Statistical Proof of Safety in Toxicological Studies
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Drug Information Journal, Vol. 31, pp. 357-361, 1997 Printed in the USA. All rights reserved.
STATISTICAL PROOF OF SAFETY IN TOXICOLOGICAL STUDIES DIETERHAUSCHKE, PHD Department of Preclinical Biometry, Byk Gulden Pharmaceuticals, Konstanz, Germany
The statistical test of the traditional hypothesis of no treatment effect is commonly used in toxicological experiments. Failing to reject the hypothesis often leads to the conclusion of evidence in favor of safety. The major drawback of this indirect approach is the fact that what is controlled by a prespecifed level is the probability of erroneously concluding hazard (producer risk). The primary concern of safety assessment, howevel; is the control of the consumer risk, that is, limiting the probability of erroneously concluding safety. In order to restrict this risk, safety has to be formulated as the alternative and hazard, that is, the opposite, has to be formulated as the hypothesis. Key Words: Toxicology; Proof of hazard; Proof of safety; Biostatistics
INTRODUCTION THE PURPOSE OF toxicology testing is the safety assessment of a new compound relative to a control. Based on this aim, statistical a-tests of the classical null hypothesis of no difference are usually performed. Failing to reject the hypothesis often leads to the conclusion that the compound has no deleterious effect in the corresponding biological model. The most important disadvantage of this indirect procedure is the fact that only the producer risk can be directly controlled by a.The primary concern, however, is control of the consumer risk. Thus, from a statistical point of view, the adequate test problem should be formulated by reversing the null hypothesis and the alternative and incorporating an a priori or a posteriori defined threshold. In this paper the direct approach will be compared with the indirect approach in the two-sample situation.
PROOF OF HAZARD Let X , be independent random variables and suppose that the distribution functions Fi(x) = F(x - pL)are continuous ( i = 0, 1 and j = 1, . . . , n,),with pa denoting the location parameter for the control (vehicle or negative group) and pI that for the compound (treatment group). Under the prior assumption of p o I p I ,that is, appropriateness of a one-sided test, the classical test problem (proof of hazard) is formulated as follows:
Presented at the DIA Workshop “Statistical Methodology in Non-Clinical & Toxicological Studies,” March 25-27, 1996, Bruges, Belgium. Reprint address: Dr. Dieter Hauschke, Department of Preclinical Biometry, Byk Gulden Pharmaceuticals, P.O. Box 10 03 10, 78403 Konstanz, Germany.
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Dieter Hauschke
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@: pI-
I 0 (compound is safe under test conditions)
H:: p, - cl0 > 0 (compound is hazardous under test conditions). Failing to reject the hypothesis by a statistical test at level ah.for example, Student’s ttest or Wilcoxon test, traditionally leads to the conclusion that the compound has no harmful effect in the experiment. Of course, a p-value greater than ahmight indicate that there is no adverse
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