# Re: st: probit modeling

 From rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.) To statalist@hsphsun2.harvard.edu Subject Re: st: probit modeling Date Wed, 15 Jan 2003 11:30:49 -0600

```Kristy Seidel <kristy.seidel@seattlechildrens.org> 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
rgutierrez@stata.com
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