High- to Low-Dose Extrapolation in Animals - ACS Symposium Series

5 High- to Low-Dose Extrapolation in Animals

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on September 27, 2016 | http://pubs.acs.org Publication Date: January 13, 1984 | doi: 10.1021/bk-1984-0239.ch005

CHARLES C. BROWN National Cancer Institute, Bethesda, M D 20205

Quantitative risk assessment requires extrapolation from results of experimental assays conducted at high dose levels to predicted effects at lower dose levels which correspond to human exposures. The meaning of this high to low dose extrapolation within an animal species will be discussed, along with its inherent limitations. A number of commonly used mathematical models of dose-response necessary for this extrapolation, will be discussed. Other limitations in their ability to provide precise quantitative low dose risk estimates will also be discussed. These include: the existence of thresholds; incorporation of background, or spontaneous responses; modification of the dose-response by pharmacokinetic processes. In recent years, as the s e r i o u s long-range h e a l t h hazards of e n v i ronmental t o x i c a n t s have become recognized, the need has a r i s e n to q u a n t i t a t i v e l y estimate the e f f e c t s upon humans exposed to low l e v e l s of these t o x i c agents. Often inherent i n t h i s estimation procedure i s the n e c e s s i t y to e x t r a p o l a t e evidence observed under one set of c o n d i t i o n s i n one p o p u l a t i o n group or b i o l o g i c a l system t o a r r i v e at an estimate of the e f f e c t s expected i n the p o p u l a t i o n of i n t e r e s t under another set of c o n d i t i o n s . The q u a n t i t a t i v e assessment of human h e a l t h r i s k from exposure to t o x i c agents has been approached by r e l a t i n g the exposure l e v e l of the suspect to measures of h e a l t h r i s k on the b a s i s of e i t h e r epidemiologic or c l i n i c a l data on human populations or experimental data on animals or other b i o l o g i c a l systems. Unfortunately, there are o f t e n s e r i o u s l i m i t a t i o n s with both approaches. Since human populations cannot be regarded as e x p e r i mental subjects with regard to d e l e t e r i o u s e f f e c t s on h e a l t h , the o b s e r v a t i o n a l data from such sources are o f t e n incomplete and not o f the d e s i r a b l e form and substance. Attendant with epidemiologic This chapter not subject to U . S . copyright. Published 1984, American Chemical Society

Rodricks and Tardiff; Assessment and Management of Chemical Risks ACS Symposium Series; American Chemical Society: Washington, DC, 1984.


58

ASSESSMENT A N D M A N A G E M E N T OF C H E M I C A L RISKS

studies are d i f f i c u l t i e s i n the accurate measurement of i n d i v i d u a l exposure patterns and the c o n t r o l of f a c t o r s that may modify or confound the q u a n t i t a t i v e measures of h e a l t h r i s k . Moreover, long delays o f t e n occur between exposure and the occurrence of a measureable e f f e c t . Such delays can range up to decades as seen i n many cases of c a r c i n o g e n e s i s a s s o c i a t e d with o c c u p a t i o n a l expo sure to c e r t a i n agents, such as asbestos induced lung cancer. Often by n e c e s s i t y , the p o t e n t i a l l y d e l e t e r i o u s e f f e c t s of chemical compounds must be t e s t e d i n laboratory animals. For the e x t r a p o l a t i o n of animal study r e s u l t s to man, much care should be placed i n the design and conduct of these s t u d i e s , since many f a c t o r s may i n f l u e n c e t h e i r r e s u l t s . These f a c t o r s include the dosage and frequency of exposure, route of a d m i n i s t r a t i o n , s p e c i e s , s t r a i n , sex and age of the animal, d u r a t i o n of the study, and v a r i o u s other modifying f a c t o r s as deemed important f o r the p a r t i c u l a r agent and e f f e c t being s t u d i e d . Attendant with information on the dose-response of the agent i n question i s the n e c e s s i t y that the experimental data must be based on exposure l e v e l s higher than those f o r which the r i s k e s t i m a t i o n i s to be made. Some c o n s i d e r a t i o n has been given to the p o s s i b i l i t y of conducting extremely large experiments at very low dose l e v e l s . Use of large numbers of experimental subjects i s necessary to reduce the s t a t i s t i c a l e r r o r so that very small e f f e c t s can be adequately q u a n t i f i e d . However, as Schneiderman, et a l . ( Ο remark, "purely l o g i s t i c a l problems might guarantee failure." Therefore, to o b t a i n r e l i a b l y measureable e f f e c t s , the experimental information must be based on l e v e l s of exposure high enough to detect p o s i t i v e r e s u l t s . Since large segments of the human populations are o f t e n exposed to much lower l e v e l s , these high exposure l e v e l data must be extrapolated to lower l e v e l s of exposure. The purpose of t h i s report i s to d e s c r i b e the current s t a t i s t i c a l methods used f o r t h i s "high to low dose" e x t r a p o l a t i o n i n experimental animal species and to i n d i c a t e the u n c e r t a i n t i e s n e c e s s a r i l y attached to the estimates made with these methodol ogies. The high to low dose e x t r a p o l a t i o n problem i s conceptually straight-forward. The p r o b a b i l i t y of a t o x i c response i s modeled by a dose-response f u n c t i o n P(D) which represents the p r o b a b i l i t y of a t o x i c response when exposed to D u n i t s of the t o x i c agent. A general mathematical model i s chosen to d e s c r i b e t h i s f u n c t i o n a l r e l a t i o n s h i p , i t s unknown parameters are estimated from the a v a i l able data, and t h i s estimated dose-response f u n c t i o n P(D) i s then used to e i t h e r : (1) estimate the response measure at a p a r t i c u l a r low dose l e v e l of i n t e r e s t ; or (2) estimate that dose l e v e l c o r responding to a d e s i r e d low l e v e l of response ( t h i s dose estimate i s commonly known as the v i r t u a l l y safe dose, VSD). Many mathematical models of t h i s dose-response relationship have been proposed for t h i s problem. The f o l l o w i n g s e c t i o n d e s c r i b e s the models c u r r e n t l y being used. One of the major difficulties inherent i n t h i s high to low dose e x t r a p o l a t i o n


5.

BROWN

Dose Extrapolation in Animals

59

problem i s that the estimates of r i s k at low doses, and c o r r e s pondingly the estimates of VSD's f o r low response l e v e l s , are h i g h l y dependent upon the mathematical form assumed f o r the underl y i n g dose-response. These d i f f i c u l t i e s are discussed i n l a t e r sections.


Mathematical Models of Dose-Response To estimate the e f f e c t s expected to be observed o u t s i d e the range o f the experimental data, a mathematical model r e l a t i n g dose, i . e . , l e v e l of exposure to the t o x i c agent, to response, i . e . , a q u a n t i t a t i v e measure of the d e l e t e r i o u s e f f e c t produced, i s necessary. In general terms, dose-response i s the r e l a t i o n between a measureable stimulus, p h y s i c a l , chemical or b i o l o g i c a l , and the response of l i v i n g matter measured i n terms of the r e a c t i o n produced over some range of the degree or l e v e l of the stimulus. The r e a c t i o n s to any one stimulus may be m u l t i p l e i n nature, e.g. loss of weight, decrease i n organ function, or even death. Each r e a c t i o n may have i t s own unique r e l a t i o n with the l e v e l of the stimulus. In a d d i t i o n , the measure of any s p e c i f i c r e a c t i o n may be made i n terms of the magnitude of the e f f e c t produced, q u a n t i t a t i v e response, whether or not a s p e c i f i c effect i s produced, quantal response, or the time r e q u i r e d to produce a s p e c i f i c e f f e c t , time to response. The d i s c u s s i o n of models w i l l be l i m i t e d to quantal response models, but s i m i l a r models may be used f o r responses measured i n other u n i t s . These responses may be acute r e a c t i o n s , sometimes o c c u r r i n g w i t h i n minutes of the stimulus, or they may be long-delayed e f f e c t s such as cancer, which may not appear c l i n i c a l l y u n t i l most of the subjects normal l i f e s p a n has elapsed. Other responses may not even appear i n the exposed subject, but may become manifest i n some l a t e r progeny. The l e v e l of the stimulus, or dose l e v e l , may also be measured i n d i f f e r e n t ways. For example, consider a subject that i s exposed to a toxicant i n i t s environment, e i t h e r through the a i r breathed, the food eaten, or through some other e x t e r n a l source of exposure. The dose l e v e l may be q u a n t i f i e d i n terms of c o n c e n t r a t i o n i n the a i r or food, or i n term of the quantity of the substance a c t u a l l y reaching the target receptor, some i n t e r n a l organ, or other t i s s u e . The former may be thought of as the environmental, or " e x t e r n a l " , exposure l e v e l , while the l a t t e r may be termed the " i n t e r n a l " exposure l e v e l . Due to the subject's biochemical and p h y s i o l o g i c a l i n t e r n a l mechanisms, the doseresponse may be quite d i f f e r e n t f o r the two measures of dose. Since the f o l l o w i n g m a t e r i a l i s a p p l i c a b l e to dose as measured on any scale, no d i s t i n c t i o n between these two general bases of measurement w i l l be made.


60



Tolerance

D i s t r i b u t i o n Models

When the response i s quantal, i t s occurrence for any p a r t i c u l a r subject w i l l depend upon the l e v e l of the stimulus. For t h i s subject under constant environmental c o n d i t i o n s , a common assump t i o n i s that there i s a c e r t a i n dose l e v e l below which the p a r t i c u l a r subject w i l l not respond i n a s p e c i f i e d manner, and above which the subject w i l l respond with c e r t a i n t y . This level i s r e f e r r e d to as the subject's tolerance. Because of b i o l o g i c a l variability among subjects i n the population, their tolerance l e v e l s w i l l also vary. For quantal responses, i t i s t h e r e f o r e n a t u r a l to consider the frequency d i s t r i b u t i o n of t o l e r a n c e s over the p o p u l a t i o n s t u d i e d . If D represents the l e v e l of a p a r t i c u l a r stimulus, or dose, then the frequency d i s t r i b u t i o n of t o l e r a n c e s , f ( D ) , may be mathematically expressed as f(D)=dP(D)/dD which represents the p r o p o r t i o n of subjects whose t o l e r a n c e s l i e between D and DfdD, where dD i s small. I f a l l subjects i n the p o p u l a t i o n are exposed to a dose of D Q , then a l l subjects with t o l e r a n c e s l e s s than or equal to Dg w i l l respond, and the propor t i o n , P ( D Q ) , t h i s represents of the t o t a l p o p u l a t i o n i s given by P(D„)

D

= £ °f(D)dD

Assuming that a l l subjects i n the s u f f i c i e n t l y high dose l e v e l , then P(°°) = jf

population

will

respond

to

a

f(D)dD = 1

F i g u r e 1 shows a h y p o t h e t i c a l t o l e r a n c e frequency d i s t r i b u t i o n , f(D)dD, along with i t s corresponding cumulative distribution, P(D). Thus, when the response i s quantal i n nature, the f u n c t i o n P(D) can be thought of as r e p r e s e n t i n g the dose-response e i t h e r f o r the p o p u l a t i o n as a whole, or f o r a randomly s e l e c t e d subject. The notion that a tolerance distribution, or dose-response f u n c t i o n , could be determined s o l e l y from c o n s i d e r a t i o n of the s t a t i s t i c a l c h a r a c t e r i s t i c s of a study population was introduced independently by Gaddum (2) and B l i s s ( 3 ) . The r e s u l t s of t o x i c i t y t e s t s have o f t e n shown that the p r o p o r t i o n of responders increases monotonically with dose and e x h i b i t s a sigmoid r e l a t i o n s h i p with the logarithm of the exposure level. This o b s e r v a t i o n l e d to the development of the l o g normal, or p r o b i t , model f o r the t o l e r a n c e frequency d i s t r i b u t i o n , f(D;u.o) = (2πσ2)-1/2

β

χ

ρ

_ l_(lo (D)-μ f 2 σ g

f

σ

>

0



BROWN

Dose Extrapolation in Animals

DOSE LEVEL

Figure 1. Relationship d os e-respons e curve.

between tolerance

d i s t r i b u t i o n and


62


while the dose-response f u n c t i o n i s given by the cumulative normal probability, P(D;u,o) -

Φ[(1ο (ϋ)-μ)/σ] 8


2

where μ and σ represent the mean and v a r i a n c e of the d i s t r i b u t i o n o f the l o g t o l e r a n c e s . This method was put i n t o i t s modern form by B l i s s ( 4 ) , and Finney (5) gives a b r i e f h i s t o r y of i t s development. T h i s dose-response model was o r i g i n a l l y proposed f o r use i n problems of b i o l o g i c a l assay, i . e . the assessment of the potency o f t o x i c a n t s , drugs, and other b i o l o g i c a l s t i m u l i , and has been p r i m a r i l y used f o r problems of dose-response i n t e r p o l a t i o n ( i . e . e s t i m a t i o n w i t h i n the range of observable response r a t e s ) , r a t h e r than dose-response e x t r a p o l a t i o n ( i . e . e s t i m a t i o n outside the range of observable r a t e s ) . Mantel and Bryan (6) and Mantel, et a l . (7^) l a t e r proposed i t s use, with s u i t a b l e m o d i f i c a t i o n , f o r the problem of e x t r a p o l a t i o n of experimentally induced e f f e c t s observed at "high" dose l e v e l s to those expected at "low" l e v e l s . T h e i r m o d i f i c a t i o n was to assume a slope shallower than that observed i n the experimental animal study. T h e i r reasons f o r t h i s m o d i f i c a t i o n were two-fold: (1) to c o n s e r v a t i v e l y guard against the p o s s i b i l i t y that the true dose-response i n the "low dose r e g i o n might be d i f f e r e n t than that observed i n the "high" dose r e g i o n ; and (2) inbred s t r a i n s of laboratory animals are more likely to show steeper dose-response r e l a t i o n s h i p s than the heterogeneous human population to which the e x t r a p o l a t i o n i s to apply. This assumed conservative slope i s a key feature of the Mantel-Bryan methodology, though i t s choice i s a r b i t r a r y . For the purpose of e x t r a p o l a t i o n , the p a r t i c u l a r slope s e l e c t e d i s not meant to represent the " t r u e " slope i n the low dose region, but r a t h e r to represent a c o n s e r v a t i v e l y shallow slope no matter what the true dose-response may be i n t h i s region. Therefore, the Mantel-Bryan method was not proposed to provide n e c e s s a r i l y v a l i d estimates of low dose r i s k , but r a t h e r to provide "conservative" estimates of t h i s r i s k . However, the " c o n s e r v a t i v e " nature of t h i s e x t r a p o l a t i o n methodology has been questioned by many authors (8-10). 11

Other mathematical models of tolerance d i s t r i b u t i o n s which produce a sigmoid appearance of t h e i r corresponding dose-response f u n c t i o n s have been suggested. The most commonly used i s the l o g l o g i s t i c function, 1

P(D;a,b) = [l+exp(a + b l o g ^ D ) ) ] " ,

b

High- to Low-Dose Extrapolation in Animals - ACS Symposium Series

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