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Currently, GSA is capable of considering the following five response distributions: Normal, Lognormal, Lognormal with shrinkage, Negative Binomial, Poisson (Figure 1). The GSA interface has an option to restrict this pool of distributions in any way, e.g. by specifying just one response distribution. The user also specifies the factors that may enter the model (Figure 2A) and comparisons for categorical factors (Figure 2B).

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Based on the set of user-specified factors and comparisons, GSA considers all possible designs with the following restrictions:

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The model with the lowest information criterion is considered the best choice. It is possible to quantify the superiority of the best model by computing the so-called Akaike weight (Figure 3).The model's weight is interpreted as the probability that the model would be picked as the best if the study were reproduced. In the example above, we can obtain 15 Akaike weights that sum up to one. For instance, if the best model has Akaike weight of 0.95, then it is very superior to other candidates from the model pool. If, on the other hand, the best weight is 0.52, then the best model is likely to be replaced if the study were reproduced. We can still use this "best shot" model for downstream analysis, keeping in mind that that the accuracy of this "best shot" is fairly low.

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For a large sample size, the amount of shrinkage is small, (Figure 5), and the "Lognormal" and "Lognormal with shrinkage" p-values become virtually identical.

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A rule of thumb suggested by limma authors is to set the low expression threshold to get rid of the drop and to obtain a monotone decreasing trend in the left-hand part of the plot.

For instance, in Figure 5 it looks like a threshold of 2 can get us what we want. Since the x axis is on the log2 scale, the corresponding value for "Lowest average coverage" is 22=4 (Figure 6). After we set the filter that way and rerun GSA, the shrinkage plots takes the required form (Figure 7).

Note that it is possible to achieve a similar effect by increasing a threshold of "Lowest maximal coverage", "Minimum coverage", or any similar filtering option (Figure 6). However, using "Average coverage" is the most straightforward: the shrinkage procedure uses log2(Average coverage) as an independent variable to fit the trend, so the x axis in the shrinkage plot is always log2(Average coverage) regardless of the filtering option chosen in Figure 6.

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That line of reasoning suggests that neither DESeq2 nor limma are perfectly equipped for dealing with abnormal features. In fact, "limma trend" has no way to deal with them at all: shrinkage is applied regardless. If such abnormality is coupled with a low level of expression, it could be a good idea to get rid of the outlying features by raising the low expression threshold. For instance, while the trend in Figure 8A is monotone and decreasing in the left hand part of the plot, there are many low expression features with abnormally low error terms. Unless we have a special interest in those features, it makes sense to raise the low expression threshold so as to get rid of them.

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