Optimal sampling times for minimum variance of clearance determination.

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Abstract
1 Clearance of a substance that follows first order kinetics can be determined from multiple plasma concentrations (the standard method) or from only one plasma concentration and an assumed volume of distribution (the simplified method). 2 On the basis of statistical considerations it is shown that the variance of the clearance determined by the standard method has a minimum when the mean sampling time is equal to the reciprocal elimination constant. For the simplified method the variance of the clearance is minimal when the sampling time is equal to the reciprocal elimination constant multiplied by one plus the ratio between the squared coefficients of variation of the concentration and the volume of distribution. 3 The sampling times determined in this way are optimal in the sense that the variance of the clearance estimate will be larger for any alternative choice of the same number of sampling times. In practice, the optimal sampling times can only be determined approximately because the elimination constant is not known exactly. The loss in precision of the clearance estimation arising herefrom will be less if the elimination constant is underestimated than if it is overestimated to the same relative extent. 4 In theory, the simplified method with optimal sampling time will give a more precise clearance determination than the standard method, if the number of optimally spaced sampling times is less than one plus the ratio between the squared coefficients of variation of the concentration and volume of distribution. In studies where each subject serves as his own control and the coefficient of variation of the volume of distribution is relatively small the simplified method will be of higher precision unless the number of samples with the standard method is unusually large.