Quantal dose-response studies

The curve is again identical in shape but this time a population has been studied and the frequency of response recorded at various drug doses. It is, therefore, known as a quantal dose-response curve. The marker of potency is now the ED50 and the y axis should be correctly labelled as shown. This is the typical dose-response curve that is tested in the examination. 

Anticonvulsants can be suitably studied by use of quantal dose-response curves. For example, to assess the potential of new anticonvulsants to control epileptic seizures in humans, these drugs are initially tested for their ability to protect animals against experimentally induced seizures. In the presence of a given dose of the drug, the animal either has the seizure or does not that is, it either is or is not protected. Thus, in the design of this experiment, the effect of the drug (protection) is all or none. This type of response, in contrast to a graded response, must be described in a noncontinuous manner. 

Figure 1 shows a hypothetical tolerance frequency distribution, f(D)dD, along with its corresponding cumulative distribution, P(D). Thus, when the response is quantal in nature, the function P(D) can be thought of as representing the dose-response either for the population as a whole, or for a randomly selected subject. The notion that a tolerance distribution, or dose-response function, could be determined solely from consideration of the statistical characteristics of a study population was introduced independently by Gaddum (2) and Bliss (3). 

The answer is 3 [Chapter 11F 1 b [4)1. Classic LD,o studies use the quantal, or all-oe-none response (e.g., the number dead per group, or, for efficacy studies, the number affected per group). Multiple dosages are used to construct a dose-response curve, and the studies are not done across species but with a well-defined homogeneous group of animals. 

The more difficult problem with whole animals concerns events which occur over long periods of time. The LD50 value must always be accompanied with an indication of the time over which the animals were observed before the experiment is terminated. If not, every treatment would be considered lethal since every animal dies eventually, or no chemical would be considered lethal since both control and treated animals would die eventually. Thus, observation periods of 24 hours or two weeks are often chosen as end points. When dealing with carcinogenesis, however, the time of the study is considered the life time of the animal which in the case of mice or rats may extend to two years or more. Furthermore, since control animals may display spontaneous tumors and the tumor incidence in both treated and control animals may be small, the total nuaiber of animals in the experiment often plays a key role in determining the accuracy of the results. The responses discussed here are classified as quantal since each animal provides only one piece of data. The animal either dies or it does not it develops tumors or it does not. The same observation cannot be repeated in the same animal and the effect of a higher dose in that animal cannot be investigated. 

VOien the response is quantal, its occurrence for any particular subject will depend upon the level of the stimulus. For this subject under constant environmental conditions, a common assumption is that there is a certain dose level below which the particular subject will not respond in a specified manner, and above which the subject will respond with certainty. This level is referred to as the subject s tolerance. Because of biological variability among subjects in the population, their tolerance levels will also vary. For quantal responses, it is therefore natural to consider the frequency distribution of tolerances over the population studied. If D represents the level of a particular stimulus, or dose, then the frequency distribution of tolerances, f(D), may be mathematically expressed as... 

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