Probit analysis

Although the LD 0 can be obtained from a log dosage-probit line by graphic estimation, bioassay data need to be subjected to probit analysis to obtain a more reliable value. This analysis will provide, in addition to the LD50, parameters such as the X2 value (for testing the heterogeneity of discrepancies between observed and expected numbers), 95% fiducial limits to the 

and the slope value ( SE). These values are required when we perform a bioassay of insecticide, and the results obtained are to be published in an entomological journal. 

The result of this transformation is that the probit for 50% mortality is 5, for 16% mortality is 4, and for 84% mortality is 6. Probits for every percent mortality between 1% and 99.9% can be obtained from Table 5.1. 

These ideas were first suggested by Bliss (1934) and were later extended by Finney (1964). Although the iterative procedure of probit analysis can be performed manually with a desk calculator (Finney, 1964), in recent years the method has been conveniently computerized (Finney, 1971 SAS Institute, 2002-2003). An example of probit analysis using the SAS system is illustrated in Appendix 5.1. 

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Finney D.J. (1971) Probit Analysis. London Cambridge University Press. 

Figure 2-9 The relationship between percentages and probits. (Source D. J. Finney, Probit Analysis, 3d ed. (Cambridge Cambridge University Press, 1971), p. 23. Reprinted by permission.

D. J. Finney, Probit Analysis (Cambridge Cambridge University Press, 1971), p. 23. 

Blast damage effects are estimated using probit analysis, discussed in section 2-6. 

Effects (LC i, values were calculated by Haskell Laboratory using probit analysis) ... 

Finney, D.K. (1977). Probit Analysis, 3rd ed. Cambridge University Press. 

Finney, D. J. "Probit Analysis", 333 pp. Cambridge Univ. Press. London (1971). 

Table 12 Lethality dose estimates for atropine derived from probit analysis...

Selected entries from Methods in Enzymology [vol, page(s)] Median effective dose, 235, 29, 31, 33 determination of median infectious dose, 235, 29-39 median lethal dose, 235, 29 moving average interpolation, 235, 32-34, 36-37, 39 probit analysis, 235, 31-36, 39 Reed-Muench method, 235, 30, 33-35 staircase method, 235, 33, 37-39 median response, 235, 29 dose range for animal experiments, 235, 29 50% end-point determination, 235, 29-30. 

Figure 4. Dose response curves representing per cent mortality (within 48 hours) of approximately 20 g mice (CRE CD BR ICR) injected with specified doses of ether soluble acetone filtrate (ESAF), ether soluble acetone precipitate (ESAP), water soluble acetone filtrate (WSAF), and water soluble acetone precipatate (WSAP) from Prorocentrum concavum (SIU 364). Each dose was administered by ip injection into 10 mice. LD50S were determined using probit analysis. A correlation coefficient (R) is provided for each LD5Q.

Experiments using a matrix of four levels of ferulic acid and four levels of moisture stress demonstrated that the combined action was additive under more stressful levels of the individual factors than in the previous tests. Duke et al. (23) tested the germination of lettuce seeds treated with phenolic acids (1 mM) at water potentials (D-mannitol) of 0, -0.2, -0.4, and -0.6 MPa. The combined action of low water potential and exposure to phenolic acids resulted in an additive detriment to germination, and the authors concluded from probit analysis that the mechanism of action from these sources was similar. Whatever their mechanisms, moisture stress and phenolic acids appear to work together in limiting growth of plants. 

Mortalities observed in tests of a series of oil dosages against adult female California red scale or eggs of the citrus red mite indicated a positive relation between increased dosage and increased kill. The fit of the points to the line was much better for oil dosages expressed as deposit than for those expressed as spray concentration. However, the variance observed indicated that statistical procedures would be required to arrive at the best fit for a line through the observed points. The method of probit analysis chosen was that proposed by Bliss (2) and modified by Finney (11) for data adjusted for mortality in the controls. 

It is known that the viscosity of a lubricating oil can be reduced by the addition of kerosene. Spray trials showed that kerosene was not appreciably toxic to the red scale. The effect of kerosene additions on the efficiency of paraftoic fractions 5 and 9 (46-M20) against red scale was therefore of interest. One-to-one mixtures of the two oils with kerosene were made on a volume basis. These mixtures were used in spray trials to establish dosage mortality values. Since the kerosene in the amoimts used was not toxic, the deposit values used for the probit analysis were based on the actual amount of the oil represented. 

Methods for acute-to-chronic extrapolations have been developed and are available as computer programs such as the acute-to-chronic estimation (ACE Mayer et al. 1994 Ellersieck et al. 2003) software, which makes use of 3 methods — regression, multifactor probit analysis, and accelerated life testing — to consider the relationship between exposure concentration, degree of response, and time course of response (Mayer et al. 1994 Sun et al. 1995 Lee et al. 1995). All methods produce confidence intervals around the LC and/or EC percentage point estimate. 

Finney DJ. 1971. Probit analysis. London (UK) Cambridge University Press, 333 p. 

Lee G, Ellersieck MR, Mayer FL, Krause GF. 1995. Predicting chronic lethality of chemicals to fishes from acute toxicity test data multifactor probit analysis. Environ Toxicol Chem 14 345-349. 

When expressing efficacy and toxicity data using probit analysis, comparison of the data is facilitated. This is illustrated in Figure 7.3. In this case we can see that the TI for the drug in question is approximately 18, while the ratio of toxicity for a nonlethal toxic effect (e.g., gastric irritation) to efficacy is approximately 2.4. By obtaining those types of data we can now express toxicity in a quantitative manner. It should also be emphasized that there is a continuum of side effects that could conceivably be plotted between lines A and C. 

Raw data for all bioassays, except algal test, were analyzed using the Toxcalc Toxicity Data Analysis and Database Software, vers. 5.0 (Tidepool Scientific Software). Point estimations were calculated by concentration/response regression using Probit Analysis as first choice and Trimmed Spearman-Karber as second, if Probit was not possible. If the raw data did not allow the respective L(E)C50 to be calculated at the highest tested concentrations, then these values... 

Ulcer index of treated animals are compared with controls. Using various doses, dose-response curves can be established for ulcer formation and gastric acid secretion. ID50 values can be calculated by probit analysis, whereby 0 % corresponds to no and 100 % to maximal stimulated gastric acid output. 

Kligman and Wooding (1967) applied the Litchfield and Wilcoxon probit analysis to cumulative irritation testing with calculation of IT 50 and ID 50 values. Their early work forms the basis for the 21-day cumulative irritation assay, which is currently widely used. 

Finney, D. "Probit Analysis", Cambridge University Press,... 

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