included.