Dose–response relationship

The dose–response relationship, or exposure–response relationship, describes the magnitude of the response of an organism, as a function of exposure (or doses) to a stimulus or stressor (usually a chemical) after a certain exposure time. Dose–response relationships can be described by dose–response curves. This is explained further in the following sections. A stimulus response function or stimulus response curve is defined more broadly as the response from any type of stimulus, not limited to chemicals. Studying dose response, and developing dose–response models, is central to determining 'safe', 'hazardous' and (where relevant) beneficial levels and dosages for drugs, pollutants, foods, and other substances to which humans or other organisms are exposed. These conclusions are often the basis for public policy. The U.S. Environmental Protection Agency has developed extensive guidance and reports on dose–response modeling and assessment, as well as software. The U.S. Food and Drug Administration also has guidance to elucidate dose–response relationships during drug development. Dose response relationships may be used in individuals or in populations. The adage The dose makes the poison reflects how a small amount of a toxin has no significant effect, while a large amount may be fatal. This reflects how dose–response relationships can be used in individuals. In populations, dose–response relationships can describe the way groups of people or organisms are affected at different levels of exposure. Dose response relationships modelled by dose response curves are used extensively in pharmacology and drug development. In particular, the shape of a drug's dose–response curve (quantified by EC50, nH and ymax parameters) reflects the biological activity and strength of the drug. Some example measures for dose–response relationships are shown in the tables below. Each sensory stimulus corresponds with a particular sensory receptor, for instance the nicotinic acetylcholine receptor for nicotine, or the mechanoreceptor for mechanical pressure. However, stimuli (such as temperatures or radiation) may also affect physiological processes beyond sensation (and even give the measurable response of death). Responses can be recorded as continuous data (e.g. force of muscle contraction) or discrete data (e.g. number of deaths). A dose–response curve is a coordinate graph relating the magnitude of a stimulus to the response of the receptor. A number of effects (or endpoints) can be studied. The measured dose is generally plotted on the X axis and the response is plotted on the Y axis. In some cases, it is the logarithm of the dose that is plotted on the X axis, and in such cases the curve is typically sigmoidal, with the steepest portion in the middle. Biologically based models using dose are preferred over the use of log(dose) because the latter can visually imply a threshold dose when in fact there is none. Statistical analysis of dose–response curves may be performed by regression methods such as the probit model or logit model, or other methods such as the Spearman-Karber method. Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose-response relationship. The organ bath preparation is a typical experimental design for measuring dose-response relationships. Dose–response curves are generally sigmoidal and monophasic and can be fit to a classical Hill equation. The Hill equation is a logistic function with respect to the logarithm of the dose and is similar to a logit model. A generalized model for multiphasic cases has also been suggested. The Hill equation is the following formula, where E {displaystyle E} is the magnitude of the response, [ A ] {displaystyle {ce {}}} is the drug concentration (or equivalently, stimulus intensity) and E C 50 {displaystyle mathrm {EC} _{50}} is the drug concentration that produces a 50% maximal response and n {displaystyle n} in the Hill coefficient.