Critical evaluation of the potential error in pharmacokinetic studies of using the linear trapezoidal rule method for the calculation of the area under the plasma level-time curve

Abstract

The linear trapezoidal rule method is commonly used for the estimation of the area under the plasma level-time curve. Error analyses are performed when the method is used in first-order absorption and first-order elimination kinetics in the one-compartment system. It is found that significant underestimations and overestimations in area during the absorption phase and postabsorption phase, respectively, can occur when the method is improperly used. During the exponential postabsorption phase the relative error is only a function of the ratio (n) of the time interval over the half-life of the two plasma data points in the interval. The error from the linear trapezoidal rule method at n = 0.5 is about 1%. The error increases to 15.5% and 57.1% when n is increased to 2 and 4, respectively. It is recommended that for most absorption studies the linear trapezoidal method be used for prepeak and plateau plasma data and the logarithmic trapezoidal method for postpeak plasma data.

Stereoselective disposition of flurbiprofen in normal volunteers.

“…The area under the curve and the area under the moment curve up to the last data point were determined using a combination of linear and log-linear trapezoidal methods (Chiou, 1978). The elimination rate constant, Xz, was obtained by log-linear regression of the terminal phase of the plasma drug concentration-time curve.…”

Intra‐ and inter‐individual variation in pharmacokinetics of intravenously infused amoxycillin and ampicillin to elderly volunteers.

“…zoidal rule and the logarithmic trapezoii method in the exponential post-absorpti phase (Chiou, 1978). The estimated area fr the last sampling time to infinity was calculal from the plasma concentration at the last san ling time divided by the terminal disposition r. constant (X2), estimated by the method of le squares from the terminal linear part of the I plasma concentration vs time curve.…”

Optimal sampling times in bioequivalence studies using a simulated annealing algorithm

“…We focus our attention on estimating the bulk of the area under the concentration-time curve, say for a time interval [0, t max + w] for some w. Then, we suggest that users employ the logarithmic trapezoidal method (Yeh and Kwan, 1978;Chiou, 1978) for estimating AUC. Technically, this focus is justified because when using this method, only the (fixed) final time point after t max + w is required if the PK model is correct and the observations are measured without error.…”