Model dose-exposure-response

Exposure-response modeling can be an important component of a totality of evidence assessment of the risk of QTc prolongation. It can be evaluated in early-phase studies and as part of the conventiontil study of QTc prolongation, and may help inform further evaluation. There are many different types of models for the analysis of concentration-response data, including descriptive pharmacodynamic (PD) models and empirical models that link pharmacokinetic (PK) models (dose-concentration-response) with PD models. 

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Model equations can be augmented with expressions accounting for covariates such as subject age, sex, weight, disease state, therapy history, and lifestyle (smoker or nonsmoker, IV drug user or not, therapy compliance, and others). If sufficient data exist, the parameters of these augmented models (or a distribution of the parameters consistent with the data) may be determined. Multiple simulations for prospective experiments or trials, with different parameter values generated from the distributions, can then be used to predict a range of outcomes and the related likelihood of each outcome. Such dose-exposure, exposure-response, or dose-response models can be classified as steady state, stochastic, of low to moderate complexity, predictive, and quantitative. A case study is described in Section 22.6. 

Type IV hypersensitivity responses are elicited by T lymphocytes and are controlled by accessory cells and suppressor T cells. Macrophages are also involved in that they secrete several monokines, which results in proliferation and differentiation of T cells. Thus, there are numerous points along this intricate pathway in which drugs may modulate the final response. To achieve a Type IV response, an initial high-dose exposure or repeated lower-dose exposures are applied to the skin the antigen is carried from the skin by Langerhans cells and presented to cells in the thymus to initiate T-cell proliferation and sensitization. Once sensitized, a second challenge dose will elicit an inflammatory response. Thus, before sensitivity can be assessed, each of the models used to evaluate dermal hypersensitivity requires as a minimum ... 

When mmor data are used, a POD is obtained from the modeled mmor incidences. Response levels at or below 10% can often be used as the POD. The POD alone, being a single-point estimate of a single dose-response curve, does not convey all the critical information present in the data from which it is derived. To convey a measure of uncertainty, the POD should be presented as a central estimate with upper and lower bounds. The POD for extrapolating the relationship to environmental exposure levels of interest, when the latter are outside the range of observed data. 

To develop a probabilistic model, one has to assign probability distributions to model inputs such as degradation rates, partition coefficients, dose-response parameters (or dose-time-response parameters), exposure values, and so on, for a model relating impacts to exposure. This chapter is concerned with several kinds of technical decisions involved in the selection of distributions. 

All of the mathematical models that relate dose to response rate are either dichotomous response models or time-to-response models (23). Dichotomous response models are concerned with whether or not a particular response (tumor) is present by a particular time (e.g., the animal s normal lifetime). In time-to-response models, the relationship between initiation of exposure and the actual occurrence of the response is determined for each animal. 

The explanation of the pharmacokinetics or toxicokinetics involved in absorption, distribution, and elimination processes is a highly specialized branch of toxicology, and is beyond the scope of this chapter. However, here we introduce a few basic concepts that are related to the several transport rate processes that we described earlier in this chapter. Toxicokinetics is an extension of pharmacokinetics in that these studies are conducted at higher doses than pharmacokinetic studies and the principles of pharmacokinetics are applied to xenobiotics. In addition these studies are essential to provide information on the fate of the xenobiotic following exposure by a define route. This information is essential if one is to adequately interpret the dose-response relationship in the risk assessment process. In recent years these toxicokinetic data from laboratory animals have started to be utilized in physiologically based pharmacokinetic (PBPK) models to help extrapolations to low-dose exposures in humans. The ultimate aim in all of these analyses is to provide an estimate of tissue concentrations at the target site associated with the toxicity. 

Because relatively low intakes (compared to those experienced by test animals) are most likely from environmental exposure at Superfund hazardous waste sites, it generally can be assumed that the dose-response relationship will be linear on the low-dose portion of the multistage model dose-response curve. The equation above can apply to these linear low-dose situations. This linear equation is valid only at low risk levels (i.e., below the estimated risk of 0.01). For risk above 0.01 the one-hit equation should be used ... 

Another option attempts to convert biomonitoring results into a form that is directly useful for risk assessment. The chapter describes both the human pharmacokinetic (PK) modeling used to relate internal concentration to dose and the development of exposure-response relationships in animal studies that use biomarker concentrations rather than applied dose (see Figure 5-2c). Finally, the chapter describes how biomonitoring studies can augment and help to interpret traditional risk assessments. 

Second, there are biometrical requirements. Various exposure response models may be used and compared. The models need to be clearly defined, and goodness of fit should be reported, both for the separate exposures as well as for the mixtures. Concentration addition, response addition, and mixed-model results may be compared as possible alternatives, especially when underpinning of mechanistic assumptions is weak. Results at one exposure level (e.g., EC50) do not necessarily predict results at other exposure levels due to different slopes and positions of the curves for separate compounds and the mixtures. Statistical tests should be executed properly to compare predicted and observed responses. If any statements about the significance of results are made, the methods of dose-response analysis need to be reported. 

The majority of experimental mixture studies have analyzed the effects that arise from simultaneous exposure to chemicals. Very few studies exist where sequential exposure to several chemicals was analyzed. Only a concept founded on an understanding of the relationship between dose or concentration and exposure duration, time to effect, and recovery can hope to deal with the effect of sequential exposures. Conceptual frameworks for descriptions of time-dependent toxicity from a mechanistic perspective are available (e.g., Rozman and Doull 2000 Ashauer et al. 2006). However, the link between existing dose-time response models and a framework for mixture effect analysis from sequential exposure has yet to be made. A recent example of an interesting study that looked at sequential exposures is from Ashauer et al. (2007b), who base their analysis on a 1-compartment model for substance uptake, plus additional parameters for effect propagation and recovery. Generalizations are not yet in sight. 

Exposures of newborns to PAHs depend on pharmacokinetic processes operating in the mother, and transfer through breast milk. Since it is difficult to characterize these pathways in humans, physiologically based pharmacokinetic (PBPK) and pharmacodynamic (PD) models need to be developed using appropriate animal models, and incorporating key parameters such as dose, exposure duration, and developmental stage (Dorman et al, 2001). Thus, development of PBPK and PBPD models for PAHs is an immediate need that will help in not only characterizing the dose-response relationship, but also extrapolation of results from animal studies to humans. 

In the future, the BMCqs and MLEqi for lethality will be determined, presented, and discussed. Results from the above models will be compared with the log probit EPA (2000) benchmark dose software (http //www.epa.gov/ncea/ bmds.htm). In all cases, the MLE and BMC at specific response levels will be considered. Other statistical models such as the Weibull may also be considered. Since goodness-of fit-tests consider an average fit, they may not be valid predictors of the fit in the low-exposure region of interest. In this case, the output of the different models will be plotted and compared visually with the experimental data to determine the most appropriate model. The method that results in values consistent with the experimental data and the shape of the exposure-response curve will be selected for AEGL derivations. 

---