Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group

Abstract

Program uses Shirley's test for the evaluation of endpoints in hematology, clinical chemistry, and urinalysis, which are assumed to be skewed distributed. Until now, no algorithm for Shirley's test for general unbalanced designs has been devised. A Shirley-type procedure is provided for estimating multiplicity-adjusted p-values or simultaneous confidence intervals for any continuous or discrete distributions and possible heterogeneous variances. Routine evaluation can be performed using the open-source R package nparcomp. The use of simultaneous confidence intervals for the relative effect is recommended, since these scale-invariant intervals allow one to claim the statistical significance of multiple endpoints as well as their biological relevance.

Are Multiple Contrast Tests Superior to the ANOVA?

“…As further results, we will also investigate the powers of the MCTP by using the Dunnett-type or Tukey-type contrast matrix C as given in eq. [5] or [6], respectively. For convenience, we will write the different contrasts in a unified way by a non-specified contrast matrix C ¼ ðc Bretz et al [1] have shown that T follows a multivariate Tðν; R; δðθÞÞ distribution with ν ¼ N À a degrees of freedom, correlation matrix R and non-centrality parameter vector δðθÞ ¼ ðδðθ 1 Þ; .…”

“…[2], and Tukey-type MCTP in eq. [6] for given b ¼ 0:9, and restriction b 2 ðqÞ ¼ max Table 1 Minimal sample sizes of the ANOVA F C in eq. [3], Grand-mean-type MCTP T with C in eq.…”

“…Thus, MCTPs provide an extensive tool for powerful multiple comparisons, for the computation of compatible SCI, and for testing the global null hypothesis. The results by Bretz et al [1] were extended to general linear models by Hothorn et al [3], to heteroscedastic models by Hasler and Hothorn [4] and Herberich et al [5], and for ranking procedures by Konietschke and Hothorn [6], Konietschke et al [7], and Konietschke et al [8]. For a comprehensive overview of existing methods, we refer to Bretz et al [27].…”

nparcomp: AnRSoftware Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals

“…and Williams-type (Williams 1972;Bretz 2006;Konietschke and Hothorn 2012) comparisons are expressed by using the contrast matrix…”

“…One-sided confidence intervals can be computed by replacing the two-sided quantile t 1−α,ν with its one-sided version (Konietschke and Hothorn 2012;Konietschke et al 2012a). Note that the SCI defined in (11) may be not range preserving, i.e., the lower bounds can be smaller than −1 and the upper bounds can be larger than 1.…”