PROBIT ANALYSIS IN TOXICOLOGICAL STUDIES (DETERMINATION OF LD50)

MASTERS SEMINARin

PROBIT ANALYSIS IN TOXICOLOGICAL STUDIES(DETERMINATION OF LD50/LC50)C.Kundavai NachiyarMVM 14015Department of Animal Husbandry Statistics and Computer ApplicationMadras Veterinary CollegeChennai - 600 007

HistoryChester Ittner Bliss (1934)Entomologist Connecticut agricultural experiment stationEffective pesticide to control insects(fed on grape leaves)By plotting the response of the insects to various concentration of pesticidesEach pesticide affected the insects at different conc

cont..Didnt 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

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.,)

ApplicationsTo 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.

ApplicationsOnce 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

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

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".

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

Median Lethal ConcentrationThe 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

Determination of LD50:Normal population assumption - free methods

Thompsons moving average interpolationUp-and-down method

Normal population assumption Probit analysis approach

(Hayes et al.,(2014))

Normal population assumption - freeThompsons moving average interpolationwidely acceptedconvenient 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))

Cont..Up-and-down method:Pyramid method To estimate the LD50 with a small number of samplesEconomical advantage Time consuming Requires a larger amount of test article (Hayes et al.,(2014))

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

Other methods

Dragstedet-Behrens method

Spearman-karber method

Probit Analysisprobability + unitConducted by three techniques:

Using tables to estimate the probits and fitting the relationship

Use of regression

Use of statistical package such as SPSS

Method AStep 1: convert % mortality to probits: Determine probits by Finneys table (Finney 1952)

Randhawa et al.,(2009)

Step 2: Take the log of the concentrations:Done by hand calculations, calculator or computer program of choice.

Toxicity of Retenone to Macrosiphoniella

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.

Log concentration Vs Probitm = 0.678LD50 = log 10 of 0.678 = 4.86

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 Abbots 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).

Computation of LD50:

Rangaswamy et al., (1995)

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

Step 4: For each yp value , find out the weighting coefficients ,w. The values of w can be obtained from the tables.

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 = rangeWhen p is close to 1, y = y1 - qA where, y1 = maximum working probit q = 1-p

Source: Experimental Statistics(2005)

Step 7: Fit a weighted regression line, y = a+ bxEstimate of estimated probit by substitute the x values. 1. Find the following values

2.3.

4.

5. Fit the regression line, find estimated probit .

Step 8:

d.f k-2

Not significant - observed and predicted values homogenous

Significant heterogeneity factor

h = / k - 2

2

Step 9 : t- test

Step 10: Computation of LD50

log LD50 = m =

y is empirical probit value for p = 0.5

Step 12: Compute the LD50: LD50 = antilog m lower limit = antilog mL Upper limit = antilog mU

EXAMPLE:

Eg:Resultb = 5.811114x = 0.761813 y = 5.47006Log LD50 m = [ ( 5 - 5.47006) / 5.811114] - 0.761813 = 0.681LD50 = antilog m = 4.786

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

Step 2:

Step 3:

Step 4:

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

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.

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

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