In dose response analyses, why are the lethal dose and the effective dose computed at 50%? Is it conventional for comparison purpose or is there a biological or mathematical reason?
I am not sure but I would assume it is by convention. The fore fathers of Pharmacology found it easy to identify the middle of the response. EC, ED, LD are all, for the purpose of comparison, presented at 50% of max.
Particular to these 2, the distance between EC and LD give you an idea of the therapeutic index (safety).
Note that not all measures at compared there. The 10-90 rise, the steepness of the response, the max, the min, etc...
LD50 or LC50 or ED50 are the most reliable values depending on which characteristics you assess. At the LD50 value is the smallest the standard deviation of the data. Generally, when characerising the efficiency of a poison we calculate the LD (LC)50 and the LD (LC)90 values with their fiducial limits. You can find more information in any toxicological textbook.
I propose you to read some of Finney"s books or articles like
Finney, D. J., 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.
There are three index to measure safety of drugs or any substance which is to be administered in body. 1) Therapeutic index= L50/ED50 2) Therapeutic ratio= LD25/ED75 3) Certain safety factor=LD1/ED99. The last one is a more convenient estimate of safety than previous ones. How ever values of minimum toxic dose (LD1) and maximum therapeutic dose (ED99) may be less precise than LD50 and ED50. For shake of convenience, We can use first and second index to measure safety of agents.
What could be alternatives for the LD50? I don´t think it is a reliable parameter for concluding anything to know which amount of "substance" kills 50 % of mice or rats. I would even think it is not responsable to transfer these results to humans.
If we know a substance is toxic, let´s just avoid it. Unless it´s not a rat poison, I don´t want to know how much I can administer to a rat before it dies.
Furthermore: Using the LD50 to calculate a dose is quite ironic. What we learn from the procedure, is that you have a 50:50 chance of survival of the animal when administering LD50. Because each animal is different. As is every human and will therefore require a personalized dose of any substance.
Please, if there is none, let us find an alternative for this testing that kills so many sentient beings every year!