[BioC] Statistical power of limma vs mixed model approach to analyze microarray and differentialproteomics/peptidomics experiments and Poisson/binomial mixed models for RNAseq data

Gordon K Smyth smyth at wehi.EDU.AU
Sun Jun 30 11:17:53 CEST 2013

On Sun, 30 Jun 2013, Tom Wenseleers wrote:

> Dear Gordon,

> Many thanks for your message! Of course, I agree with you that mixed 
> model theory as such is pretty complicated and still to some extent in 
> development. But what I find easier is the specification part of the 
> model, where all you have to do is specify the formula that captures the 
> dependencies/sources of correlation in the data and the fixed factors 
> plus possible interactions that you want to fit,

You can use the same model formula (for fixed factors) with limma. This is 
true even for a two colour design, provided you use lmscFit() instead of 

> as opposed to the design matrix in limma, which (at least I sometimes 
> find) tricky to specify for more complex multifactorial designs (even 
> with functions designMatrix() and contrast.fit()).

The designMatrix() function hasn't existed for nine years.  (It was 
renamed to modelMatrix.)  Are you using an up-to-date version of limma?

> Also, the new R packages lmerTest and lsmeans would make a mixed model 
> approach much easier than before, as you can now easily get the desired 
> tests and log2 ratio contrasts and lsmeans (plus confidence limits) for 
> the different treatment levels out of the lme4 fit (as you could in SAS 
> before already for a long time, but alas not in R). I am not saying that 
> all this would be trivial, but it could be made quite easy with a 
> dedicated package I believe.
> The method would indeed analyze two-colour designs as single-colour 
> ones, and take into account the pairing of R and G labels on the same 
> array using a random factor. The difference though would be that many 
> sources of dependency/correlation could readily be taken into account, 
> e.g. repeated use of the same sample due to dye swaps and technical 
> replication, replicate spots on the same slide, repeated use of samples 
> with the same genetic background, etc etc... Maanova does indeed allow 
> for this approach to some extent, although I believe lme4 combined with 
> lsmeans and lmerTest would be much faster and would allow for more 
> complex designs (e.g. with hierarchically nested random factors, 
> multiple crossed random factors, random slopes models, etc, the SAS 
> example e.g., 
> http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_hpmixed_sect035.htm, 
> could not be fit using Maanova I believe, whereas I could do it no probs 
> with lme4). And the possible generalization to RNAseq data I think would 
> be very interesting. Maybe I'll start doing some simulations to 
> systematically compare the statistical power of these different 
> approaches for some different experimental designs (many thanks also for 
> the Altman paper, in my case I was surprised to find though that I 
> seemingly got a better statistical power even with a simple 
> single-factor (2 group) 2-colour randomized block design analysed with a 
> mixed model, for which the Altman paper claims that the power of the 
> different approaches should be comparable).

Is your simple design a direct comparison of A vs B on the same arrays, 
without any common reference?  If so, then I don't think that there is any 
extra information in the data that could be extracted by a mixed model. 
So, if the mixed model is giving a lot more DE genes, I would worry that 
it is not holding its size correctly.  It would be a good idea to do some 
simulations to check that the mixed model method is controlling the type I 
error rate at the correct level.

Best wishes

> Oh yes, and was meaning RGList of course :-)
> Well, I'll keep you posted if I make some further progress with this - 
> and let me know if you would be interested in co-developing or helping 
> out in some way with such a package!
> Cheers,
> Tom
> -----Original Message-----
> From: Gordon K Smyth [mailto:smyth at wehi.EDU.AU]
> Sent: 30 June 2013 05:42
> To: Tom Wenseleers
> Cc: Bioconductor mailing list
> Subject: Statistical power of limma vs mixed model approach to analyze microarray and differentialproteomics/peptidomics experiments and Poisson/binomial mixed models for RNAseq data
> Dear Tom,
> I must say that this is first time I have heard anyone suggest that a 
> mixed linear model is easier or simpler than an ordinary linear model. 
> Having used the lme4 package myself, the opposite seems true to me by a 
> very long way.
> Do you know that mixed models have been proposed and implemented several 
> times for microarray data?  For example the maanova package or the 
> lmscFit() separate channel approach of the limma package.  A recent 
> paper by Naomi Altman and myself gives a comparison of some of the 
> approaches:
>   http://www.biomedcentral.com/1471-2105/14/165
> For some designs, a mixed model or separate approach can indeed recover 
> more information than a classic log-ratio analysis.  I don't fully 
> follow the approach that you describe, but it sounds to have some 
> similarities with the limma separate channel approach as well as with 
> maanova.
> limma can be generalized to RNA-seq, see
>   http://www.statsci.org/smyth/pubs/VoomPreprint.pdf
> limma does allow for a treatment of randomized block designs but, apart 
> from this exception, it is certainly true that RNA-seq analysis methods 
> do not allow random effect models.  So there is a gap in the market if 
> you are keen to fill it.
> There isn't any data object class called RGLimma that I know of.  Do you 
> mean RGList?
> Best wishes
> Gordon
>> Date: Sat, 29 Jun 2013 02:49:53 +0000
>> From: Tom Wenseleers <Tom.Wenseleers at bio.kuleuven.be>
>> To: "bioconductor at r-project.org" <bioconductor at r-project.org>
>> Subject: [BioC] Statistical power of limma vs mixed model approach to
>> 	analyze microarray and differential proteomics/peptidomics experiments
>> 	and Poisson/binomial mixed models for RNAseq data
>> 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 mode! ls (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 at bio.kuleuven.be
>> http://bio.kuleuven.be/ento/wenseleers/twenseleers.htm

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