Estimating integrals using quadrature methods with an application in pharmacokinetics

A. J. Bailer, W. W. Piegorsch

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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
Issue number4
StatePublished - 1990

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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