The LD50 (lethal dose 50%) is the dose that has a 50% probability of causing dea

Question

The LD50 (lethal dose 50%) is the dose that has a 50% probability of causing death; a higher LD50 means the substance is less toxic. Typical units are milligrams per kilogram, which means that the lethal dose in milligrams is divided by the animal mass in kilograms. The test seems to be in the process of being phased out, although papers continue to appear in which it is estimated (e.g., Muralidhara et al. 2001. Acute, subacute and subchronic oral toxicity studies of 1,1-dichloroethane in rats: Application to risk evaluation. Toxicological Sciences 61:135-145. The 1,1 dichloroethane is a solvent often found as a contaminant of drinking water and a pollutant at hazardous waste sites). Muralidhara et al. (2001) reported that “the number of fatalities in groups of 8 rats at each dosage level (in grams/kilogram) were as follows: 0 rats/8 rats – 0 g/kg; 0/8 – 1; 0/8 – 2; 0/8 – 4; 4/8 – 8; 5/8 – 12; and 8/8 – 16.”

a. Assuming that a normal distribution of mortality versus the logarithm of the dose (i.e., a lognormal distribution) is appropriate, estimate the LD50. (Note – All deaths occurred within 24 h of dosing so this portion of their data addressed only acute effects of the compound.)

b. Discuss your level of confidence in the result and how you might modify a subsequent experiment to better estimate this LD50.

Explanation / Answer

a) LD50 can be estimated by using the following R code

k=c(0,0,0,4,5,8)
d=c(1,2,4,8,12,16)
z=log10(d)
fit=lm(k~z)
summary(fit)

Coefficients:
(Intercept) z
-1.554 6.437

b)p-value: 0.0163

hence at 1% level of significance i.e we take the regression

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