Cover Image

PAPERBACK
$49.00



View/Hide Left Panel

the sample size n are shown in Table 1. (Note that the values of h1 and h2 are implicit functions of n.) These results are based on a one-stage model (k = 1) with a spontaneous response rate p0 = 0.10, and a nominal significance level of γ = 0.05 with r = 10 in the case n = 50. The value of σ2 = V(logeMTD) = 8.196 is based on the variance of the MTD of the 191 experiments considered previously by Krewski et al. (1990b). Using common logarithms, V(log10MTD) = 1.546.

The dependency of the correlations between log10TD50 and logeMTD on the Weilbull shape parameter k is illustrated in Table 2 for a sample size of n = 50. These results, including the limiting cases as k → 0 or ∞, are also based on (D.13). Note that the correlation remains high regardless of the value of k.

Annex E: Correlation Between TD50s For Rats and Mice

In this annex, we derive analytical expressions for the correlation between TD50 values for rats and mice. Letting Yrats and Ymice denote the logarithms (basee) of the estimated TD50s for rats and mice, we seek an expression for ρ = Corr(Yrats, Ymice). Following Bernstein et al. (1985) we assume initially that the MTD for rats is directly proportional to that for mice, with

Using the notation of annex D, we will denote the logarithms of the MTDs for rats and mice by Xrats and Xmice, so that

Note that (E.2) implies that V(Xrats) = V(Xmice) = σ2

As in annex D, we assume that the TD50s for rats and mice are uniformly distributed about their respective MTDs. From (D.10), we may then write



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 169
APPENDIX F 169 original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. the sample size n are shown in Table 1. (Note that the values of h1 and h2 are implicit functions of n.) These results are based on a one-stage model (k = 1) with a spontaneous response rate p0 = 0.10, and a nominal significance level of γ = 0.05 with r = 10 in the case n = 50. The value of σ2 = V(logeMTD) = 8.196 is based on the variance of the MTD of the 191 experiments considered previously by Krewski et al. (1990b). Using common logarithms, V(log10MTD) = 1.546. The dependency of the correlations between log10TD50 and logeMTD on the Weilbull shape parameter k is illustrated in Table 2 for a sample size of n = 50. These results, including the limiting cases as k → 0 or ∞, are also based on (D.13). Note that the correlation remains high regardless of the value of k. ANNEX E: CORRELATION BETWEEN TD50S FOR RATS AND MICE In this annex, we derive analytical expressions for the correlation between TD50 values for rats and mice. Letting Yrats and Ymice denote the logarithms (basee) of the estimated TD50s for rats and mice, we seek an expression for ρ = Corr(Yrats, Ymice). Following Bernstein et al. (1985) we assume initially that the MTD for rats is directly proportional to that for mice, with Using the notation of annex D, we will denote the logarithms of the MTDs for rats and mice by Xrats and Xmice, so that Note that (E.2) implies that V(Xrats) = V(Xmice) = σ2 As in annex D, we assume that the TD50s for rats and mice are uniformly distributed about their respective MTDs. From (D.10), we may then write

OCR for page 169
APPENDIX F 170 original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. where h1 and h2 are the same for rats and mice since g1 and g2 defined in (D.4) and (D.5) respectively are the same for rats and mice. Assuming that Yrats and Ymice are conditionally independent, given MTDmice (and hence MTDrats from (D.1)), we have Hence where ρ = Corr(Yrats, Xrats) is given in (D.13) of annex D. Based on the n = 127 compounds from the CPDB considered in section 6.1, we find σ2rats = 10.065 ≈ σ2mice = 8.873. For σ2 = 10, we have ρ = 0.943. The assumption (D.1) of strict proportionality between MTDrats and MTDmice can be relaxed. Let V(Xrats) = σ2rats and V(Xmice) = σ2mice . As in (D.3), we have and Assuming Yrats and Ymice are conditionally independent, given Xrats and Xmice, we have and hence

OCR for page 169
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. APPENDIX F (Xrats, Xmice) = 7.638, and ρ = 0.763 171 For the n = 127 compounds considered in section 6.1, we estimate Cov

OCR for page 169
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution.APPENDIX F 172