The role of experimental design in the removal of technical variance
Optimizing your design based on the experimental goal is
an important part of a successful microarray experiment.
In fact, the importance of pre-planning cannot be stressed enough.
One question you may want to ask before designing your experiment is how
much power you wish to have to detect differentially expressed genes with a
ratio greater or equal to x, and how high of a false positive rate (FDR)
you are willing to allow. This will
determine the number of replicates you use.
For example,
(Wolfinger et al.)
found that in order to have 85% power to detect a 2-fold change with a 1:20,000
false positive rate, seven replicates were needed.
This number could change drastically depending on the type of array
technology (single or dual channel), quality (reproducibility) of the arrays,
the number of genes on each array, and the chosen false positive rate. Another question you want to ask is what are the most
important samples, or comparisons you want to make, and how many experimental
factors will be involved? For
single-channel array experiments, it is obvious that more replicates should be
done for samples of greater importance. For
dual-channel array experiments, the many possible choices for designs make for a
more complex problem. Depending on your answer to the above questions, you will
choose from one of two main types of experimental designs- the universal
reference design or the flipped dye design.
The flipped dye design is more efficient for simple designs involving few
factors, or for designs where one important factor of interest will be compared
to many other factors, such as in a time series.
Circular designs are complex versions of the flipped dye design and will
be discussed only briefly at the end of this section.
The universal reference design may be more appropriate for designs
involving many factors of equal importance, such as comparing the expression
profiles of a large number of tissue types, or for experiments that will likely
be part of a larger meta-analysis in the future.
In this section we will concentrate on the issues of experimental design
as they relate to normalization and the removal of biases.
The rationale for the flipped dye design is that it
allows for the estimation and removal of gene specific dye effects.
These dye effects have been shown to be reproducible across independent
arrays by the use of Control vs. Control arrays.
Any deviation from a ratio of 1 in these arrays is due to either dye
effect or residual error. Figure x
shows ratio estimates for two genes on six arrays (3 sets of 2 replicates) using
three different measurements: the raw data, the estimated ratio after dye effect
has been removed by the use of control-vs-control arrays, and the ratio after
dye effect has been removed by the flipped dye method (described below).
As can be seen, the extra control array estimates of dye effect are very
close to the effect estimated by the arrays themselves.
The simplest flipped dye design consists of merely two arrays: one array
with sample A labeled with cy3 and sample B with cy5, and the other array with
sample B labeled with cy3 and sample A with cy5.
This allows gene-specific dye effects to be averaged out.
The best estimate of the log transformed treatment effect for any gene x
in this experiment would simply be the average of the ratios,
[log(A1/B1)
+ log(A2/B2)] / 2 = [log(cy3/cy5) - log(cy3/cy5)] / 2,
and so the dye effects are averaged out. With
more replicates, it is possible to obtain both an estimate of the dye effect,
and a measurement of variance, or confidence, in your result.
For any balanced design, where each sample is labeled with cy3 and cy5 an
equal number of times, the ratio estimates may be calculated as averages, and
the dye effects will be removed. For
arrays done in triplicate, a simple average would weight one dye more than the
other skewing the results; instead, the effects of dye could be removed using an
ANOVA model with dye included as a factor, or as an alternative, table 1
illustrates how dye effects could be normalized by hand.
It is the same process as above with the added step of taking the average
of the replicate ratios prior to averaging over the dye flipped estimates. Dye
normalization greatly improves the reproducibility of replicates per gene.
Including flipped dye arrays in an experiment is one
requirement for having a statistically optimal design, which balances all the
factors in the experiment- arrays, dyes, and treatments.
(Here, treatments denote any other factor of interest, whether it is a
toxin, mouse strain, tissue type, or age group.)
Balanced designs do not confound any two experimental factors, meaning
that the effect of each factor can be estimated and normalized out of the data.
When factors are confounded with each other, their effects are
indistinguishable. For example, an
experiment done in triplicate without any flipped dye arrays will have treatment
completely confounded with dye effects, because each sample is only labeled with
one dye each, and there is no way to separate their effects.
Having confounding factors in your experiment is something to avoid,
unless neither of the confounded factors are of interest.
This leads us to the universal reference design, where dye is indeed
confounded with treatment, but in this case all the treatments of interest are
labeled with the same dye, so the dye effects with the reference can be divided
out.
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