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I am trying to use a glm with a binomial distribution (logit link) to analyse data from a dose response curve for the lethal effects of different bacterial strains. I now want to obtain estimates of the lethal dose 50 (LD50).

My model is simply of the form:

survival ~ a + b*dose

Thus since I have a logit link, obtaining the estimates for the LD50 (i.e. p=0.5) simply means dividing -a/b. However, I am also wanting to know the confidence intervals for these estimates and that's where I am unsure about what to do. If anyone would have a suggestion for this, that would be great.

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  • $\begingroup$ Depending on your sample size, you could use bootstrapping to obtain CIs. $\endgroup$ – boscovich Nov 30 '12 at 19:10
  • $\begingroup$ Hi Andrea, Thanks for your reply. I have 5 datapoints per dose (4 doses). Could you please further explain how the bootstrapping could be done in this case? (sorry, I haven't really used this much). Cheers, Ricardo $\endgroup$ – ricardo Dec 1 '12 at 14:37
  • $\begingroup$ Have a look at this link. $\endgroup$ – Hans Roggeman Feb 2 '14 at 3:03
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There is a package "drc" for estimation of LD50 and its confidence intervals.

In another way, your glm results can be treated by a simple function "dose.p" in package MASS that calculates LD50 and its SE.

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