[BioC] technical reps, limma - theory
Naomi Altman
naomi at stat.psu.edu
Tue Jul 19 19:13:50 CEST 2005
Consider the simple one-way design, with biological and technical
reps. Generally we would consider the biological reps to be blocks. (For
simplicity, we can think of this as a one-channel analysis). The usual
ANOVA seems to be at odds with what we get from limma (ignoring the eBayes
step, which clearly cannot be recovered from the classical treatment).
The usual ANOVA (t treatments, b biological reps, n technical reps within
biological reps, giving ntb arrays)
source df MS F
treatment t-1 MS(T) MS(T)/MS(B)
bio rep b-1 MS(B) MS(B)/MSE (although we don't
really care about this)
error=T*B ntb-t-b+1 MSE
However, the Limma manual suggests using duplicateCorrelation and block to
handle block designs, and this gives a different ANOVA. In particular, the
error d.f. for this ANOVA is ntb-t. Using this method, the within block
correlation is used in computing the t-statistics for the treatment, so you
do not get the simple 1-way ANOVA that would come from ignoring block, but
you cannot recover the p-value from the usual ANOVA, either.
If you put in bio rep as a fixed factor, then Limma will use the MSE as the
denominator for the contrast tests, so this also does not recover the ANOVA.
I have not tried this computation with replicate spots (only replicate
arrays) but either:
1) the usual ANOVA is right and duplicateCorrelation is doing something odd
2) duplicate Correlation is right and I don't understand the usual ANOVA
3) both methods are correct for somewhat different models, and I don't
understand the statistical implications of this
I am not discounting 3 - as the statisticians in the crowd know, there are
2 versions, constrained and unconstrained, for the simplest case of
balanced ANOVA with fixed and random effects which lead to different
p-values for some effects and both are defensible for almost any data set.
Anyways, I would like to understand this better. So, I would welcome comments.
Naomi S. Altman 814-865-3791 (voice)
Associate Professor
Bioinformatics Consulting Center
Dept. of Statistics 814-863-7114 (fax)
Penn State University 814-865-1348 (Statistics)
University Park, PA 16802-2111
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