[BioC] Dose-Response: Regressiion and ANOVA

[Liaw, Andy]

> From: Arne.Muller at aventis.com
> 
> Dear All,
> 
> I'm interested in your experience of analyzing dose-response 
> experiments. I've an unbalanced design with 3 studies and 
> within each study 4 to 5 doses of a drug (the doses do not 
> exactmy the same in each study).
> 
> Usually I run an anova per gene
> 
> anova(lm(Intensity ~ Study + Dose + Study:Dose))
> 
> where Study and Dose are factors, and for the linear model I 
> use a treatment contrast with the control dose (no treatment) 
> as the base.
> 
> Actually I'm realy interested in a dose-response, i.e. 
> consistent down- or up-regulation of a gene by dose. I have 
> turned the Dose factor into a continous variable and taken 
> the log10 of the dose. The model formular stays the same as above.
> 
> For the factorial desgin I get 112 genes a with significant 
> dose effect, and for the regression model (dose is the 
> regressor and study stays a factor) I get 280 genes at the 
> same significance level.
> 
> Can I conclude that the regression model is more sensitive? 
> Is there a way to find out where the differences come from 
> and why there are so many differences?
> 
> There a strong difference using un-transformed or log 
> transformed values for dose, and since the control dose is 
> 0.0mM which value to add for the log transformation. Are any 
> rules of thumb for the value to add?
> 
> I'd be happy to read about your experience of analyzing 
> dose-response experiments and whether you use a factorial or 
> regression desgin.
> 
> 	kind regards,
> 
> 	Arne

Arne,

I think I've mentioned this before.  For questions like these, you're likely
to be much better served by consulting a statistician in your organization.
There's only so much that can be done over a mailing list, and it might not
be sufficient for your full understanding.

There are a few possible reasons why the `regression' models seem more
sensitive than the `factorial' models.  In the `factorial' models, you use
up d-1 degrees of freedom for the main effect of dose (assuming there are d
doses), plus more for the interaction.  In the `regression' model, the dose
only took up 1 df, thus you have more residual df for estimating the MSE.
If the dose effect is close enough to being linear within the range being
considered, the `regression' model will be more sensitive.  That doesn't
mean that the dose effect is linear, but that there's a significant linear
component in the dose effects.

Regarding transformation of dose, that is also related to the linearity of
dose effects.  If the effect is linear in log(dose), using log(dose) will be
more powerful (i.e., more sensitive), obviously.  The treatment of zero dose
has been dealt with quite a bit in the statistics literature, but I'm not
familiar with that.

HTH,
Andy