Experimental design for estimating integrals by numerical quadrature, with applications to pharmacokinetic studies

Many experimental situations, including bioavailability studies, require the estimation of integrals by numerical quadrature applied to dependent variable observations with measurement error. A strategy is described for selecting values for the independent variable (e.g. time). The strategy minimizes the expectation of the square of the difference between the exact integral and the quadrature approximation. This approach was applied to simulated pharmacokinetic problems, including the estimation of bioavailability. Results indicate that the procedure is potentially useful in reducing the variance of resulting estimates and that it appears to be robust with respect to prior assumptions about model parameter values.