In a Science paper from 2009 (http://www.ncbi.nlm.nih.gov/pubmed/19729616), an approach was presented for estimating the significance of differential gene expression in response to shRNA-knockdowns of different regulator genes that surprisingly does not require replicates for individual knockdowns. The method first computes a Z-statistic Z(i,j) for each expression level observation O(i,j) of each transcript i in each knockdown experiment j, by subtracting the mean and dividing by the variance of the transcript's expression levels in off-target control shRNA experiments. Then, the authors generate permutated Z-scores, by swapping the observed expression levels in the targeted shRNA experiments with each of the expression levels in the controls before re-computing the Z-scores. Finally, to obtain false-discovery rate (FDR) estimates for each Z(i,j), they compute the average number of permuted Z-scores greater than the real Z-score Z(i,j) (by determining the counts for each knockdown experiment and averaging across permutations, if I understand correctly) and divide this average by the number of real Z-scores Z(i,) greater than the real Z-score Z(i,j) for the current knockdown of interest (across all knockdowns). The precise procedure is described in the Supporting Online Material of the paper.
Although I can imagine that the lack of replicates for individual knockdowns can be compensated by integrating information across multiple knockdowns, there are a two things I don't understand:
1) The way the authors compute the Z-statistics, negative values can be obtained for some observations; hence, when comparing the permutated Z-scores against the real Z-scores, a "greater-than"-comparison would only treat negative and positive Z-scores in a consistent manner, if absolute values are used, which is not the case in the manuscript.
2) I would expect false-discovery rate estimates to be in a range between 0 and 1; however, in the above approach, if there is no real Z-score among other knockdown samples greater than the real Z-score for the current knockdown of interest, and the average number of permutated Z-scores greater than the current real Z-score of interest is greater than one, this would result in FDR values > 1.
I would greatly appreciate comments on whether I have misinterpreted the approach, or which alternative statistical procedure you would recommend to analyze similar perturbation data.
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It sounds like they are just using the variance between control and samples for determining differential expression, which can be a good approach if assuming most genes are not differentially expressed between control and experimental conditions (usually a safe assumption).
An important point to note is that in contrast to other methods this approach does not just provide a single differential expression statistic per gene, but one FDR-estimate for every gene/knockout-combination (and without replicates for the knockouts). Thus, there is no way to compute a within-class variance for samples and compare it to the within-class variance of the controls, because each knockout is just one sample.