Log-probit plots

Fig. 6. Dose—response regression line for mortaUty data (represented by x) expressed by log-probit plot.

Figure 2 represented a log-probit plot of the observed inhibition of purified bovine erythrocyte acetylcholinesterase as a function of concentration for several of the transformation products of aminocarb. The observation that these inhibition curves are parallel suggests a similar mechanism of interaction for the various derivatives. The parameter I5f. (the concentration of inhibitor required to achieve 50% inhibition oi the enzyme activity) for each of the inhibitors were calculated and are recorded in Table 1. These values are reported relative to the parent compound aminocarb = 1. Also included in Table 1 are the relative toxicities of several of these products to house crickets (Acheta domesticus). It had been our intention to develop bioassay tests using the target insect itself, the eastern spruce budworm (Choristoneura fumiferana). However, spray tower results were quite variable and it was considered that genetic variability of the stock culture made the production of uniform test batches difficult to achieve. Using the house crickets, an LD q of 130-155 ppm for aminocarb standard was observed over the course of more than 25 bioassays. Also included in Table 1 are observations by Abdel-Wahab and Casida (19) using human plasma or house fly head cholinesterases. 

Figure 2. Log-probit plot of acetylcholinesterase inhibition as a function of concentration of aminocarb and transformation products.

The occurrence of histamine release is also treated as an all-or-none response to permit log-probit plotting. The delayed depressor response plus tachycardia is judged to have or have not occurred after each single bolus injection of the drugs. The percentage of animals responding at each dose level is then determined and the data handled by the Litchfield-Wilcoxon method. 

Pre-emergence herbicidal test data were evaluated after 8, 21, and 42 days for both test series. The herbicidal response of each TFMS compound at each time interval was rated (in terms of % kill by comparing with a control sample containing no herbicidal treatment) on a 0-100 scale (where 0 = no activity, 50 = 50% kill, 100 = complete kill, etc.). No significant changes in relative herbicidal activity were observed after 21 days. The 21-day herbicidal activity ratings were used to prepare log-probit plots from which LD90 values were determined for each TFMS compound in the presence and absence of Tween 80 (see Results). 

Figure 1. Log-probit plot for the 4-Cl-TFMS derivative acting on Foxtail Grass...

FIGURE 8.4 Cumulative size distribution of gelatin (lime-cured type B, bloom number 225) microparticles prepared at high pH obtained using a Coulter Counter and plotted as a log-probit function. (From Lou, Y. and Groves, M.J. (1995). J. Pharm. Pharmacol., 47, 97-102. With permission.)... 

Data analysis is done by the method of Litchfield and Wilcoxon. Mean dose - response curves are plotted on log-probit paper. Best fit to straight lines on these scales is determined by computerized regression. The cumulative ED50 values for vagal and sympathetic inhibition and the cumulative ED95 values for neuromuscular blockade are determined from the lines and 95 % confidence limits are calculated. Differences in potency are considered significant when P < 0.05. 

In the future, the BMCqs and MLEqi for lethality will be determined, presented, and discussed. Results from the above models will be compared with the log probit EPA (2000) benchmark dose software (http //www.epa.gov/ncea/ bmds.htm). In all cases, the MLE and BMC at specific response levels will be considered. Other statistical models such as the Weibull may also be considered. Since goodness-of fit-tests consider an average fit, they may not be valid predictors of the fit in the low-exposure region of interest. In this case, the output of the different models will be plotted and compared visually with the experimental data to determine the most appropriate model. The method that results in values consistent with the experimental data and the shape of the exposure-response curve will be selected for AEGL derivations. 

A question often asked by students of toxicology is Why does the probit versus log-dose plot so often come out as a straight line . This remarkably simple question is difficult to answer. It may be approached in two stages. 

Given that a log-normal distribution curve may be used to describe the relationship regarding tolerance of the species in question to compound x, then the probit-log dose plot must yield a straight line. This is because the probit scale is related to the percentage mortality scale (i.e. the scale on the y-axis) in precisely the same way as the percentage mortality is related to the log dose (i.e. the scale on the x-axis). 

Figure 2 shows the standard dosage-mortality lines for 7-hexachlorocyclohexane (line 4), parathion (line C), and p,p -DDT (line F) plotted according to the probit-log dosage procedure of Bliss (1). Line B is the corresponding dosage-mortality line resulting when... 

Figure 2-10 The probit transformation converts the sigmoidal response vs. log dose curve into a straight line when plotted on a linear probit scale. Source D. J. Finney, Probit Analysis, 3d ed. (Cambridge Cambridge University Press, 1971), p. 24. Reprinted by permission.

Alternatively, plotting the dose-response curve on logit-log paper is convenient for the direct estimation of D. Probits are not used... 

Figure 22. Data from Table 18 plotted showing the log of dose on the x-axis and the mortality probit on the y-axis...

The data are plotted (for illustration) as the probit vs. log Pr-vt. The value of Pt-s, is computed from P solid line corresponds to a least-squares fit of the PB data. The TB data (M) fall significantly to the left of the line. The numbers in parentheses indicate the sample size (see Figure 8). 

The data are converted to the coordinate system of probits as a function of log (time). First the mortality data must be converted to response data. One may do this with one of two plausible assumptions (a) that the mortality at 90 minutes corresponds to 100% response, or (b) that the mortality at both 31 and 90 minutes corresponds to 100% response, and one then lumps the data. The mortality data are converted to response data by expressing each as a percentage of the mortality selected as the 100% response. These data are plotted against the logi0 (time). Data based on the two assumptions are given in Table I-B. 

Further evidence that the slope of the concentration-response curve may be related in a predictable way to the physiochemical properties of the odorant molecule comes from a study of the relative detectability of members of an homologous series of aliphatic acetates ( ). Probit regression lines were first derived from the concentration-response data for each member of the series. The slopes of these lines, when plotted against log carbon chain length, yielded an approximately linear relation. 

Figure 4.5 is a plot of the percentage affected versus the natural log of the peak overpressure. This demonstrates the classical sigmoid shape of the response versus log dose curve. Figure 4.6 includes a plot of the probit variable (with a linear probit scale) versus the log of the peak overpressure. The straight line confirms the form of Eq. (4.3) and the resulting fit is Y = -16.7 + 2.03 ln(P°), where P is the peak overpressure in Pa, or N/m. ... 

FIGURE 4.5. Plot of percentage affected versus the log of the peak overpressure for Example 32 Dose-response correlation via probits. 

FIGURE 1-2. When dose versus response is plotted as the log of die dose given va-sus the percent cumulative response, the graph b a straight line. The probit scale is a weighted number assigned to the percent cumulative response in order to simplify calculations by using whole numbers that correspond to one or more standard deviations from the LD ... 

---