Optimal design for determination of AUC with no prior pharmacokinetic knowledge

Objectives: To develop a method for choosing sample intervals that provide accurate estimates of area under the concentration-time curve (AUC) when using the log trapezoidal method. The developed method will only require single individual or mean pooled concentration data and will not require prior pharmacokinetic knowledge for the drug of interest, as in the case where proposed analysis is via non-compartmental analysis methods. 

Methods: An algorithm was written using the R programming language. Optimal sample intervals were determined by minimising trapezoidal integration error. Trapezoidal error was approximated using the sample interval and the second derivative of a function describing the concentration data. Time intervals that minimised the integration error were found using a genetic algorithm followed by a quasi-Newton method. The best function describing the data was obtained by fitting sum of exponential models using maximum likelihood estimation. 

To evaluate the method, a dataset of 5000 random pharmacokinetic profiles were simulated consisting of two- and three-compartment pharmacokinetics without first order absorption and one-, two- and three-compartment pharmacokinetics with first order absorption. Each profile randomly sampled rate constants and macro-constants from uniform distributions designed to provide distinct phases in the concentration-time profile. Nine concentration observations were sampled from the profile with residual unexplained variability applied to represent real data. These data were subsequently used to test the methods ability to estimate AUC, maximum concentration (Cmax) and time of maximum concentration (tmax). Empirically selected sample times were used as a comparator. The comparator was a sampling regimen empirically designed by a  knowledgeable pharmacometrician. 

Results: The final method produced sample times that were equivalent (occasionally superior) to empirically selected sample times in estimating AUC, Cmax and tmax. Alterations to the method allowed for the algorithm to choose a final concentration time (tlast) that ensured three terminal half-lives were within the sampling period. This method was often superior to the empirical method. 

Conclusion: A method was developed that produces sampling intervals of equal or better quality to those selected empirically by a pharmacometrician, and may be particularly useful for users with limited pharmacometric training. This method removes the subjectivity of choosing sample times and allows for users to quickly determine optimal sampling intervals for determining AUC, Cmax and tmax. The sample times are easily re-optimised if the number of required samples is increased or decreased. Being developed in R, this method can be made easily accessible and is highly customisable. 

Jim Hughes

  • University of South Australia