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In toxicodynamics and pharmacodynamics, Loewe additivity (or dose additivity) is one of several common reference models used for measuring the effects of drug combinations. [1] [2] [3]
Let and be doses of compounds 1 and 2 producing in combination an effect . We denote by and the doses of compounds 1 and 2 required to produce effect alone (assuming this conditions uniquely define them, i.e. that the individual dose-response functions are bijective). quantifies the potency of compound 1 relatively to that of compound 2.
can be interpreted as the dose of compound 2 converted into the corresponding dose of compound 1 after accounting for difference in potency.
Loewe additivity is defined as the situation where or .
Geometrically, Loewe additivity is the situation where isoboles are segments joining the points and in the domain .
If we denote by , and the dose-response functions of compound 1, compound 2 and of the mixture respectively, then dose additivity holds when
The Loewe additivity equation provides a prediction of the dose combination eliciting a given effect. Departure from Loewe additivity can be assessed informally by comparing this prediction to observations. This approach is known in toxicology as the model deviation ratio (MDR). [4]
This approach can be rooted in a more formal statistical method with the derivation of approximate p-values with Monte Carlo simulation, as implemented in the R package MDR. [5] [ clarification needed ]
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
Synergy is an interaction or cooperation giving rise to a whole that is greater than the simple sum of its parts. The term synergy comes from the Attic Greek word συνεργία synergia from synergos, συνεργός, meaning "working together".
In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.
Heritability is a statistic used in the fields of breeding and genetics that estimates the degree of variation in a phenotypic trait in a population that is due to genetic variation between individuals in that population. The concept of heritability can be expressed in the form of the following question: "What is the proportion of the variation in a given trait within a population that is not explained by the environment or random chance?"
The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. To each cooperative game it assigns a unique distribution of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties. Hart (1989) provides a survey of the subject.
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The dose–response relationship, or exposure–response relationship, describes the magnitude of the response of an organism, as a function of exposure to a stimulus or stressor 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.
In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models.
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In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized. A material where such a coupling is intrinsically present is called a magnetoelectric.
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Ting-Chao Chou is a Chinese American theoretical biologist, pharmacologist, cancer researcher and inventor. His 353 scientific papers have been cited in 40,108 times in over 1,469 biomedical journals as of October 15, 2022. He derived the median-effect equation (MEE) from the physico-chemical principle of the mass-action law, and introduced the median-effect plot in 1976. With Paul Talalay of the Johns Hopkins University School of Medicine, he derived the combination index equation (CIE) for multiple drug effect interactions, and introduced the concept of combination index (CI) for quantitative definition of synergism (CI<1), additive effect (CI=1), and antagonism (CI>1) using computerized simulations. This article has received 7,731 citations internationally in a broad spectrum of journals. Since all terms of MEE and CIE are dimensionless relativity ratio thus generally applicable regardless in vitro, in animals and in clinical trials, or physical states, resulting in econo-green bioresearch and new drug evaluation and bio-development. This integrated theory and algorithms allow conducting small number of dose-data points, conservation of laboratory animals and reducing the number of patients in clinical trials. Consequently, this allows saving time and cost and resources as well as increasing efficiency and cost-effectiveness in medical, pharmaceutical research and new drug development with automated computer simulation. With colleagues, T.C. Chou is inventor/co-inventor of 40 U.S. Patents, mainly for anticancer agents. He was induced to Johns Hopkins Society of Scholars in 2019.
Antibiotic synergy is one of three responses possible when two or more antibiotics are used simultaneously to treat an infection. In the synergistic response, the applied antibiotics work together to produce an effect more potent than if each antibiotic were applied singly. Compare to the additive effect, where the potency of an antibiotic combination is roughly equal to the combined potencies of each antibiotic singly, and antagonistic effect, where the potency of the combination is less than the combined potencies of each antibiotic.
Up-and-down designs (UDDs) are a family of statistical experiment designs used in dose-finding experiments in science, engineering, and medical research. Dose-finding experiments have binary responses: each individual outcome can be described as one of two possible values, such as success vs. failure or toxic vs. non-toxic. Mathematically the binary responses are coded as 1 and 0. The goal of dose-finding experiments is to estimate the strength of treatment (i.e., the "dose") that would trigger the "1" response a pre-specified proportion of the time. This dose can be envisioned as a percentile of the distribution of response thresholds. An example where dose-finding is used is in an experiment to estimate the LD50 of some toxic chemical with respect to mice.
Additive effect in pharmacology describes the situation when the combining effects of two drugs equal the sum of the effects of the two drugs acting independently. The concept of additive effect is derived from the concept of synergy. It was introduced by the scientists in pharmacology and biochemistry fields in the process of understanding the synergistic interaction between drugs and chemicals over the century.
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