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Appendix I: Aggregation
Pages 515-536

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From page 515...
... The third discusses methods for aggregating uncertainty and interindividual variability in predicted risk.
From page 516...
... nonthreshold end points caused by exposure to an environmental mixture of m toxic agents may be conveniently expressed under a few general assumptions. First, assume that the m agents are present in an environmental mixture at corresponding concentrations Ci, where i=1,2,...,m' each of which produce, in exposed people, corresponding lifetime, time-weighted average biologically effective dose rates Dij, each causing one or more of n quantal (all or none)
From page 517...
... Under the stated assumptions, Pij=qjj=0 for any jth end point Tj that is unaffected by Dij alone, regardless of concurrent doses from any other agents. The quantity of interest aggregate increased probability P of occurrence of any of the n end points caused by any of the m toxic agentsmay therefore be expressed as P=Prob(Ol1 uOl2 ~ ~l,n (J2,1 U (Jm,1 U Um,n)
From page 518...
... D, and hence P may represent quantities subject to uncertainty or interindividual variability characterized by different probability distributions. If distributed variates are involved, a meaningful confidence bound on P cannot generally be obtained by performing the indicated summations with the same bound on all values of q, Q
From page 519...
... The estimated aggregate cancer potency in bioassay animals may then be used to extrapolate a corresponding potency of that compound in a human of average susceptibility (EPA, 1986, 1992~. Neither this interspecies extrapolation nor the issue of human interindividual variability in cancer susceptibility (discussed in Chapter 10)
From page 520...
... This alternative to EPA's procedure, however, depends on the validity of the independence assumption regarding tumor-type occurrence within bioassay animals, which is the subject of this appendix (I-21. In some of the few studies that have focused on tumor-type associations within individual animals, a few significant associations have been noted, mostly negative associations involving one or two specific tumor types among associated pairs.
From page 521...
... conducted on behalf of the National Research Council's Committee on Risk Assessment for Hazardous Air Pollutants. DATA DESCRIPTION Tumor-type associations among individual animals were examined for both control and treated animals using pathology data from 62 B6C3F1 mouse studies and 61 F/344N rat studies obtained from a readily available subset of the NTP carcinogenesis bioassay database.
From page 522...
... 522 Mice: Lung: Liver: Lymphoma: SCIENCE AND JUDGMENT IN RISK ASSESSMENT alveolar/bronchiolar adenomas or carcinomas hepatocellular adenomas, hepatocellular carcinomas, and hepatoblastomas histiocytic, lymphocytic, mixed, NOS, or undifferentiated. TABLE I-1 NTP Studies from Which Data Were Used CHEMICAL MICEa RATSa O-Chlorobenzalmalononitrile (CS-2)
From page 523...
... CZymbal-gland and clitoral or preputial-gland effects in treated animals. dLiver and skin effects in treated animals.
From page 524...
... This fact was the basis for concluding probable "spurious" negative correlations involving rapidly lethal tumor types in previous assessments of tumor-type associations in rodents (Breslow et al., 1974; Storer, 1972~. Unambiguous detection of associations in onsets of different tumor types requires either serial-sacrifice information or animal- and tumor-specific lethality information (Hoer and Walburg, 1972; Wahrendorf, 1983; Lagakos and Ryan, 1985; Mitchell and Turnbull, 1990)
From page 525...
... Adjusted p-values accounting for multiple tests of a zero-correlation null hypothesis were obtained for all control and all treated rats and mice using Hommel's modified Bonferroni procedure (Wright, 1992~. In the absence of serial sacrifice or lethality information, associations between onsets of pairs of tumor types in individual NTP-bioassay animals were evaluated using two crude techniques.
From page 526...
... 526 SCIENCE AND JUDGMENT IN RISK ASSESSMENT TABLE I-2 Correlations Between Tumor Prevalence at Death/Sacnfice in Control Groups SPECIES Adjusted Tumor Types Sex Corr. np-value pm-value RATS Adrenal x Leukemia Females 0.060 27940.017 0.272 Males 0.025 27860.257 1 Adrenal x Thyroid Females 0.041 26920.138 1 Males -0.024 25930.342 1 Thyroid x Leukemia Females -0.032 29420.120 1 Males -0.045 28270.076 1 Pituitary x Leukemia Females -0.158 3057CO.001 <0.020 Males -0.080 2990<0.001 <0.020 Mammary x Leukemia Females -0.074 3088<0.001 <0.020 Males -0.025 3045< 0.001 1 Mammary x Pituitary Females 0.076 3057<0.001 <0.020 Males 0.027 29900.301 1 Pituitary x Thyroid Females -0.002 29160.982 1 Males 0.026 27840.254 1 Pituitary x Adrenal Females -0.029 27700.268 1 Males -0.010 27390.659 1 Mammary x Adrenal Females -0.015 27940.597 1 Males 0.008 27860.835 1 Mammary x Thyroid Females -0.011 29420.642 1 Males 0.008 28270.846 1 MICE Liver x Lung Females -0.003 30580.978 0.204 Males -0.022 30110.322 1 Liver x Lymphoma Females -0.029 30590.185 1 Males -0.053 30140.017 0.204 Lung x Lymphoma Females -0.054 30710.018 0.204 Males -0.008 30160.791 1 Pituitary x Lung Females 0.014 28980.592 1 Males 0.025 27250.879 1 Pituitary x Liver Females 0.020 28910.393 1 Males -0.074 27240.307 1 Pituitary x Lymphoma Females -0.041 28990.058 0.580 Males 0.011 27270.806 1 Source: Bogen and Seilkop, 1993.
From page 527...
... , where the liver-related correlations were both positive. Terminal-sacrifice animals represented 66 to 68% of all the control mice and 53 to 63% of all control rats referred to in Table I-2.
From page 528...
... When leukemia and Zymbal's gland tumors in animals dying before terminal sacrifice were assumed to be lethal and all other tumor types incidental, the Mitchell-Turnbull test yielded similar results to those obtained using the unmodified age-stratif~ed analysis. In particular, it provided strong evidence that the small, negative associations between leukemia and pituitary-gland tumors in control rats were not due to chance or to differential lethality (males, p
From page 529...
... 1984. Exploration of the negative correlation between proliferative hepatocellular lesions and lymphoma in rats and mice-establishment and implications.
From page 530...
... The first model is a simple one in which a predicted low level of exposure-related increased risk R is well approximated by the product of U (a purely uncertain variate) and V (a purely heterogeneous variate that models interindividual variability)
From page 531...
... for the ratio N/n is simply a normalized binomial distribution that has smaller and smaller variances around the true value r as nacho. The key point is that in the relationship between n uncertain individual risks and the corresponding uncertain population risk, many of the uncertain characteristics of each of the individual risks are not independent, but rather reflect quantities such as potency-parameter estimation error or model-specification error that pertain identically or in much the same way to all individuals at risk, and thus do not in any sense "cancel out" upon summation.
From page 532...
... . The expected value, (N>= n, of population risk has traditionally has been used in defining riskacceptability criteria addressing N; however, criteria intended to be conservative with respect to uncertainty associated with N ought logically to refer to some upper confidence bound on N
From page 533...
... is, for practical purposes, equivalent to pure uncertainty pertaining to those values insofar as the characterization of individual risk is concerned. However, the real distinction between unidentifiable person-to-person variability and true uncertainty is revealed by their different impacts on estimated population risk.
From page 534...
... are both easily estimated, even in cases involving complex risk models with uncertain and interindividually variable parameters. These estimates may generally be sufficient for regulatory decisionmaking purposes seeking to address both uncertainty in population risk and differences in individual risk.
From page 535...
... 1987. Integrating uncertainty and interindividual variability in environmental risk assessment.


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