SAS Programming to Calculate AUC in Pharmacokinetic Studies —Comparison of Four Methods in Concentration Data

AUC is an important parameter in pharmacokinetic studies. There are different ways to calculate AUC. Sometime, the statistician or pharmacokineticist has to choose one particular method to calculate AUC depending on the actual concentration data. Among many pharmacokinetic approaches and modeling analyses, traditional trapezoidal, log-linear trapezoidal, Lagrange polynomial integration, and Purves method are commonly used in calculation of AUC. This paper will discuss the four methods of AUC calculation in pharmacokinetic studies of drug. SAS will be used in application of those methods. A comparison of the four methods will be presented and analysis of the strength and weakness of these methods based on sample data will be performed. In conclusion, some general comments and suggestions will be provided. INTRODUCTION PK (pharmacokinetic) is the kinetics of drug absorption, distribution, and elimination. It studies how the drug is absorbed, distributed and eliminated in the body. The major measurements of PK study are plasma and urine. So, in most of time the PK study data is plasma concentration data. The AUC (the area under curve) can be presented graphically as the area under the plasma concentration versus time curve. AUC is an important parameter in PK analysis. AUC analysis, often used as a measure of drug exposure, plays many important roles in pharmacokinetics. AUC provides a measure how much and how long a drug stays in a body. There are different ways to calculate AUC. Sometimes, the statistician or pharmacokineticist has to choose one particular method to calculate AUC depending on the actual concentration data. There are two major different approaches to calculation of AUC: one is compartmental modeling analysis; the other is model independent (non-compartmental) analysis. Among the non-compartmental approach, traditional trapezoidal, log-linear trapezoidal, Lagrange polynomial integration, and Purves method are currently being used. 1) The linear trapezoidal method The linear trapezoidal method is the most intuitional method of numerical integration of area under the curve. The linear interpolation is presumed between any two adjacent concentration time points. A straight line as Y i-1 = a + bt i-1 can be approximated