Rodney B. Murray

Manual of pharmacologic calculations with computer programs

Manual of Pharmacologic Calculations with Computer Programs. By R. J. Tallarida and R. B. Murray. New York, Heidelberg and Berlin, Springer‐Verlag, 1981. ix, 150 p. 24·5 cm. Unpriced.

Chi-Square Test

The chi-square (x2) test is applicable to many situations in which experimental frequencies are compared to theoretical frequencies based on a hypothesis. For example, in tossing a die many times one expects that each of the values one to six will occur one-sixth of the time. Thus, in 600 tosses the expected frequencies, denoted e 1e2,…,e6, are each 100. We denote the actual frequencies, or observed frequencies, by ol, o2,…, o6.

The pupillary effects of oploids

Morphines miotic action on the pupil is an easily recognizable and quantifiable effect in man. The neural pathways responsible for regulating pupil size are reasonably well defined. Yet, the mechanisms behind this and related effects of opioids on the eye in humans and laboratory animals have just begun to be explored. In this review, we have attempted to organize the available information on pupillary actions of opioids, emphasizing the dynamic nature of the responses, their species specificity, possible mechanisms of action, and the recently discovered development of tolerance to these actions. Our current knowledge regarding differences among the opioids, the effects of endogenous opioid peptides and the role of the various opiate receptor subtypes in pupillary effects is also summarized.

Mann-Whitney Test

When two groups are drawn from populations that are normally distributed, the methods of Procedures 39 and 40 are used to determine whether the groups are drawn from the same or from different populations; in other words, is there a significant difference between the means of each group? When we have no knowledge of the distribution, different methods are used to determine whether the samples are drawn from the same or from different populations. In pharmacologic work the groups are usually a control group and a drug-treated group.

Area under a Curve: Trapezoidal and Simpson’s Rules

Simpson’s rule is a method for evaluating the area under a curve from values of the ordinate and the abscissa. Thus, this method accomplishes the same objective as that of the trapezoidal rule (discussed subsequently). It may be shown, however, that Simpson’s rule gives a closer approximation to the area, than does the trapezoidal rule.

A scale for assessing the severity of diseases and adverse drug reactions: Application to drug benefit and risk

Physicians were interviewed to assess their willingness to risk adverse drug reactions among patients. These untoward reactions were ranked according to severity and weighted against the primary illness being treated. A specially designed questionnaire in the form of a matrix was used. Severity was divided into seven classes denoted by progressively increasing numerical scores, W1 to Wτ, whose values could be calculated from analysis of the completed questionnaires. The questionnaires presented several cases, in each of which an illness of specified severity was to be treated with a drug whose untoward reactions differ in severity from that of the primary illness. Each case involved a different permutation of the severities. Analysis of the completed questionnaires yielded the mean values of the scores which were found to range from W1 = 1.00 (the mildest case) to Wτ = 817 (the most serious case). It is our opinion that this type of scale is preferable to nonnumerical descriptions of severity such as “mild” or “serious,” since, when combined with data on frequency of occurrence, a numerical scale permits a determination of expectation of both benefit and risk.

Dunnett’s Test (Comparison with a Control)

An experimenter frequently wishes to compare the mean of some control group with that of another group. Methods for doing this are presented in Procedures 39, 40, and 42. When there are several (p) groups, and the comparison is between each of these p means and the control mean, we may use the Dunnett test. Analysis of variance* may be used in this case also, but it may result in confidence limits that are wider than necessary.

Graded dose—response

The dose—response relation of many agonists yield sigmoidal (S-shaped) curves when the response is plotted against the logarithm of the dose (see Figure 8.1). There is no generally accepted theory that explains the shape of such curves; yet, we find that such curves are often approximately linear between 20% and 80% of the maximum response. In particular, many isolated tissue preparations display this linear segment. The data in the 20%–80% region may therefore be subjected to linear regression as given in Procedure 3, in which y = effect, or percent effect, and x = log dose. The regression line so determined might be used in the comparison of potency (Procedure 10) or in the analysis of the action of a competitive antagonist (Procedure 15). In each of these applications the regression lines are made parallel, and equieffective doses are determined.

Litchfield and Wilcoxon I: Confidence Limits of ED50

The use of the probit conversion for drawing smooth quantal log dose—effect curves was discussed in Procedure 9. Since there are no values of the probit corresponding to 0 and 100% effects the method of Procedure 9 does not handle such complete log dose—effect curves. The problem of analyzing such complete curves was addressed by Litchfield and Wilcoxon who gave a method for “correcting” the 0 and 100% effects. Although their method preceded the widespread use of calculators and computers, it is still widely used for determining ED50 and its 95% confidence limits.

pA 2 Analysis I: Schild Plot

The pA2 is a measure of the affinity of a competitive antagonist for its receptor. The determination of the pA2 is made from experiments in which a fixed concentration of the antagonist is used along with graded concentrations of an agonist acting on the same receptor. The presence of the antagonist shifts the agonist dose—response curve to the right as seen in Figure 15.1.