Kristy Seidel <[email protected]> asks:
> Can anyone suggest a reference for how to calculate the confidence limits of
> an LD50 (i.e. 50% lethal dose level) obtained from a probit model? The data
> is from a drug toxicity experiment in mice. I've figured out how to derive
> the LD50s from the model parameter estimates, but I'm stuck on how to
> calculate the variance of the LD50 estimate.
There have already been a couple of responses to this post on the list. I'll
simply add that such calculations are performed quite easily in Stata 8:
. quietly probit y logdose
. local ld50 LD50:exp(-_b[_cons]/_b[logdose])
. local ld90 LD90:exp((invnorm(0.9)-_b[_cons])/_b[logdose])
. nlcom (`ld50') (`ld90')
LD50: exp(-_b[_cons]/_b[logdose])
LD90: exp((invnorm(0.9)-_b[_cons])/_b[logdose])
------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
LD50 | 2.754348 .3953593 6.97 0.000 1.979458 3.529238
LD90 | 4.090754 1.228219 3.33 0.001 1.683489 6.498019
------------------------------------------------------------------------------
Two things to note:
(1) Formulas were obtained from Collett (2003, p. 107-8).
(2) The confidence intervals are calculated as
point estimate +/- (z critical value)*se
and not those based on Fieller's theroem. -nlcom- uses the above formula
so as to be more general.
--Bobby
[email protected]
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