[R] Poisson mixed effects model

[Richard Reiss]

Hello,

I am fitting a Poisson mixed effects model.  I have the number of eggs
(Eggs) laid by a quail and looking at the effect of dosage of a chemical
(Dose) in the study.  I have counts of eggs laid by week of the study,
so I am including the week number (Week) as a random effect.  I'm using
the lme4 package.

I have,

> mod1 <- lmer(Eggs~Dose + (1|Week),family=poisson)
> summary(mod1)
Generalized linear mixed model fit using PQL 
Formula: Eggs ~ Dose + (1 | Week) 
 Family: poisson(log link)
   AIC   BIC logLik deviance
 112.2 117.8 -53.11    106.2
Random effects:
 Groups Name        Variance Std.Dev.
 Week   (Intercept) 0.011693 0.10813 
number of obs: 48, groups: Week, 12

Estimated scale (compare to 1)  1.339789 

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  4.699e+00  3.656e-02  128.53   <2e-16 ***
Dose        -4.768e-04  4.177e-05  -11.41   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Correlation of Fixed Effects:
     (Intr)
Dose -0.324


My problem is that I need to find the lower limit on the dose that
causes a 10% effect.  I can get the dose that causes a 10% effect, but
getting the lower-limit is not straightforward.  Thus, I have
reparameterized the model in terms of this dosage and want to re-fit.
The reparameterized model is:

Log(E(Eggs)) = A - (B/A*0.1)*Dose

where E(Eggs) is the expected value from the Poisson distribution, A is
the intercept and B is the dose causing a 10% reduction.  Is it possible
to directly fit A and B in this case within lmer (and other R models)?
I don't see how to code this? Can someone point me to documentation that
shows how to do this?

Thanks.

Rick