For evaluation of toxic action of a substance, different doses of the toxic agent are administered equally to individuals in groups randomly selected from a natural population of some test animal. The toxic effect may be death or any other observable end-point induced by the toxic agent in the test- animal.

The dose required to produce the toxic end-point and the number of individuals affected are noted and a frequency histogram is plotted. The resultant curve, when frequency of toxic response is plotted gradually rising doses of toxic agent, tends to follow a Gaussian or Normal distribution around a mean value when a large number of samples are analysed and a typical bell-shaped curve is obtained.

The middle part of the dome corresponds with the maximum number of individuals affected whereas the response on the left hand side represents the weak and susceptible members while on the right hand side it represents hardy and resistant individuals. Susceptible and weak members respond to lower doses whereas hardy and resistant individuals are not affected even by high doses.

When cumulative frequency of the toxic response is plotted against gradually rising amount of toxic agent on a logarithmic scale we obtain a typically sigmoid or S-shaped curve. The central part of the curve (between points A and B in usually sufficiently straight for drawing some meaningful conclusions (such as ED50 or LD50). However, this is not so in a number of cases. To arrive at some meaningful and reliable conclusions the curve has to be straightened. In practice it is seen that much wider range of curve can be straightened by plotting the points on probit basis. The procedure is especially useful when the extreme ends of curve have to be used.

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Statistically derived Standard Deviations (SD), which is a measure of dispersion of values around the mean, provide an idea of the characteristics of the dose response curve for the total population. In a normally distributed population the mean ± 1 SD represents 68.1% of the population, mean ± 2 SD represents 95.5% and the mean ± 3 SD represents 99.7% of the population. The probit units correspond to deviations around the mean, for example + 1, + 2, + 3, …… and -1,-2,-3………………. Deviations whereas the mean value itself has a zero deviation. In order to avoid negative numbers the probit units are derived by adding 5 to these deviations. The probits and percent response corresponding to different values of deviations. The percent response at each dose is converted to probit units and plotted against the dose administered on log scale. The resultant line is usually a straight line which may be termed as the Regression line. A number of meaningful conclusions can be drawn from the regression line.

In fact in profit transformation we adjust the toxic response data to an assumed normal population distribution. This method of handling the data is convenient and allows for rather a precise determination of the lethal dose or effective doses and provides an idea of slope of the regression line. We can obtain the dose enough to kill any percentage of a normal population simply by drawing a line paralled to X-axis from the point of the required percentage on Y-axis and then from the point where it intersects the regression line, a line paralled to Y-axis is drawn. The dose depicted by the point where this line intersects X-axis is the required dose.

A chemical whose regression line starts at a lower concentration is considered more toxic than those with parallel line but starting at a higher concentration. However, it must be borne in mind that the range of values covered by the confidence limits is narrowest at the mid-point and widest at both extremities.

The slope of the regression line gives an idea of the toxic potential of the chemical agent and allows for a quick comparison of toxicity of two or more toxic agents. A gentle slope means that for a small rise in toxicity larger doses are required. A steep slope indicates that for small rise in quantity of the chemical agent rather a large rise in toxic action is witnessed. In regression lines, A and B represent toxicity of two chemicals which are capable of killing 50% of a natural population at the same dose.

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However, the slopes of these lines are different which shows that chemical A is toxic even at very low doses, doses at which chemical B has no toxic action. The toxic action of chemical B starts at a higher dose but climbs up rapidly so that beyond the point of 50% mortality all doses of the chemical are more toxic than those of chemical A.

The same chemical may be tested for two or more end points of the toxic responses over a much wider range of doses. For example, a chemical which causes anaesthesia at lower doses may cause mortality at higher doses. If we draw regression lines for the different effects (anaesthesia and mortality) of the same chemical, on the same scale, we may end up with two parallel regression lines.

In many cases such parallel lines have been found to be associated with a similar mechanism of action and that the effect which occurs at a higher dose is just an extension of the response at lower dose. However, it must be borne in mind that this may not be true for a number of cases and almost entirely different mechanisms may be involved in producing the two different types of responses.