probit analysis
TRANSCRIPT
INTRODUCTION
HISTORY
APPLICATIONS
DETERMINATION OF LC50 0
CASE STUDY
CONCLUSION
REFERENCES
Probit Analysis is a specialized regression model ofbinomial response variables.
Remember that regression is a method of fitting a line tothe data to compare the relationship of the response variable(Y) to the independent variable (X).
Y = a + b X + e Where ,
a = intercept b = the slope of the line e = error term
Binomial response variable refers to a response variable with only two outcomes.
For example:
• Flipping a coin: Heads or tails
• Testing beauty products: Rash/no rash
• The effectiveness or toxicity of pesticides: Death/no death.
Probit analysis can be conducted by oneof three techniques:
• Using tables to estimate the probits andfitting the relationship by eye,
• Hand calculating the probits, regressioncoefficient, and confidence intervals,
• Using statistical packages such asSPSS,SAS, etc..
The idea of probit analysis was
originally published in Science by
Chester Ittner Bliss in 1934. He worked as anentomologist for the Connecticut agriculturalexperiment station and was primarily concernedwith finding an effective pesticide to control insectsthat feed on grape leaves (Greenberg 1980).
By plotting the response of the insects tovarious concentrations of pesticides, he couldvisually see that each pesticide affected the insectsat different concentrations, i.e. one was moreeffective than the other. However, he didn’t have astatistically sound method to compare thisdifference
• The most logical approach would be to fit aregression of the response versus theconcentration, or dose and compare betweenthe different pesticides. Yet, the relationshipof response to dose was sigmoid in nature andat the time regression was only used on lineardata.
• Therefore, Bliss developed the idea oftransforming the sigmoid dose-response curveto a straight line.
• In 1952, a professor of statistics at theUniversity of Edinburgh by the name of DavidFinney took Bliss’ idea and wrote a bookcalled Probit Analysis (Finney 1952).
• Today, probit analysis is still the preferredstatistical method in understanding dose-response relationships.
• Probit analysis is used to analyze many kinds of dose-response or binomial response experiments in a variety offields.
• Probit Analysis is commonly used in toxicology todetermine the relative toxicity of chemicals to livingorganisms.
• Probit analysis acts as a transformation from sigmoid tolinear and then runs a regression on the relationship.
• Once a regression is run, the researcher can use the outputof the probit analysis to compare the amount of chemicalrequired to create the same response in each of the variouschemicals. There are many endpoints used to compare thediffering toxicities of chemicals, but the LC 50 (liquids) orLD 50 (solids) are the most widely used outcomes of themodern dose-response experiments.
Bioassay is the combination of two words:Bios-life : Assay-determination.
It is defined as estimation or determinationof concentration or potency of a physical,chemical or biological substance (agent)by means of measuring and comparing themagnitude of the response of the test with that ofstandard over a suitable biological system understandard set of conditions.
Bioassay stands for determination ofrelative toxicity of insecticides by studying andexamining their effects on living organisms.
In broad sense, the term “bioassay” or“biological assay” refers to the procedures forthe determination of relation between aphysiologically active agent and the effectwhich it produces in the living organism.
In bio-analysis the response produced by thetest compound is compared with that of standardsample the way similar to other analytical methodsbut here the biological system is involved in thedetermination.
In the usual experiments, the magnitude ofeffects of different treatments are comparedwhereas in bio-assays the potencies of treatmentsare compared.
Principle of bioassay
The bioassay compares the test sample with asame Internationally applicable standardsubstance. It determines the quantity of testsample required to produce an equivalentbiological response to that of standard substance.
In the field of agriculture, practically allchemical programmes involving response of anorganism to a chemical fall in the realm of bio-assay.
Bioassay in the field of agriculture
In Entomology
In the determination of potency of newchemicals.
To measure the level of resistance to insecticidesin chemicals.
Bio-assay may be used in place of chemicalmethods or supplement chemical methods inanalysing insecticides.
It is a simple and easily adopted technique to theassay of new insecticides.
• The bioassay involves a stimulus applied to asubject and the response of the subject to thestimulus.
• The stimulus may be a pesticide, a fungicide, avitamin. The intensity of the stimulus may bevaried so as to vary the dose given to thesubject. The dose can be measured as aweight, a volume or a concentration.
• The subject may be an insect, a plant, abacterial culture.
Concept of bioassay
Conti….• When a stimulus is applied to a subject there
may be a change in some characteristics of thesubject. For example, weight of the wholesubject or of some particular organ maychange, an analytical value may change or thesubjects may die. Such changes in the subjectare known as responses.
• Response may be quantitative as in the caseof weight or qualitative as in the case ofmortality.
Types of bio-assay
Direct assay
Indirect assays based upon quantitativeresponses
Indirect assays based upon quantalresponses.
– The assays in which the responses arequalitative are called as quantal responseassays.
• In most of the biological assays, the responses arequalitative in nature.
• For example, in the assay of insecticides theresponse is mortality of insects.
• Quantal response assays are closely related to directassays.
• In quantal response assay, the strength of apreparation is characterized by the mediantolerance or the dose that induces 50%responses.
• If the response is mortality it is called medianlethal dose and is denoted by LD 50.
• If the response is not mortality, it may becalled median effective dose (ED 50), medianknock down dose (KD 50), median anti-feedingdose ( AD 50) and etc…
• Most commonly used measurement is LD 50.
• Here the dose levels are chosen first.
• The dose levels should range between alowest range, to which virtually no subjectswill respond, and a highest dose, to whichvirtually all subjects will respond.
• The proportion of subjects responding to eachdose is observed.
• The LD 50 is then determined by usingappropriate methods.
• LD 50 - This value represents the lethal dose of thepoison per unit weight which will kill 50 per centpopulation of test animals or organisms. It isexpressed as milligrams per kilogram of bodyweight.
• LC 50 - The lethal concentration of toxic compoundmixed in external medium i.e. water that kills halfof the population of test animals is used.
• Toxicity – Ability of a chemical to bring aboutchanges in the biological system of the targetorganism.
Methods of finding LD50
• Dragstedet-Behren’s method
• Spearman-karber method
• Probit analysis
• The most common way of estimation of LD50is from the regression line relating the log-dose to a transformed percentage response.
• There are many transformations, in thoseprobit transformation is one of the mostcommon method.
• Probit is the short form of probability + unit.
• The probability is the value of the normalequivalent deviation. Since it (Z) may bepositive or negative , a constant or unity isadded to make it positive. The constant istaken as 5.
How to calculate LC50 using probit analysis??
Procedure
• Before proceeding to estimate LC50, it has to beseen whether natural mortality is anticipated.when natural mortality is anticipated, themortality rates should be corrected using Abbot’sformula. It is given by
• corrected mortality, P* = p – c
1-c
Where, p= proportion of mortality for a given dose,
c= proportion of mortality for a zero dose( naturalmortality).
• In the process of estimating the LD50, we useempirical probits, expected probits andworking probits.
• The empirical probits are read directly fromthe tables.
• Using the relation between log-dose andempirical probits, the expected probits areobtained.
• Using the expected probits and mortality ratesthe working probits are determined.
1. Complete the column upto 5.
• Column 1- Dose(D)
• Column 2- no. of insects(n)
• Column 3- no.of insects killed(r)
• Column 4- log(10D) (x)
• Column 5- proportion killed(p)
2. Obtain the empirical probits(ye) corresponding to pvalues. Enter them in column 6.
Steps
Source ; manual for testing insecticides on rice
3. Fit a regression line using empirical probitsand log-dose. From this line estimate theexpected probits(Yp). Enter these Yp in column 7.
Here we will have a regression equation like
Yp = a + bx
4. For each Yp value , find out the weightingcoefficients ,w. The values of w can be obtainedfrom the tables.
5. Multiply each w by the corresponding n to getnw. enter nw values in column 9.
Table
Dose No. of insects
No.of insects killed
Log(10D) Proportion killed
Empiricalprobits
Expected probits
D n r x p ye yp
Weighing coefficients
nw Working probits
Estimated probits
w nw y 𝑦
Source ; manual for testing insecticides on rice
6. For each p and Yp determine the workingprobits (y) as explained below,
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
And these y values are entered in column10.
Source ; manual for testing insecticides on rice
7. Enter in column 12 to 16 the product ofcomputed values from respective columns asindicated below
Column 12- nwx
Column 13-nwy
Column 14 nwx 2
Column 15- nwxy
Column 16-nwy 2
And find the summations of these columns.
) )((
• Step 13 : Using Feller’s theorem compute the confidence limits for m.
mL, mU= 𝑚 + (𝑔
1−𝑔)(𝑚 −𝑥
_) ± tSE(m)
Where
𝑔 =𝑡2.𝑉(𝑏)
𝑏²
SE(m)=1
𝑏(1−𝑔)√ 1 − 𝑔 𝑉(𝑦
−) + (𝑚 −𝑥−)2𝑉(𝑏)
𝑉(𝑦_) =
1
∑𝑛𝑤
𝑉(𝑏)= 1
𝑆𝑆(𝑥)
14.In original units ,
LD50=𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝑚)
10
lower limit =𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝑚𝐿)
10
Upper limit=𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝑚𝑈)
10
•Probit Analysis is a type of regression used withbinomial response variables. It is very similar to logit, butis preferred when data are normally distributed.
•Most common outcome of a dose-response experimentin which probit analysis is used is the LC50/LD50.
•Probit analysis can be done by eye, through handcalculations, or by using a statistical program.
Case study - 1
TOXICITY OF INSECTICIDES AGAINST Sitophilus zeamais and
Sitophilus oryzae
B.S. Srinivasacharayulu and T.D.Yadav
• Location – IARI farm
• Insecticides like deltamethrin, etrimofos,chlorpyriphos-methtyl, fluvalinite and malathionwere tested against the adults of the s. zeamaisand s. oryzae.
• S. zeamais- maize
• S. oryzae- wheat
• The mortality was observed and moribund insectswere also counted as dead.
• The percent mortality was calculated and datawas subjected to probit analysis to workout LC50and LC95 values.
Results
Toxicity of insecticides against S.zeamais and S. oryzae
Insecticide Heteroge
neity*
Regression
equation
LC50 LC95 Standard
error
Fiducial limits
LC50
S.zeamaisDeltamethrin 4.614 Y=2.32X+2.13 0.1738 0.8877 0.0548 0.1375-0.2225
Fluvalinate 6.588 Y=2.73X+1.15 2.5719 10.3431 0.0405 2.1409-3.0859
Chlorypriphos
methyl
2.934 Y=2.50X+1.50 2.5119 11.4815 0.0412 2.0857-3.0252
Etrimfos 3.604 Y=2.34X+1.74 0.2473 1.2540 0.0436 0.2016-3.0252
Malathion 4.814 Y=1.74X+2.28 3.6578 32.4709 0.0574 2.8022-4.7044
S.oryzaeDeltamethrin 3.9767 Y=2.49X+1.54 0.2452 1.1277 0.0412 0.2038-0.2989
Fluvalinate 2.4180 Y=2.89X+0.44 3.7832 14.0860 0.0374 3.2114-4.5009
Chlorypriphos
methyl
2.5250 Y=2.44X+1.84 1.9728 9.3608 0.0490 1.5631-2.4324
Etrimfos 2.2864 Y=3.93X-1.19 0.3759 0.9884 0.0265 0.3374-0.4285
Malathion 1.3280 Y=2.37X+1.50 3.0199 14.8935 0.0424 2.4940-3.6568
*= significant at 0.05percentY=probit killX =log( concentration*100)
The lowest LC50 value of 0.1738 ppm was obtained against s.zeamais with deltamethrin.
At LC95 level deltamethrin remained most toxic followed by etimfos, fluvalinite, chlorpyriphos-methtyl, and malathion.
In case of S.oryzae, deltamethrin proved most toxic with LC50 value of 0.2452 ppm.
But at LC95 value, etrimofos was found most toxic with the value of 0.9884 ppm followed by deltamethrin(1.1277ppm).
Case study - 2
BIOEFFICACY AND PERSISTANCE OF INSECTICIDES
AGAINST Sitophilus oryzae(L.), Callosobruches chinensis(L.), and C.
maculatus(F.) ON WHEAT AND COWPEA.
RAJANI B. RAJPUT
• Objective – to evaluate bioefficacy of insecticidesagainst sitophilus oryzae(l.), callosobrucheschinensis(l.), and c. maculatus(f.) on wheat andcowpea.
• Location – laboratory, Dept. of AgriculturalEntomolgy, UAS.Dharwad.
• Insecicides used – cypermethrin, deltamethrin,fenvelerate, dichlovaras, malathion and spinosad.
• Concentrations = 5 + 1
• The mortality was observed and moribund insectswere also counted as dead.
• The percent mortality was calculated and data wassubjected to probit analysis to workout LC50 andLC95 values.
Results
Toxicity of insecticides on mortality of insects
Insecticide
Regression
equation
Chi
square LC50
Fiducial limits
LC90
Fiducial limits
LL UL LL UL
S. oryzaeFluvalinate Y=0.04X-0.30 0.63 29.52 13.40 51.07 181.77 123.83 643.21
Malathion Y=0.03X-0.26 0.39 12.64 8.97 28.12 83.87 62.36 187.09
Deltamethrin Y=1.21X-0.68 0.40 0.66 0.35 1.11 1.61 1.20 2.69
Spinosad Y=1.55X-0.004 0.46 0.08 0.77 0.36 0.83 0.77 1.62Cypermethrin Y=0.10X-0.18 1.89 3.10 1.53 7.54 24.92 18.35 57.97
Dichlorvos Y=0.02X-0.23 0.30 13.60 8.80 30.53 97.34 72.32 212.70
C.chinensisFluvalinate Y=0.017X-0.27 0.32 23.87 7.57 36.64 154.03 109.62 403.20
Malathion Y=0.03X-0.73 0.76 23.13 3.94 34.29 82.20 63.38 149.72
Deltamethrin Y=1.04X-0.59 1.23 0.96 0.18 1.16 1.79 1.38 2.90
Spinosad Y=1.60X-1.00 0.26 0.24 0.20 0.49 0.96 0.70 1.62Cypermethrin Y=0.11X-0.46 1.16 5.25 4.65 8.18 24.80 18.91 46.57
Dichlorvos Y=0.03X-0.60 1.63 23.67 16.28 43.86 95.80 73.65 172.86
*= significant at 0.05percentY=probit killX =logconcentration
Insecticide
Regression
equation
Chi
square LC50
Fiducial limits
LC90
Fiducial limits
LL UL LL UL
C.maculatus
Fluvalinate Y=0.03X-0.58 0.54 20.74 13.22 33.08 84.93 64.91 160.9
8
Malathion Y=0.03X-0.91 1.11 34.33 14.66 45.90 120.25 85.09 382.0
6
Deltamethrin Y=1.26X-0.83 0.58 0.76 0.32 1.15 1.67 1.31 2.66
Spinosad Y=1.02X+0.22 0.80 0.05 0.01 0.33 1.04 0.67 2.18
Cypermethrin Y=0.10X-0.15 1.08 2.64 16.95 55.85 23.07 16.95 55.85
Dichlorvos Y=0.01X+0.03 1.00 4.96 1.37 29.03 107.00 84.62 170.4
5
*= significant at 0.05percentY=probit killX =logconcentration
The lowest LC50 value of 0.08 ppm was obtained against S.oryzae with spinosad. Hence spinosad was found to be more toxic against S.oryzae.
In case of C.maculatus , spinosad proved to be most toxic with LC50 value of 0.05 ppm followed by deltamethrin.
In case of C.chinensis , spinosad proved most toxic with LC50 value of 0.2452 ppm.
Even at LC90 value for all insects, spinosad remains more toxic than all other insecticides.
Case study - 3
RELATIVE TOXICITY OF PYRETHROID AND NON PYRETHROID INSECTICIDES TO THE ADULTS OF GREY WEEVIL, MYLLOCERUS UNDECIMPUSTULATUS MACULOSUS
D.S .SINGH and J.P.SINGH
• Location –Division of Entomology, IARI,New
Delhi.
• Insecicides used –labdacyhothrin, cypermethrin,
bifenthrin, decamethrin, fenvalerate, fluvalinate,
malathion, endosulfan.
• The mortality was observed and moribund insects
were also counted as dead.
• The percent mortality was calculated and data
was subjected to probit analysis to workout LC50
and LC95 values.
Results
Table.1.Toxicity of insecticides against adults of Grey Weevil
Insecticide Heterogen
eity*
Regression
equation
LC50 SEm Fiducial limits
labdacyhothrin 3=2.407 Y=2.625x-4.460 0.004018 0.0538 0.003159-
0.005122
cypermethrin 4=3.149 Y=1.868x-1.914 0.005023 0.0640 0.003763-
0.006705
bifenthrin 4=0.708 Y=2.783x-5.830 0.007780 0.0458 0.006327-
0.009568
decamethrin 4=6.978 Y=1.845x-2.292 0.008954 0.0574 0.006910-
0.011620
fenvalerate 3=1.732 Y=2.144x-4.591 0.029720 0.0583 0.022840-
0.038670
fluvalinate 3=1.796 Y=2.338x-6.050 0.053210 0.0510 0.042280-0.066970
malathion 3=0.052 Y=1.884x-5.224 0.273500 0.0656 0.203400-
0.367800
endosulfan 4=2.546 Y=2.496x-9.878 0.914100 0.0412 0.759100-
1.104000
→RR
RS↓
Lambdacyhalotrin
cypermethrin
bifinthrin decamethrin fenvalerate fluvalinate
Lambdacyhalotrin
1.00 1.25 1.94 2.23 7.40 13.24
cypermethrin 0.80 1.00 1.55 1.78 5.92 10.59
bifinthrin 0.52 0.64 1.00 1.15 3.82 6.84
decamethrin 0.45 0.56 0.87 1.00 3.22 5.94
Fenvalerate 0.13 0.17 0.26 0.30 1.00 1.79
Fluvalinate 0.07 0.09 0.15 0.17 0.56 1.00
Table.2.Relative susceptibility*and Relative resistance of myllocerusundecimpustulatus maculosus to pyrethroids.
On the basis of LC50 value ( table 1) , lambdacyhalothrin was found to be more toxic than all other insecticides.
Using table 2.Cypermethrin, bifenthrin, decamethrin, fenvalerate and fluvalinite were 0.80, 0.52, 0.45, 0.13 and 0.07 times less toxic than lambdacyhalothrin.
Similarly Cypermethrin, bifenthrin, decamethrin, fenvalerate and fluvalinite were 1.25, 1.94, 2.33, 7.40, and 13.24 times respectvelymore tolerant than lambdachyhalothrin.
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