8 posts were merged into an existing topic: Hierarchical Gompertz model
Thanks @martinmodrak and @jroon for the interesting comments and feedback. Martin, I had a look at the preprint, interesting paper; it seems we’re working in very similar areas.
I think (hope) that some of the fitting difficulties you’ve encountered may be avoided in our case, where most of the data are expected to cover the full range of the sigmoid response. To give a bit more context, we are measuring cell survival following treatment with ~4000 drugs at around 10 different concentrations in a high-content phenotypic screen. Concentrations were chosen such that the sigmoid response should be covered for a large fraction of drugs. Of course, there will be drugs with very high levels of toxicity or very low efficacies which would result in all measured responses being located in the tail ends of the sigmoid response. In fact, this was one of the motivations for using a hierarchical model with partial pooling: to learn the distribution of critical model parameters from all measurements to improve estimation on the level of individual drugs.
Thanks to your explorations, I started adopting a similar re-parametrisation of the four-parameter log-logistic model of the form
\text{LL4}'(x; b, c, \theta, \kappa) = c + \frac{(\theta-c) \exp{\left(-\kappa\right)}}{1 + \exp{\left(b \log{x} - \kappa\right)}}
I can see the advantage of this parametrisation in the asymptotic regimes
\begin{aligned}
\lim_{x\to\infty}\textrm{LL4}'(x) &= c\\
\lim_{x\to0}\textrm{LL4}'(x) &= c + (\theta - c) \exp{\left(-\kappa\right)}\,.
\end{aligned}
For example in the presence of (lots of) data at very low concentrations x\to 0, the model should inform on c, \theta and \kappa , whereas the initial parametrisation (see my initial post) would only help with estimating d.
Unfortunately I have been unsuccessful fitting the re-parametrised model to data. I don’t understand (yet) why this happens but will update once I’ve done some more testing.
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Hi @jroon and @martinmodrak. It might be better to move these last discussions involving @jroon’s Gompertz model to a different post (or perhaps to the original post). The reason being that my original question deals with quite a different generative model (a four-parameter log-logistic model); I think keeping these two discussions separate will make it easier for future readers to identify relevant posts.
Perhaps an admin/mod can move these posts (@martinmodrak)?
Cheers,
Maurits
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Good point, I moved them to the Gompertz topic! Thanks for reminding me.
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