Effect models dose-response functions

Multiple Agents. When we have infoimation about the exposure levels of several agents, we can assume that the model parameters are functions of all the exposures simultaneously. In particular, let s assume that we have information about the exposure of an individual to m agents. Let d/s) denote the exposure to the yth agent at age s,j=l,..., m. The following dose-response function has been used in the past to evaluate the effects of several agents combined (Hazelton et al. 2001,... 

The approach used for the estimation of loss of life in floods shows considerable resemblance to the approach that is used in the Dutch major hazards policy. In both cases, the probability of a critical event (loss of containment or flood) is estimated using fault tree analysis, after which the physical effects associated with that critical event are considered (using e.g. dispersion or flood propagation models) and related to mortality estimates (using dose-response functions or flood mortality functions). But while the potential for evacuation is often limited when it comes to explosions or toxic releases, it could be significant when it comes to floods. 

Many of the above types of effects are evident in rodents and monkeys with PbB levels exceeding 30 fig/dl, but some effects on learning ability are apparent even at maximum PbB exposure levels below 20 Hg/d. The problem of extrapolating exposures, and therefore the results of animal research to human populations are discussed in another review by Smith (this volume). Until the function describing the relationship of exposure indices in different species is available, the utility of animal models for deriving dose-response functions relevant to humans may be limited. However, consistent observations of altered behaviour across several species and humans at PbB levels below 30 fig/d tend to converge to indicate lead effects on CNS function at lead levels previously considered safe. ... 

FIGURE 3.6 Classical model of agonism. Ordinates response as a fraction of the system maximal response. Abscissae logarithms of molar concentrations of agonist, (a) Effect of changing efficacy as defined by Stephenson [24], Stimulus-response coupling defined by hyperbolic function Response = stimulus/(stimulus-F 0.1). (b) Dose-response curves for agonist of e = 1 and various values for Ka. 

The Furchgott method can be effectively utilized by fitting the dose-response curves themselves to the operational model with fitted values of x (before and after alkylation) and a constant KA value. When fitting experimental data, the slopes of the dose-response curves may not be unity. This is a relevant factor in the operational model since the stimulus-transduction function of cells is an integral part of the modeling of responses. Under these circumstances, the data is fit to (see Section 3.13.3 and Equation 3.49)... 

This allows the calculation of an effect expected according to the concept of response addition for any concentration of the mixture. Again, the estimated individual effect may be taken from a concentration-response relationship derived on the basis of dose-response observations. It has to be noted that, in mixtures of many substances, the effects to be estimated for the individual contributors become rather small therefore, a high-quality estimation of the concentration response, particularly in the low effect region, is needed. In such cases, it might be useful to consider models other than the standard probit or logit functions for description of the data. 

Dose-response models describe a cause-effect relationship. There are a wide range of mathematical models that have been used for this purpose. The complexity of a dose-response model can range from a simple one-parameter equation to complex multicompartment pharmacokinetic/pharmacodynamic models. Many dose-response models, including most cancer risk assessment models, are population models that predict the frequency of a disease in a population. Such dose-response models typically employ one or more frequency distributions as part of the equation. Dose-response may also operate at an individual level and predict the severity of a health outcome as a function of dose. Particularly complex dose-response models may model both severity of outcome and population variability, and perhaps even recognize the influence of multiple causal factors. 

Response Surface Model A dose-response surface is an extension of dose-response lines (isobols) to three dimensions. In this representation there can be a dose-response surface representing additivity and surfaces above and below suggesting deviation from additivity. Tam et al. [90] studied the combined pharmacodynamic interactions of two antimicrobial agents, meropenem and tobramycin. Total bacterial density data, expressed as CFU (colony forming units), were modeled using a three-dimensional surface. Effect summation was used as the definition of additivity (null interaction hypothesis) and the pharmacodynamic model was assumedi to take the functional form... 

The dose escalation with overdose control (EWOC) is a Bayesian approach similar to CRM. It is a dose-escalation scheme based on controlling the probability of overdosing a patient and not on targetting toxicity between 20% and 30% of the MTD, as in the original CRM (41,42). This method, like CRM, sequentially modifies the dose-response curve by including the information of all the patients previously included in the trial, but in this case, the dose-effect relationship deals with a two-parameter model, which can be considered as a tolerance function between two bounds (d iin and dnmx) ... 

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