An evaluation of numerical integration algorithms for the estimation of the area under the curve (AUC) in pharmacokinetic studies

Six numerical integration algorithms based on linear and log trapezoidal methods as well as four cubic-spline methods were proposed for estimation of area under the curve (AUC). These six different algorithms were implemented using IMSL/IDL^TM command language and evaluated using data simulated under five different dosing conditions and two different sampling conditions. Comparisons between AUC estimations using these six different algorithms and the theoretical results were made in terms of both overall AUC values and the superimposability of the concentration-time profiles. In well designed studies with ample data points, the algorithm based on IMSL/IDL^TM function CSSHAPE with concavity preservation gave the best performance. In contrast, when the frequency of blood collection was limited, the algorithm based on the log trapezoidal rule proved to be stable with reasonable accuracy, and is recommended as the practical method for numerical interpolation and integration in pharmacokinetic studies. Algorithms based on the combination of the log trapezoidal rule and cubic-spline methods using IMSL/IDL^TM function CSSHAPE can be developed to enhance overall performance.