ESTIMATING INTEGRALS USING QUADRATURE METHODS WITH AN APPLICATION IN PHARMACOKINETICS

被引:22
作者
BAILER, AJ [1 ]
PIEGORSCH, WW [1 ]
机构
[1] NIEHS,STAT & BIOMATH BRANCH,RES TRIANGLE PK,NC 27709
关键词
AREA UNDER CURVE; EXPONENTIAL DISPOSITION MODELS; MEAN SQUARED ERROR; NEWTON-COTES QUADRATURE; NUMERICAL INTEGRATION;
D O I
10.2307/2532462
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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 prespective 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.
引用
收藏
页码:1201 / 1211
页数:11
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