[R] Probit Analysis

[Dipjyoti Chakraborty]

Respected Sir/Madam,



I have a question regarding calculation of LD50 (Lethal Dose) and IC50 (50%
inhibitory concentration) of an antimicrobial experiment.



I have used a compound isolated from a plant and observed its effect on the
fungus *Fusarium oxysporum* by the food poisoning method. Solutions of the
compound at concentrations of 0, 50, 100, 150, 200 and 250µg/ ml were added
to sterilized medium in Petri dish (9cm dia.) and after transferring the
mycelia of fungal strains, the dishes were incubated in the dark. When the
mycelium of fungi reached the edges of the control (0µg/ ml) dishes, the
antifungal indices were calculated. Each test was repeated three times and
the average was calculated. The formula to calculate antifungal index (AI)
was



AI % = (1- Da / Db) * 100

Where Da = diameter of growth zone in experiment (cm); Db = diameter of
growth zone in control (cm).



The results are as follows



Concentration (µg/ ml)

0

50

100

150

200

250

AI% (average of 3 replicates)

0

10

21.59

33.89

47.96

59.93















I have the Version 2.3.1 (2006-06-01) of R loaded in my computer and want to
calculate LD50 and if possible IC50 values with the data. I have checked the
Help menu---Manuals in PDF---An introduction to R. There is an example of
calculating LD 50 in Chapter 11, page no. 63.




Please suggest some functions on R or the method by which I can do the
calculations. I am not at all used to programming language so a detailed
solution would be very much helpful.

 I am sending the full analysis that I am doing just below this letter. I am
also sending it as attachment.
There is a warning message that i have marked in red--if it is not in color
in your mail---then just see the message after the comand >fmp <-
glm(Ymat~x,family = binomial(link=probit), data = Fusarium.
It says non integer counts in a binomial glm! in: eval(expr, envir, enclos)

Actually I am not quite sure I am doing the correct thing for probit
analysis. You can see that I do get a value of ld50 at the last step, but I
do not know whether my methodology is correct.


> Fusarium <- data.frame(x = c(0,50,100,150,200,250), n = rep(90,6),

+ y = c(90,81,75.4,58.5,51.3,65.1))

> Fusarium$Ymat <- cbind(Fusarium$y, Fusarium$n - Fusarium$y)

> fmp <- glm(Ymat ~ x, family = binomial(link=probit), data = Fusarium)

Warning message:

non-integer counts in a binomial glm! in: eval(expr, envir, enclos)

> summary(fmp)



Call:

glm(formula = Ymat ~ x, family = binomial(link = probit), data = Fusarium)



Deviance Residuals:

       1         2         3         4         5         6

 3.26268  -0.06454  -0.15297  -2.48265  -1.99479   3.13791



Coefficients:

              Estimate Std. Error z value Pr(>|z|)

(Intercept)  1.5767662  0.1345939  11.715  < 2e-16 ***

x           -0.0056714  0.0007908  -7.172 7.41e-13 ***

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



(Dispersion parameter for binomial family taken to be 1)



    Null deviance: 84.795  on 5  degrees of freedom

Residual deviance: 30.662  on 4  degrees of freedom

AIC: 58.283



Number of Fisher Scoring iterations: 5



> summary(fml)



Call:

glm(formula = Ymat ~ x, family = binomial, data = kalythos)



Deviance Residuals:

     1       2       3       4       5

 1.386   0.838  -2.021  -2.151   2.398



Coefficients:

             Estimate Std. Error z value Pr(>|z|)

(Intercept)  2.069867   0.284782   7.268 3.64e-13 ***

x           -0.006615   0.001591  -4.157 3.22e-05 ***

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



(Dispersion parameter for binomial family taken to be 1)



    Null deviance: 35.262  on 4  degrees of freedom

Residual deviance: 17.083  on 3  degrees of freedom

AIC: 44.426



Number of Fisher Scoring iterations: 4



> ld50 <- function(b) -b[1]/b[2]

> ldp <- ld50(coef(fmp)); ldl <- ld50(coef(fml)); c(ldp, ldl)

(Intercept) (Intercept)

   278.0220    312.8854


Thanking you in anticipation.

Sincerely yours.


-- 
Dipjyoti Chakraborty
C/o Dr Adinpunya Mitra
Natural Products Biotechnology Lab
Agriculture & Food Technology Depart.
IIT-KGP
Kharagpur-721 302-India