Quantal response

Due to the second criterion, time-to-tumor models were eliminated from consideration. These models require more detailed experimental data than is generally available. Moreover, it is difficult and unproductive to interpret the distribution of time-to-tumor in the context of human exposures. In most cases, the time-to-tumor variable would be integrated over a human lifetime, thus reducing the model to a purely dose-dependent one. Therefore we restrict our attention to quantal response models that estimate lifetime risks. 

Armitage, P. and Allen, J. (1959). Methods of estimating the LD50 in quantal response data. J. 

Waud, D. (1972). Biological assays involving quantal responses. J. Pharmacol. Exp. Therap. 183 577-607. 

The single most important statistical consideration in the design of bioassays in the past was based on the point of view that what was being observed and evaluated was a simple quantal response (cancer occurred or it didn t), and that a sufficient number of animals needed to be used to have reasonable expectations of detecting such an effect. Though the single fact of whether or not the simple incidence of neoplastic tumors is increased due to an agent of concern is of interest, a much more complex model must now be considered. The time-to-tumor, patterns of tumor incidence, effects on survival rate, and age of first tumor all must now be captured in a bioassay and included in an evaluation of the relevant risk to humans. 

Portier, C.J. and Bailer, A.J. (1989). Testing for increased carcinogenicity using a survival-adjusted quantal response test. Fundam. Appl. Toxicol. 12 731-737. 

Hewlett, P.S. and R.L. Placket. 1959. An unified theory for quantal responses to mixtures of drugs Non-interactive action. Biometrics 15 591-610. 

Placket, R.L. and P.S. Hewlett. 1952. Quantal responses to mixtures of poisons. J. Royal Statistical Society, Series B 14 143-163. 

As indicated above, detection of evoked quantal responses (either through minimal stimulation or paired recordings) provides a suitable setting to determine neurotransmitter release probability and alterations in rate of vesicle fusion. However, in synapses with multiple release sites, such as the calyx of Held, isolation of evoked quantal responses is nearly impossible and truly quantal release is hard to detect except in the case of spontaneous neurotransmission. Therefore, under these conditions, the rate of synaptic vesicle fusion can be determined by deconvolution of synaptic currents with the quantal unitary current. This approach is valid only when the synaptic current can be assumed to result from the convolution between a quantal current and quantal release rates. This assumption is not valid in cases where post-synaptic mechanisms, such as receptor saturation and desensitization, alter quantal events and thus shape synaptic responses during repetitive stimulation (Neher and Sakaba, 2001). 

In single-species risk prediction for individual toxicants and toxicant mixtures, the effect is expressed as the proportion of an exposed population that is likely to be somehow affected by toxic action (quantal responses), or as a reduction in performance parameters such as growth, clutch size, and juvenile period (continuous responses). Both concentration addition- and response addition-based methods are commonly applied for both response types. Assemblage-level risk prediction has only been introduced more recently (e.g., De Zwart and Posthuma 2005) and is founded on similar principles while focusing on the fraction of species that are likely affected by mixture exposure. 

When sufficient data are available, use of the benchmark dose (BMD) or benchmark concentration (BMC) approach is preferable to the traditional health-based guidance value approaches (IPCS, 1999a, 2005 USEPA, 2000 Sonich-Mullin et al 2001). The BMDL (or BMCL) is the lower confidence limit on a dose (the BMD) (or concentration, BMC) that produces a particular level of response or change from the control mean (e.g. 10% response rate for quantal responses one standard deviation from the control mean for a continuous response) and can be used in place of the NOAEL. The BMD/BMC approach provides several advantages for dose-response evaluation 1) the model fits all of the available data and takes into account the slope of the dose-response curve 2) it accounts for variability in the data and 3) the BMD/BMC is not limited to one experimental exposure level, and the model can extrapolate outside of the experimental range. 

Quantal response A response that is all-or-none rather than graded. 

Plackett RL, Hewlett PS. 1963b. Quantal response to mixtures of poisons. J R Stat Soc B 14 141-163. 

Q10 (temperature coefficient) The increase in the rate of a chemical process due to raising the temperature by 10 C. quantal responses Are all-or-none responses, or qualitative responses, e.g. death or survival (in contrast to quantitative responses which are continuous variables). The underlying distribution is the binomial distribution. Log dose-response lines for quantal responses are frequently sigmoidal in shape, and since this is the same form as the integrated frequency distribution curve, the slope of the... 

Leff model). For quantal responses it reflects the cumulative probability distribution. 

The Dixon Up-Down technique was first described in the statistical literature in 1947. It is designed to estimate an ED50 in clinical trials or toxicological tests, when a quantal response is measured (see Figure 9.1). However, it should be... 

N. Flournoy, A clinical experiment in bone marrow transplantation Estimating a percentage point of quantal response curve, in Case Studies in Bayesian Statistics, C. Gastonis, J. S. Hodges, R. E. Kass, and N. D. Singpurwalla (Eds.). Springer, New York, 1993, pp. 324-336. 

Morgan BJT. Analysis of Quantal Response Data. NY Chapman and Hall, 1992. 

Benchmark-dose calculations for quantitative outcomes (e.g., birth weight or IQ) are more complicated than those for quantal responses, such as presence or absence of a defect. Although Crump (1984) discussed how to calculate a BMD for a quantitative outcome. Gay lor and Slikker (1992) were the first to develop the approach in any detail. Their first step is to fit a regression model characterizing the mean of the outcome of interest as a function of dose and assuming that the data are normally distributed. The next step is to specify a cutoff to define values... 

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