I think what you want are confidence intervals for $x$ given some probability $p$ (not prediction or predictional intervals - and I don't know what predictional intervals are).

Because the model you're fitting is

$$\log \left(\frac{\text{prob}}{1-\text{prob}}\right)=a+b x$$

you want confidence intervals for $x$

$$x = \frac{\log \left(\frac{\text{prob}}{1-\text{prob}}\right)-a}{b}$$

You can get the lower and upper limits for a 95% confidence interval for $x$ with the following:

prob = 0.5;
upper= tt /. Solve[prob == 1 - 1/(1 + Exp[parms.{1, tt} - 1.96 Sqrt[{1, tt}.cov.{1, tt}]]), tt]
lower= tt /. Solve[prob == 1 - 1/(1 + Exp[parms.{1, tt} + 1.96 Sqrt[{1, tt}.cov.{1, tt}]]), tt]

I'm having a hard time understanding the seemingly inconsistent and non-standard GLM language you are using. Below I'm just attempting to state what I think you have in terms of more standard statistical language (or if you want, jargon).

If you use the command

GeneralizedLinearModelFit[p, x, x, ExponentialFamily -> "Binomial"]

you have a dataset named p with a single predictor variable x such that response variable y has a Bernoulli distribution (equivalent to a binomial distribution with a sample size of 1) with parameter $P$ (not to be confused with the name of your dataset) equal to

$$P=1-1/(1+e^{c0 +c_1 x})$$

or equivalently

$$\log(P/(1-P))=c_0+c_1 x$$

where $x$ is the relative concentration of odorant $A$ with $x=A/(A+B)$.

If you knew $c_0$ and $c_1$, then you could determine the value of $x$ that satisfies

$$P=1-1/(1+\exp{(c0+c_1 x}))$$

But you only have a sample of binomial results from a variety of relative concentrations. To obtain confidence intervals for the above value of $x$ when $P=0.5$ you would use the commands I gave earlier. (And, sorry, using $c_0$ sometimes displays as $c0$. Don't know why.)

You can probably find more concrete examples of what you want from searching for "LD50 confidence intervals".

Thanks Jim

There is a 95% probability the means will be found in the "confidence interval" while 95% of the data will be found in the "prediction interval". The meaning of this using the code that generated the plot here in is not clear to me. What ever it is I need the values for x shown on the plot and of course I need to understand what they mean. The data comes from high speed puffs of odorant mixtures (70ms) in response to different odorant ratios [A]/[B], the x axis is the log( [A]/[B]). The response is binomial, 0 or 1, replicated 12 times for A and 12 times for be B but randomized. The y axis is the probability of detecting A in the presents of B at the concentration ratio x. If B is a blank, x at y=0.5 is a threshold. Our interest is in x at y=0.5 when B is a different odorant. Any help with this would be great.

Attachments:

Threshold (A).jpg