Dose-response assessment statistical models

Allen BC, Kavlock RJ, Kimmel CA, Faustman EM (1994b) Dose-response assessment for developmental toxicity III. Statistical models. Fundam Appl Toxicol, 23 496-509. 

UCL takes into account measurement uncertainty in the study used to estimate the dose-response relationship, such as the statistical uncertainty in the number of tumors at each administered dose, but it does not take into account other uncertainties, such as the relevance of animal data to humans. It is important to emphasize that UCL gives an indication of how well the model fits the data at the high doses where data are available, but it does not indicate how well the model reflects the true response at low doses. The reason for this is that the bounding procedure used is highly conservative. Use of UCL has become a routine practice in dose-response assessments for chemicals that cause stochastic effects even though a best estimate (MLE) also is available (Crump, 1996 Crump et al., 1976). Occasionally, EPA will use MLE of the dose-response relationship obtained from the model if human epidemiologic data, rather than animal data, are used to estimate risks at low doses. MLEs have been used nearly universally in estimating stochastic responses due to radiation exposure. 

Although rarely presented in a dose-response assessment, in nearly all cases the lower bound on the incremental probability of a response will be zero or less (see Figure 3.7). That is, the statistical model that accounts for the uncertainty in the results of an animal study also accommodates the possibility that no response may occur at low doses and that, in fact, there may be fewer responses (e.g., cancers) than observed in the control population at some low doses. The possibility of reduced responses at low doses also is shown by the lower confidence limit of data on radiation-induced cancers in some organs of humans including, for example, the pancreas, prostate, and kidney (Thompson et al., 1994). 

For food allergens, validated animal models for dose-response assessment are not available and human studies (double-blind placebo-controlled food challenges [DBPCFCs]) are the standard way to establish thresholds. It is practically impossible to establish the real population thresholds this way. Such population threshold can be estimated, but this is associated with major statistical and other uncertainties of low dose-extrapolation and patient recruitment and selection. As a matter of fact, uncertainties are of such order of magnitude that a reliable estimate of population thresholds is currently not possible. The result of the dose-response assessment can also be described as a threshold distribution rather than a single population threshold. Such distribution can effectively be used in probabilistic modeling as a tool in quantitative risk assessment (see Section 15.2.5)... 

A risk assessment is defined as a qualitative and quantitative process conducted by EPA to characterize the nature and magnitude of risks to public health from exposure to hazardous substances, pollutants, or contaminants released from specific sites. Risk assessments include the following components hazard identification, dose-response assessment, exposure assessment, and risk characterization. Statistical and biological models are used in quantitative risk... 

Benchmark Dose (BMD) modeling is an alternative method to the NOAEL/ LOAEL approach (Cmmp, 1984 Dourson et al., 1985 Barnes et al., 1995 U.S. EPA, 2000a). The method fits flexible mathematical models to the dose-response data and then determines the dose associated with a specified incidence of the adverse effects. Once this dose is estimated, then an RfD is estimated with the use of one or more uncertainty factors or Chemical Specific Adjustment Factors (CSAF) as described above. Advantages over the NOAEL/LOAEL approach include (1) the BMD is not limited to the tested doses (2) a BMD can be calculated even when the study does not identify a NOAEL and (3) unlike the NOAEL approach, the BMD approach accounts for the statistical power of the study. Numerous examples of BMD use in the dose-response assessment part of the risk assessment process are available on the U.S. EPA s Integrated Risk Information System (IRIS) (2004b). 

Uncertainty on tlie other hand, represents lack of knowledge about factors such as adverse effects or contaminant levels which may be reduced with additional study. Generally, risk assessments carry several categories of uncertainly, and each merits consideration. Measurement micertainty refers to tlie usual eiTor tliat accompanies scientific measurements—standard statistical teclmiques can often be used to express measurement micertainty. A substantial aniomit of uncertainty is often inlierent in enviromiiental sampling, and assessments should address tliese micertainties. There are likewise uncertainties associated with tlie use of scientific models, e.g., dose-response models, and models of environmental fate and transport. Evaluation of model uncertainty would consider tlie scientific basis for the model and available empirical validation. 

The following example is based on a risk assessment of di(2-ethylhexyl) phthalate (DEHP) performed by Arthur D. Little. The experimental dose-response data upon which the extrapolation is based are presented in Table II. DEHP was shown to produce a statistically significant increase in hepatocellular carcinoma when added to the diet of laboratory mice (14). Equivalent human doses were calculated using the methods described earlier, and the response was then extrapolated downward using each of the three models selected. The results of this extrapolation are shown in Table III for a range of human exposure levels from ten micrograms to one hundred milligrams per day. The risk is expressed as the number of excess lifetime cancers expected per million exposed population. 

The CA concept uses the toxic unit (TU) or the toxicity equivalence factor (TEF), defined as the concentration of a chemical divided by a measure of its toxicity (e.g., EC50) to scale toxicities of different chemicals in a mixture. As a consequence, the CA concept assumes that each chemical in the mixture contributes to toxicity, even at concentrations below its no-effect concentrations. The IA or RA concept, on the other hand, follows a statistical concept of independent random events it sums the (probability of) effect caused by each chemical at its concentration in the mixture. In the case of IA, the only chemicals with concentrations above the no-effect concentration contribute to the toxicity of the mixture. The IA model requires an adequate model to describe the (full) dose-response curve, enabling a precise estimate of the effect expected at the concentration at which each individual chemical is present in the mixture. The concepts generally are used as the reference models when assessing mixture toxicity or investigating interactions of chemicals... 

Historically, risk assessment for noncancer endpoints has been based on the identification of a no observed adverse effect level (NOAEL) from a toxicity study with an animal model. The NOAEL is then divided by appropriate uncertainty factors to take potential inter- and intraspecies differences in response into account. However, this approach does not take into account the size of the toxicity study or the shape of the dose-response curve. The benchmark dose (BMD) approach has been suggested as an alternative to a NOAEL (Crump 1984). A BMD is a dose or concentration that produces a predetermined change (e.g., 10% or 1 standard deviation) in response rate of an adverse effect (called the benchmark response or BMR). A BMDL is the statistical lower confidence limit on the dose or concentration at the BMD. The BMD and BMDL are calculated using mathematical dose-response models, which make appropriate use of sample size and the shape of the dose-response curve (EPA 2009b, 2000a). The BMDL is like a NOAEL (i.e., as a point of departure) and is divided by an appropriate composite uncertainty factor to derive a reference value. 

Figure 7.1 also depicts changes via behaviors, such as occupation, ambient exposure, and predisposition, such as genetic. Logically, it is correct regardless of the shape of the dose-response model. At low dose or at environmental (ambient) exposures, cancer risk assessment models used in regulatory law are either linear or linearized that is, each is a cumulative distribution function of lifetime cancer risk and thus is a monotonic function. Hormetic cancer dose-response models are also probabilistic however, they are nonmonotonic (they are relations). The EPA summarizes the reasons for using statistical and probabilistic methods in risk assessment as follows (EPA 2005) ... 

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