A Comparative Study of Some Approaches for Estimating Tolerance Limits
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0092-86 I 51200 1 Copyright 0 2001 Drug Information Association Inc.
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A COMPARATIVE STUDY OF SOME APPROACHES FOR ESTIMATING TOLERANCE LIMITS MAXPETZOLD PhD student, Department of Statistics, Goteborg University, Goteborg, Sweden
In a dose finding study the aim is to come up with a safe and eflcient drug administration. By comparing the estimated tolerance limits of the concentrations with a predetermined desired interval, that is, the therapeutic window, one may be able to adjust the drug dosage to attain a large proportion of the population within the window. For drugs with a therapeutic window situated at high concentrations close to toxic levels, one has to achieve a balance between attaining a large proportion of the population at eflciently high levels on one hand and the risks of an overdose on the other hand. In such cases, it is important to use the proper estimation approach for the upper tolerance limit. Here, the conservative estimation approach intended for a drug with potentially adverse side effects is compared with the expectation approach intended for a drug with harmless side effects. It is shown in an example that the expectation approach can be considerably more eflcient when used in the latter case, an advantage that is rarely discussed when proposing estimators. Key Words: Dose finding study; Population pharmacokinetics; Tolerance limits
INTRODUCTION THE QUESTION OF HOW much drug should be used and how it should be administered for a given therapeutic purpose cannot readily be answered. Basically, two different methods have been used to answer this question in a population: empirical and population kinetic. The kinetic method, which is considered in this paper, is based upon the hypothesis that therapeutic and toxic responses are related to the amount of drug in the body or to the plasma drug concentration. The desired range of concentrations [v,, vz] in which the chances of successful therapy is high defines the therapeutic window. Precise limits of the therapeutic window are not de-
Reprint address: Max Petzold, Department of Statistics, Goteborg University, Box 660, SE-405 30 Goteborg, Sweden. E-mail: Max.PetzoldOstatistics.gu.se.
finable but approximate limits will be determined by the location of the maximal efficacy; Rowland and Tozer (1) provide a further introduction to therapeutic windows. Knowing the therapeutic window, it is possible to find the appropriate dosage for a population. In a dose finding study, the estimated statistical tolerance limits of the concentrations from sample data may be compared with the therapeutic window. While the (statistical) tolerance limits provide information about where the population sampled is likely to be concentrated, the dosage of the drug can be calibrated in a repeated study to attain a large proportion of the population within the desired concentration interval [v,,vz]. If the upper tolerance limit w is less than v2 the dosage can be increased, and if w is larger than v2 the dosage must be reduced.
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