Dear all,
I was just analyzing some data from a differential (dual label LC/MS) single factor peptidomics experiment using both a per-feature mixed model approach (using lme4's lmer function, using a model of the form intensity/abundance ~ (1|run)+label+treatment, and testing significance and calculating least square means of the differential expression ratios for the different treatments using lmerTest and lsmeans, using a Satterthwaite df approximation) and an empirical Bayes standard deviation shrinkage method as implemented in limma (by putting my data in an RGLimma object). To my surprise, I am finding more statistically significantly differentially expressed features using the mixed model approach than using limma (independent of the types of normalizations I use in limma, and I did check that the sd vs abundance was flat). Before, I have also observed the same phenomenon in some microarray datasets.

I am wondering if this would point towards a mixed model approach having superior statistical power than limma, even for this very simple design. Could this be the case? I only did 8 replicate runs in this case (corresponding to arrays in 2-color microarray exps), so not terribly many... Could it be that limma has superior statistical power for the analysis of relatively small designs with few experimental replicates (where the SD shrinkage could be beneficial), but that for larger number of replicates and also for complex designs (in particular when there are multiple sources of dependencies in the data) a mixed model approach would work better?

Also, would a mixed model approach in general not be much easier to specify (just requiring the model formula to be specified, as opposed to all the contrasts, which becomes pretty tedious for complex designs) and statistically be more flexible and powerful for multifactorial experiments (e.g. easily allowing for treatment interaction effects to be tested, and also allowing for multiple crossed random factors, e.g. to take into account several dependencies in the data, e.g. owing to spatial correlations in the microarray slides/print tip effects, other random factors, e.g. due to the use of samples with multiple genetic backgrounds or the presence of repeated measures factors, etc). For repeated measures designs I would also think that mixed model fits obtained using nlme could be even more flexible, e.g. allowing for various custom error covariance structures (e.g. to take into account temporal autocorrelations, etc); in fact, even lmer supports unstructured covariance models (which would allow variances to be different in your different groups, which I think could be quite common). Model selection, on the other hand, would appear a little more tricky, but also feasible, e.g. by minimizing the AIC of a model that is fit over all features/genes combined (as in http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_hpmixed_sect035.htm#statug.hpmixed.hpmeg4b).

Finally, an important advantage that I would see of using this approach is that it would readily generalize to RNAseq data if one would use generalized mixed models (glmer's) with a Poisson error structure (correcting for the total nr of mapped reads, etc and other important covariates) (or, alternatively, using a binomial error structure, to analyze the proportion of reads mapping to a particular gene). Overdispersion in the data in this approach could readily be taken into account by including an observation-level random factor in the model, cf. https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/015867.html. The advantage here again would be that complex designs, e.g. with multiple crossed random factors, could readily be taken into account (to my understanding, edgeR or DEseq do not allow for this, right?). Would anyone perhaps have any thoughts why not to go for such a generic approach?

Would there perhaps be any market for a package to analyze differential expression in limma RGLimma and ESet data (or CountDataSet or DGEList objects for RNAseq data) using the approach I outline above? If there is enough interest, I would be keen to develop it, as it would seem pretty straightforward to do...

Cheers,
Tom Wenseleers


_______________________________________________________________________________________

Prof. Tom Wenseleers
*      Lab. of Socioecology and Social Evolution
           Dept. of Biology
           Zoological Institute
           K.U.Leuven
           Naamsestraat 59, box 2466
           B-3000 Leuven
           Belgium
* +32 (0)16 32 39 64 / +32 (0)472 40 45 96
* tom.wenseleers@bio.kuleuven.be
http://bio.kuleuven.be/ento/wenseleers/twenseleers.htm



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