Say I have two conditional media for bacteria growth: a bacteriocidal drug and control. I want to see the effect of my bacteriocide on culture growth, so I set up 6 flasks: three with drug, three without. I take three independent measurements from each flask at each of many timepoints. I model the growth of my bacteria with this equation:
$$ B(t) = \frac{B_{max}}{1+e^{k(t_{50}-t)}} $$
where $B(t)$ is the measured density of bacteria at a given time and $t_{50}$ is the time at which the bacteria are at half their max. I want to test differences in $B_{max}$ and $t_{50}$ for my drug vs. control, so I will use GEE.
How can I specify a custom, non-linear equation for GEE so I can get parameter estimates, confidence intervals, and significance values for my two treatments? Keep in mind that this is an example and I am looking for a way to do this with any model equation. The GEE dialogue only provides some basic ones, and I can't find a way to expand upon these. Alternatively, the nonlinear regression options don't appear to allow multiple levels of repeated measures.
