Dose-Response Relationships models

Benchmark Dose (BMD)—Usually defined as the lower confidence limit on the dose that produces a specified magnitude of changes in a specified adverse response. For example, a BMDio would be the dose at the 95% lower confidence limit on a 10% response, and the benchmark response (BMR) would be 10%. The BMD is determined by modeling the dose response curve in the region of the dose response relationship where biologically observable data are feasible. 

No data were located regarding PBPK/PD modeling to explain the biological basis for the dose-response relationship in humans or animals after exposure to diisopropyl methylphosphonate. 

Dose-Response Extrapolation Models. A dose-response model is simply a hypothetical mathematical relationship between dose-rate and probability of response. For example, the simplest form of such a model asserts that probability of tumor initiation is a linear multiple of dose-rate (provided the dosage is well below the organism s acute effect threshold for the substance in question). In general, we will express dose-response models as follows ... 

Drug-receptor interactions Dose-response relationships Molecular modeLs of receptors and signal transduction mechanisms Biotr an s fo r m ati on Ph ar macokine t ios Ph armacody namics... 

Ideal for studying the dose-response relationship for QT interval prolongation taking into account all the pharmacological properties of a compound The dog model is one of the most widely used anesthetized rabbits (especially female rabbits) have also been proposed for high sensitivity It provides complementary information with respect to in vitro tests (activity of metabolites, measurement of plasma drug concentrations, calculation of the volume of distribution) Possibility to induce experimental TdP... 

Models for determining the dose-response relationship vary based upon the type of toxicological hazard. In the dose-response for chemical carcinogens, it is frequently assumed that no threshold level of exposure (an exposure below which no effects would occur) exists, and, therefore, any level of exposure leads to some finite level of risk. As a practical matter, cancer risks of below one excess cancer per million members of the population exposed (1 x 10 ), when calculated using conservative (risk exaggerating) methods, are considered to represent a reasonable certainty of no harm (Winter and Francis, 1997). 

To model the uptake of ozone and other gases for establishing dose-response relationships at specific sites, local dose must be accurately deBned. In the past, this has not been done for specific sites. Fairchild... 

For non-threshold mechanisms of genotoxic carcinogenicity, the dose-response relationship is considered to be linear. The observed dose-response curve in some cases represents a single ratedetermining step however, in many cases it may be more complex and represent a superposition of a number of dose-response curves for the various steps involved in the tumor formation (EC 2003). Because of the small number of doses tested experimentally, i.e., usually only two or three, almost all data sets fit equally well various mathematical functions, and it is generally not possible to determine valid dose-response curves on the basis of mathematical modeling. This issue is addressed in further detail in Chapter 6. 

Dose-response assessment today is generally performed in two steps (1) assessment of observed data to derive a dose descriptor as a point of departure and (2) extrapolation to lower dose levels for the mmor type under consideration. The extrapolation is based on extension of a biologically based model (see Section 6.2.1) if supported by substantial data. Otherwise, default approaches that are consistent with current understanding of mode of action of the agent can be applied, including approaches that assume linearity or nonlinearity of the dose-response relationship, or both. The default approach is to extend a straight line to the human exposure doses. 

The linear component of the LMS model, qi (i.e., one of the parameters of the polynomial), is approximately equivalent to the slope at low doses of the dose-response relationship between the tumor incidence and the dose. This linearity at low dose is a property of the formulation developed for the multistage model and is considered by proponents to be one of its important properties. This linear component of the polynomial, qi, is used to carry out low-dose extrapolation. The linear response at low doses is considered to be conservative with regard to risk, as the dose-response relationship at low doses may well be sublinear. Although supralinearity at low doses cannot be excluded, it is usually considered to be unlikely. 

The 95% confidence limits of the estimate of the linear component of the LMS model, /, can also be calculated. The 95% upper confidence limit is termed qi and is central to the US-EPA s use of the LMS model in quantitative risk assessment, as qi represents an upper bound or worst-case estimate of the dose-response relationship at low doses. It is considered a plausible upper bound, because it is unlikely that the tme dose-response relationship will have a slope higher than qi, and it is probably considerably lower and may even be zero (as would be the case if there was a threshold). Lfse of the qj as the default, therefore, may have considerable conservatism incorporated into it. The values of qi have been considered as estimates of carcinogenic potency and have been called the unit carcinogenic risk or the Carcinogen Potency Factor (CPF). 

The limitations of the use of biomarkers in healthy volunteers must be recognised. For example, although there have been attempts to simulate migraine headache in volunteers, to date none of these models can be considered adequate to serve as a surrogate endpoint. Patients with migraine are not difficult to recruit and are usually healthy apart from their migraine. In this case, it maybe more appropriate to establish tolerability and pharmacokinetics in healthy volunteers and then to select a maximum well-tolerated dose with which to perform a small proof of principle clinical trial in patients. This will need to be followed by larger trials to establish the dose-response relationship. 

SSDs are being routinely used for the display and interpretation of effects data (Parkhurst et al. 1996 Posthuma et al. 2002). An SSD for atrazine (shown in Figure 7.3) displays the typical S-shaped curve associated with many chemical dose-response relationships. Each point on the curve represents an LC50 for a particular species exposed to atrazine under standard toxicity test protocols. The SSD approach uses only a single statistically derived endpoint from each available toxicity test (e.g., the LC50 or EC50). In contrast, all data collected during any specific toxicity test can be used in a hierarchical model. The ability to use all available data to make inferential decisions is a marked improvement over the standard SSD effects distribution. 

---