Probit units

Probit units define the median as probit five, and then each standard deviation unit is one probit unit above or below. The dose-response curve so produced is linear, when the logarithm of the dose is used (Fig. 2.7). 

Figure 2.7 Dose-response relationship expressed as probit units.

FIGURE 2.5 Dose-response relationship expressed in probit units. 

Figure 2.2a to c and Figure 2.3a and b show that the transformation of the doses to log dose, and the use of probit units for responses, makes it much easier to interpret the graphs. However, there are several difficulties with dose-response graphs. 

Figure 6.3 Dose response relationship, mortality in probit units.

Figure 5.1 shows that all three graphs used to characterize the relationship between the dose of toxic chemical and the frequency of toxic effect—i.e., the frequency histogram, the cumulative dose-effect curve, and the linear probit plot—put the logarithm of the dose on the x-axis. The reason the probit plot is linear is because of a clever invention a statistically derived scale that represents cumulative-effect frequency on the y-axis. Called probit units, or simply probits, this scale is based on a particular statistic, the standard deviation of the mean. Standard deviations correspond to fixed percentages of a population, and they can therefore be used in place of percentages to represent the fraction of a population that manifests a toxic effect. The mean dose corresponds to a standard deviation of zero because it is located in the exact middle of the bell curve. In terms of standard deviations, a disease frequency of 50% of the population is equivalent to zero standard deviations. One standard deviation below and above the mean corresponds, respectively, to manifestation... 

FIGURE 5.1 Three representations of the increase in the frequency of a toxic effect (death) as a function of toxic chemical dose. Top The frequency of mortality at each dose as a percent of the population, also referred to as the incremental frequency of the effect (similar to Figure 3.1a). Middle Total mortality at each dose as a percent of the population, also referred to as the cumulative frequency (similar to Figure 3.1h). Bottom Same as middle panel Total mortality at each dose as a percent of the population, also referred to as the cumulative frequency, but with mortality scaled in probit units instead of percent. Note the use of a logarithmic scale for dose on the x-axis. (Reprinted with permission from Curtis Klaassen, ed., Casarett Doull s Toxicology The Basic Science of Poisons [New York McGraw-ffill, 2001], 19.)... 

The quantal dose-effect curve provides a guide to toxic effect frequencies relative to exposure under the conditions of the laboratory toxicity test. Doses corresponding to other toxic effect frequencies may be extrapolated from cumulative dose-effect curves. For example, the 10% toxic dose, or TD,q, represents a dose corresponding to a cumulative-effect incidence of 10% of the test population it is determined by finding the dose that corresponds to a 10% cumulative-effect frequency (in the sigmoidal curve) or 3.7 probit units (in the probit plot). The 75% toxic dose, or TD75, is the dose corresponding to 75% cumulative-effect incideuce or 5.8 probits. 

Many methods exist for representing the response-dose curve.1 For single exposures the probit (probit <= probability unit) method is particularly suited, providing a straight-line equivalent to the response-dose curve. The probit variable Y is related to the probability P by2... 

The effective, toxic, or lethal dosage for 50 percent of the animals in the group can be estimated as shown. This graph shows the relationship between these parameters. The proximity of the ED50 and TD50 indicates the margin of safety of the compound. (Probits are units of standard deviation, where the median is probit 5.)... 

Before we learn probit analysis, we need to know what probits are. Probits are probability units that are derived from the normal probability curve. As shown in Figure 5.3, the standard deviation (SD) has the property that in a large number of samples, approximately 68% of individuals in a population will lie within one SD of the mean, 96% will lie within two SDs, or 99.7% within three SDs. 

The probit method is perhaps the most widely used method for calculating toxicity vs. concentration or dose. As its name implies, the method used a probit transformation of the data. A probit is a unit of divergence from the mean of a normal distribution equal to one standard deviation. The central value of a probit would be 5.0, representing the median effect of the toxicity test. A disadvantage of the method is that it requires two sets of partial kills. However, a confidence interval is easily calculated and can then be used to compare toxicity results. There are several programs available for the calculation, and as discussed below, they provide comparable results. 

Although the toxic units and additive index are useful in determining toxicity in some cases, they have disadvantages. Their values depend on the relative proportion of chemicals in the mixture. Also, because of the logarithmic form of the concentration in log-linear transformations such as Probit and Logit, it is desirable to have a toxicity index which is logarithmic in the toxicant concentration. For these reasons, Konemann (1981) introduced a multiple toxicity index (MTI) ... 

Figure 2.2 Dose-response relationships drawn on three different models for four populations, (a) Doses and responses in linear scale, (b) Doses in log scale and responses in linear scale, (c) Doses in log scale and responses in probits. (1) Sensitive population with normally distributed sensitivity and LD50 = 2.5 units. (2) A mixed population with 75% of (1) and 25% resistant individuals. (3) Intermediate sensitive population with normally distributed sensitivity, but more scattered than (1), and LD50 = 5 units. (4) Less sensitive, but normally distributed population, similar to (1), but with LD50 = 6.5 units.

Whilst threshold values merely enable one to take good or bad decisions a probit ( probability unit (-relation allows one to assess the probability of a certain consequence, e.g. death, occurring due to a causative factor such as toxic exposure. For example, we have for the exposure to chlorine... 

Probit functions were evaluated as the most often used tools for determining the effects of major accidents, probably due to the fact that these functions are included in the EFFECTS software. Furthermore, it was determined that the values of the limits of acute toxicity are not always the same when applying different methods. For example the value of IDLH for chlorine differs in order of tens. The ERPG has the lowest difference in the values in the order of units. This can be caused by the absence of literature sources. 

A fixed mass of toxic gas has been released almost instantaneously from a process unit. The release occurs at night with calm and clear conditions. If the gas obeys the probit equation for fatalities... 

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