What I'm trying to do is predict some biodata based on time. Because the biodata are not normally distributed, I have modeled them with a poisson using a log link function ( E[y] = exp[BX]). What I'm trying to do is estimate the time at which the predicted curve reaches a certain threshold. (i.e., y=1 when x=?). Obtaining a point estimate is fairly straightforward, but I would like to place a confidence interval around that time (e.g., x = 5+-1).
My initial idea was to flip the x and the y and generate prediction intervals as one normally would. However, x is normally distributed while y is poisson, so that's not a good solution. Any other ideas?