Quantal effect models

A fixed effect model, also known as a quantal effect model, relates a certain drug concentration with the statistical likelihood of a predefined, fixed effect to be present... 

The PD models fall under two categories graded or quantal of fixed-effect model. Graded refers to a continuous response at different concentrations, whereas the quantal model would evaluate discrete response such as dead or alive, desired or undesired and are almost invariably clinical end points. 

It is curious that the striking deviations of electrochemical kinetic behavior from that expected conventionally, which are the subject of this review, have not been recognized or treated in the recent quantum-mechanical approaches, e.g., of Levich et al (e.g., see Refs. 66 and 105) to the interpretation of electrode reaction rates. The reasons for this may be traced to the emphasis which is placed in such treatments on (1) quantal effects in the energy of the system and (2) continuum modeling of the solution with consequent neglect of the specific solvational- and solvent-structure aspects that can lead, in aqueous media, to the important entropic factor in the kinetics and in other interactions in water solutions. However, the work of Hupp and Weaver, referred to on p. 153, showed that the results could be interpreted in terms of Marcus theory, with regard to potential dependence of AS, when there was a substantial net reaction entropy change in the process. 

The reactions to aiqr one stimulus may be nultiple in nature, e.g. loss of weight, decrease in organ function, or even death. Each reaction may have its own unique relation with the level of the stimulus. In addition, the measure of any specific reaction may be made in terms of the magnitude of the effect produced, quantitative response, whether or not a specific effect is produced, quantal response, or the time required to produce a specific effect, time to response. The discussion of models will be limited to quantal response models, but similar models may be used for responses measured in other units. These responses may be acute reactions, sometimes occurring within adnutes of the stimulus, or they may be long-delayed effects such as cancer, which may not appear clinically until most of the subjects normal lifespan has elapsed. Other responses may not even appear in the exposed subject, but may become manifest in some later progeny. 

Compliance model Compliance as an outcome modeled as a response or utilized as a covariate expressed in the nonlinear mixed effect model Indicator variable Compliance as a quantal (i.e., 0 = compliant ... 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

In connection with electronic strucmre metlrods (i.e. a quantal description of M), the term SCRF is quite generic, and it does not by itself indicate a specific model. Typically, however, the term is used for models where the cavity is either spherical or ellipsoidal, the charge distribution is represented as a multipole expansion, often terminated at quite low orders (for example only including the charge and dipole terms), and the cavity/ dispersion contributions are neglected. Such a treatment can only be used for a qualitative estimate of the solvent effect, although relative values may be reasonably accurate if the molecules are fairly polar (dominance of the dipole electrostatic term) and sufficiently similar in size and shape (cancellation of the cavity/dispersion terms). 

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. 

Continuum models are the most efficient way to include condensed-phase effects into quantum-mechanical calculations, and this is typically accomplished by using the self-consistent reaction field (SCRF) approach for the electrostatic component. Therefore it is very common to replace the quantal problem by a classical one in which the electronic energy plus the coulombic interactions of the nuclei, taken together, are modeled by a classical force field—this approach usually called molecular mechanics (MM) (Cramer and Truhlar, 1996). 

A number of dose-response models have been developed for BMD analyses. The form of the model used and the necessary inputs for the modeling depend on the type of data to be modeled. For quantal data (e.g., his-topathology incidence data), the incidence of the effect of interest and the total size of the group are needed, and for continuous data (e.g., liver enzyme activity), the group size, mean, and a measure of variability (i.e., standard deviation or standard error) are required. 

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