Estimating integrals using quadrature methods with an application in pharmacokinetics

A. J. Bailer, Walter W Piegorsch

Research output: Contribution to journalArticle

26 Citations (Scopus)

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-Cotes numerical quadrature procedures is examined from the perspective of minimizing mean squared error (MSE). The MSEs are examined for a variety of functions commonly encountered in pharmacokinetics. It is seen that the simplest Newton-Cotes 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.

Original languageEnglish (US)
Pages (from-to)1201-1211
Number of pages11
JournalBiometrics
Volume46
Issue number4
StatePublished - 1990
Externally publishedYes

Fingerprint

biopharmaceuticals
Numerical Quadrature
Quadrature Method
Pharmacokinetics
Integral Method
Mean Squared Error
pharmacokinetics
Trapezoidal Rule
Quadrature Rules
Area Under Curve
Dose
Curve
dosage
methodology
Research
Class

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

Cite this

Estimating integrals using quadrature methods with an application in pharmacokinetics. / Bailer, A. J.; Piegorsch, Walter W.

In: Biometrics, Vol. 46, No. 4, 1990, p. 1201-1211.

Research output: Contribution to journalArticle

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