title: Estimating integrals using quadrature methods with an application in pharmacokinetics.
abstract: The estimation of integrals using numerical quadrature is common in many biological studies. For instance, in biopharmaceutical research the area under curves is a useful quantity in deriving pharmacokinetic parameters and in providing a surrogate measure of the total dose of a compound at a particular site. In this paper, statistical issues as separate from numerical issues are considered in choosing a quadrature rule. The class of Newton-Côtes numerical quadrature procedures is examined from the perspective of minimizing mean squared error (MSE). The MSE are examined for a variety of functions commonly encountered in pharmacokinetics. It is seen that the simplest Newton-Côtes procedure, the trapezoidal rule, frequently provides minimum MSE for a variety of concentration-time shapes and under a variety of response variance conditions. A biopharmaceutical example is presented to illustrate these considerations.
authors.affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056.
authors.forename: A J
authors.initials: AJ
authors.lastname: Bailer
authors.forename: W W
authors.initials: WW
authors.lastname: Piegorsch
mesh_terms: D000818:Animals; D006801:Humans; D008433:Mathematics; D015233:Models, Statistical; D010599:Pharmacokinetics