![Eg:Result
b = 5.811114
x = 0.761813
y = 5.47006
Log LD50 m = [ ( 5 - 5.47006) / 5.811114] - 0.761813
= 0.681
LD50 = antilog m = 4.786](https://image.slidesharecdn.com/probitanalysisintoxicologicalstudiessemi-160713055238/85/Probit-analysis-in-toxicological-studies-36-320.jpg)
Probit analysis in toxicological studies
- 1. C.Kundavai Nachiyar MVM 14015 Department of Animal Husbandry Statistics and Computer Application Madras Veterinary College Chennai - 600 007
- 2. History Chester Ittner Bliss (1934) Entomologist – Connecticut agricultural experiment station Effective pesticide to control insects(fed on grape leaves) By plotting the response of the insects to various concentration of pesticides Each pesticide affected the insects at different conc
- 3. cont.. Didn’t have statistical sound method to compare this difference Logical approach- fit regression of response Vs conc or dose and compare between the different pesticides Developed the idea of sigmoid dose- response curve to a straight line 1952 – David Finney – book – Probit Analysis
- 4. What is it? Type of regression analysis for binomial response variables Transforms the sigmoid dose response curve to straight line Binomial response variables – response variables with only two outcomes (Vincent et al.,)
- 5. Applications To analyze many kinds of dose-response or binomial response experiments in a variety of fields. Toxicology - determine the relative toxicity of chemicals to living organisms. Transformation from sigmoid to linear and then runs a regression on the relationship.
- 6. Applications Once a regression is run, the researcher can use the output of the probit analysis To compare the amount of chemical required to create the same response in each of the various chemicals LC 50 (liquids) or LD 50 (solids) are the most widely used outcomes of the modern dose-response experiments
- 7. What is LD50? Median Lethal Dose lethal dose of the chemical per unit weight which will kill 50 per cent population of test animals or organisms milligrams per kilogram of body weight. 1927 - J.W. Trevan - to estimate the relative poisoning potency of drugs developed the LD50test
- 8. Importance of LD50: Depending on how the chemical will be used, many kinds of toxicity tests may be required Different chemicals cause different toxic effects, comparing the toxicity of one with another is hard To compare the toxic potency or intensity of different chemicals, researchers must measure the same effect One way is to carry out lethality testing -"quantal" test It measures an effect that "occurs" or "does not occur".
- 9. Utility: Aid in developing emergency procedures To help develope guidelines for the use of appropriate safety clothing and equipment. For the development of transportation regulations Aid in establishing occupational exposure limits Safety Data Sheets
- 10. Median Lethal Concentration The concentration of the chemical in air that kills 50% of the test animals during the observation period Environmental studies - the concentration of a chemical in water
- 11. Determination of LD50: Normal population assumption - free methods Thompson’s moving average interpolation Up-and-down method Normal population assumption Probit analysis approach (Hayes et al.,(2014))
- 12. Normal population assumption - free Thompson’s moving average interpolation widely accepted convenient tables are available for estimation of the value of the LD50 with confidence limits four doses must be at equal log dose intervals the number of animals per dose level must be equal. (Hayes et al.,(2014))
- 13. Cont.. Up-and-down method: Pyramid method To estimate the LD50 with a small number of samples Economical advantage Time consuming Requires a larger amount of test article (Hayes et al.,(2014))
- 14. Normal population assumption: Probit analysis approach Either by graphic means or by mathematical calculation To evaluate the acute toxicity data Transformation of both the cumulative response probability and dosage data
- 16. Probit Analysis probability + unit Conducted by three techniques: Using tables to estimate the probits and fitting the relationship Use of regression Use of statistical package such as SPSS
- 17. Method A Step 1: convert % mortality to probits: Determine probits by Finney’s table (Finney 1952) Randhawa et al.,(2009)
- 18. Step 2: Take the log of the concentrations: Done by hand calculations, calculator or computer program of choice. Toxicity of Retenone to Macrosiphoniella
- 19. Step 3: Graph the Probits Vs the Log Concentration: Hand fit the line by eye that minimizes the space between the line and the data. Step 4: Find the LD50: Find the probit of 5 in the y-axis, then move down to the x-axis and find the log of the concentration associated with it. Then take the inverse of the log. That value is LD50 value.
- 20. 0 1 2 3 4 5 6 7 1.01 0.89 0.71 0.58 0.41 probitmortality log concentration Log concentration Vs Probit m = 0.678 LD50 = log 10 of 0.678 = 4.86
- 21. Method B: Use of regression . Assumes that the relationship between number responding and concentration is normally distributed. Before proceeding to estimate LD50, it has to be seen whether natural mortality is anticipated. The mortality rates should be corrected using Abbot’s formula corrected mortality, P* = p – c 1-c p = proportion of mortality for a given dose, c = proportion of mortality for a zero dose (natural mortality).
- 22. Computation of LD50: Rangaswamy et al., (1995)
- 23. Computation of LD50: Step 1: Complete the column up to 5. Step 2: Obtain the empirical probits(ye) corresponding to p values.(Finney table). Step 3: Fit a regression line using empirical probits(ye) and log-dose(x). From this line estimate the expected probits(yp). yp = a + bx
- 24. Step 4: For each yp value , find out the weighting coefficients ,w. The values of w can be obtained from the tables.
- 25. Step 6: For each p and yp determine the working probits (y) y = y0 + pA Where, y0 = minimum working probit, p = proportion of mortality A = range When p is close to 1, y = y1 - qA where, y1 = maximum working probit q = 1-p
- 27. Step 7: Fit a weighted regression line, y = a+ bx Estimate of estimated probit by substitute the x values. 1. Find the following values
- 28. 2. 3.
- 29. 4. 5. Fit the regression line, find estimated probit .
- 30. Step 8: d.f k-2 Not significant - observed and predicted values – homogenous Significant –heterogeneity factor h = χ / k - 2 2
- 31. Step 9 : t- test
- 32. Step 10: Computation of LD50 log LD50 = m = y is empirical probit value for p = 0.5
- 34. Step 12: Compute the LD50: LD50 = antilog m lower limit = antilog mL Upper limit = antilog mU
- 35. EXAMPLE:
- 36. Eg:Result b = 5.811114 x = 0.761813 y = 5.47006 Log LD50 m = [ ( 5 - 5.47006) / 5.811114] - 0.761813 = 0.681 LD50 = antilog m = 4.786
- 37. Method C: Use of statistical package such as SPSS: Step 1: Simply input a minimum of three columns into the Data Editor Number of individuals per container that responded Total of individuals per container Concentrations
- 39. Step 2:
- 40. Step 3:
- 41. Step 4:
- 42. Summary: Type of regression used with binomial response variables, preferred when data are normally distributed. Used in LC50/LD50 calculation can be done by eye, through hand calculations, or by using a statistical program Based on the availability of resources, time& preference of researcher
- 43. REFERENCES: Ahmed, M., 2015. Acute Toxicity (Lethal Dose 50 Calculation) of Herbal Drug Somina in Rats and Mice. Pharmacology & Pharmacy, 6:185-189. Akcay and Aytac, 2013.The Calculation of LD50 Using Probit Analysis. The FASEB Journal, 27:1217-18. Akhila.J.S., Shyamjith,Deepa and M.C.Alwar,2007. Acute toxicity studies and determination of median lethal dose. Current Science, 93(7): 917-920. Bhar,L.(date unknown). Probit Analysis. Indian Agricultural Statistics Research Institute, New Delhi.Retrieved January 28, 2016, from https://www.researchgate.net/file.PostFileLoader.html Finney, D. J. and Ed.,1952. Probit Analysis.Cambridge, England, Cambridge University Press.
- 44. Finney, D. J. and W. L. Stevens, 1948. A table for the calculation of working probits and weights in probit analysis. Biometrika, 35(1-2): 191-201. Hayes, A .W and C.L. Kruger,2014. Hayes' Principles and Methods of Toxicology.6th edn, CRC Press. Natrella,M.G., 2005. Experimental Statistics. Dover publication, Inc. Randhawa, M.A.,2009. Calculation Of Ld50 Values From The Method Of Miller and Tainter, 1944. J Ayub Med Coll Abbottabad. 21(3): 184-185. Rangaswamy, R. 1995. A Textbook Of Agricultural Statistics.New Age International (P)limited, publishers.new delhi., 469-494. Vincent,K., (date unknown). Probit Analysis. Retrieved February 2, 2016, from userwww.sfsu.edu/efc/classes/biol710/probit/ProbitAnalysis.pdf
- 45. THANK YOU