31 Dose Response - CEE 597 - Lecture 31 Dose-Response...

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EE 597 - cture 31 CEE 597 Lecture 31 Dose-Response Models 11 April 2007 Jery Stedinger Lecture 31 1
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Bush restores water purity standard Ithaca Journal 11/1/2001 11 April 2007 Jery Stedinger Lecture 31 2
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Readings for Health Risk Analysis Paustenbach –history & background on health risk analysis Packet Molak - Toxic Chemicals Non-cancer Risk Analysis, 1997 Packet NRC 1983 – basic ideas and steps Packet McClellan A Risk Assessment Primer, updates NRC 1993 Packet nderson et al asic ideas; dose sponse analysis scaling acket Anderson et al. – basic ideas; dose-response analysis, scaling Packet Crump, “Methods for Carcinogenic Risk Assessment” Packet Hattis and Kennedy – the goal, issues in analysis Readings p. 156 Calabrese, “Hormesis: Changing view…” Packet 11 April 2007 Jery Stedinger Lecture 31 3
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Readings for Health Risk Analysis - 2 Rodricks &Taylor – recent background related to foods Readings p.43 Ames et al. – what are the risks? Readings p. 76 Epstein/ Swartz’s comment –not really? Readings p. 96 Abelson in Science –Health risk issues recapped Packet Colborn et al. , Our Stolen Future – Beyond cancer… Packet Rhomberg , Are chemicals…? Packet Steingraber, Having Faith Packet 11 April 2007 Jery Stedinger Lecture 31 4
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comic 11 April 2007 Jery Stedinger Lecture 31 5
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Difficult extrapolations introduce uncertainty to risk assessment into risk assessment 11 April 2007 Jery Stedinger Lecture 31 6
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Dose Response Models Environmental Contaminants How do we relate dose d to probability A(d) that the dose causes cancer? We need a reasonable functional relationship! This is a modeling exercise: We seek to fit a probability model to a data set to describe the relationships between the probability of a response and the application of an agent pp g 11 April 2007 Jery Stedinger Lecture 31 7
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One-hit Model: Important Very simple; Linear response; No threshold; No repair d = dose k = potency = “arrival rate” of hits = k d υ aa a e o s d A(d) = Pr{ at least one hit} = 1 – Pr{ no hits} {} = 1 – υ 0 e - υ /0! <<Poisson distribution; P(0) =±1±–exp[±–k±d±]± ± ± k d for k d << 1 <<first-order approximation 11 April 2007 Jery Stedinger Lecture 31 8 pp
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Multi-hit Dose Response Model Results from assuming cancer occurs whenever cell “hit” m times: A(d) = Pr[ > m hits in a Poisson Process with υ = kd ] +1 = υ m e - υ /m! + υ m+1 e - υ /(m+1)! + … = υ m e - υ /m! { 1 + υ /(m+1) + υ 2 /[(m+1)(m+2)] + … } where for υ = k d << 1, e - υ = e -kd is essentially 1 so that A(d) (kd) m /m! <<This is low-dose cancer risk model. 11 April 2007 Jery Stedinger Lecture 31 9
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Weibull Model Results from applying low-dose multi-hit model to individual cells. If each of n susceptible cells has a probability cd m of becoming a cancer, then for the entire organism: P{ no cancer cells} = [ 1 – c d m ] n <<no cancer every cell which for small c d m is { no cancer from m its } = [exp( d) m n exp( n d m P{ no cancer from m-hits } = [exp( – c d) ] = exp(– c n d ) Thus probability of cancer for organism is A(d) ±= ±1±–exp[ ±–q ±d m ] where q = c n is is a eibull distribution 11 April 2007 Jery Stedinger Lecture 31 10 This is a Weibull distribution .
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Multi-Stage Model 1 hit
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31 Dose Response - CEE 597 - Lecture 31 Dose-Response...

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