General models for quantal response to the joint action of a mixture of drugs
| Autor: | C. S. Smith, J. R. Ashford |
|---|---|
| Rok vydání: | 1964 |
| Předmět: |
Statistics and Probability
education.field_of_study Distribution (number theory) Mathematical model Basis (linear algebra) Applied Mathematics General Mathematics Population Function (mathematics) Agricultural and Biological Sciences (miscellaneous) Action (philosophy) Joint probability distribution Applied mathematics Statistics Probability and Uncertainty General Agricultural and Biological Sciences Representation (mathematics) education Mathematics |
| Zdroj: | Biometrika. 51:413-428 |
| ISSN: | 1464-3510 0006-3444 |
| DOI: | 10.1093/biomet/51.3-4.413 |
| Popis: | This paper is concerned with mathematical models for the representation of the joint action of mixtures of drugs. The organisms under examination are assumed to embody one or more separate physiological systems, each of which may be affected by any of the drugs in the mixture. The effect of the mixture on a given physiological system is assumed to take the form of a quantitative 'reaction', whose level is expressed as the difference between a function of the doses of the drugs (the 'effect function') and the 'tolerance' of the particular system. The tolerances of the various systems are assumed to follow a characteristic joint distribution in the population of organisms. A particular type of quantal or semi-quantal response is assumed to occur when the combined reaction of the various systems, which may be regarded as a vector quantity, falls within a prescribed region in the 'reaction space'. The probability of response may then be expressed as the integral of the joint tolerance distribution over a region whose boundaries are functions of the doses. It is emphasized that, as far as the probability of response is concerned, the choice of the number of systems and of the form of the tolerance distribution is arbitrary, in that a given situation may be expressed in terms of a variety of different representations. The derivation of various types of single and multiple system models is examined and it is shown how a group of infinite system models may be generated from the multiple system representation. The concept of interaction is discussed and a mathematical definition of non-interactive joint action is derived. The analysis of semi-quantal response data is considered and it is shown that it is impossible to determine whether one or more physiological systems is involved on the basis of quantal response data alone. The classification of models for the analysis of quantal response data is then examined. It is shown that definitions of 'similar ', 'partially similar' and 'independent' action given in the literature do not correspond to any specific properties of the probability of response. Alternative criteria for similar and independent action are put forward. A new model for the joint action of a mixture of drugs, which combines additivity of the doses with non-parallelism of the dosage-response lines for the individual drugs, is derived from the infinite system representation. An example is given of the application of this new model, in comparison with a non-additive model, to the analysis of data from surveys of lung disease in coal miners. |
| Databáze: | OpenAIRE |
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