Modifications of the Closure Principle for Analyzing Toxicological Studies
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Drug Information Journal, Vol. 31, pp. 403412, 1997 Printed in the USA. All rights reserved.
MODIFICATIONS OF THE CLOSURE PRINCIPLE FOR ANALYZING TOXICOLOGICAL STUDIES LUDWIGA. HOTHORN, PHD University of Hannover, Hannover, Germany
A Drug Information Association Workshop on “Statistical Methodology on Non-Clinical and Toxicological Studies” was held on March, 25-27, 1996. The purpose of this meeting was to discuss the appropriateness of current and new biostatistical methods in this field of drug development. This paper proposes a simple closure test for dose-response relationships under real data conditions. This approach takes into account deviation from variance homogeneity and monotonicity assumptions. Moreovel; this approach can be easily adapted for “any” kind of two-sample tests, for example, nonparametric, dichotomous, censored, and so forth. Power was compared by a simulation study for selected conditions. Key Words: MED; Closure principle; Trend test; Toxicological studies
INTRODUCTION THIS ARTICLE DESCRIBES a simple closure testing procedure for dose-response relationships under real data conditions. Although this approach can be used for randomized clinical trials, pharmacological studies, and several toxicological studies, for example, reproductive toxicity, repeated toxicity studies (1) are considered here for analyzing the dose-response relationship. A oneway design: {C-, D,, . . , Dk) (with C- . . . negative control; D . . . dose group; with k not too small E 2,3,4) is assumed and multiple endpoints of a different scale, for example, approximate gaul3ian distributed (eg, body weight), a highly skewed distribution (eg, ASAT enzyme), dichotomous (eg, number of animals that diednumber of animals
Presented at the DIA Workshop “Statistical Methodology in Non-Clinical and Toxicological Studies,” March, 25-27, 1996, Bruges, Belgium. Reprint address: Prof. Dr. L. A. Hothorn, Herrenhauser Str. 2, D-30419 Hannover, Germany.
at risk), or ordered categorical (eg, scored histopathological findings). Independent univariate analyses of the dose-response relationship should be performed, however, based on the same methodology. Only model-free approaches should be discussed here, because a priori in such “screening” studies a model for the profile cannot be assumed, even for a single endpoint. The purpose of toxicological studies is safety assessment by comparing the doses to the concurrent negative control (many-toone comparisons). Traditionally, the classical hypotheses are used: null-hypothesis for no difference and alternative hypothesis for a difference (or one-sided for an increase). In this setting, type I error a represents producer’s risk and type I1 error p consumer’s risk. A direct control of producer’s risk (via a priori definition of a) is possible, but control of consumer’s risk is of primary concern in risk assessment. ~ h ~~ ~ ~~ (2,3)f ~ ~ proposed the reversing of the hypotheses in the Sense of a k-smple equivalence problem. For this approach a threshold 6 must be de-
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