RNA-Seq is the new kid on the block, but there is still something to be learned from the stodgy microarray. One of the lessons is hidden in a tech report by Daniela Witten and Robert Tibshirani from 2007: “A comparison of fold-change and the t-statistic for microarray data analysis“.
The tech report makes three main points. The first is that it is preferable to use a modified t-statistic rather than the ordinary t-statistic. This means that rather than comparing (normalized) means using
where is the standard deviation of the replicates (respectively ) of gene i in two different conditions, it is better to use
where minimizes the coefficient of variation of .
The second point made is that the intuition that reproducibility implies accuracy is not correct (fold change had been proposed for use instead of a t-statistic because the results were more reproducible).
The third point, in my opinion the most important one, I quote directly from the report:
“A researcher should choose the measure of differential expression based on the biological system of interest. If large absolute changes in expression are relevant to the system, then fold-change should be used; on the other hand, if changes in expression relative to the underlying noise are important, then a modified t-statistic is preferable.”
How does this pertain to RNA-Seq? Microarray experiments and RNA-Seq both measure expression but the translation of methods for the analysis of one platform to the other can be non-trivial. One reason is that in RNA-Seq experiments accurately measuring “fold-change” is difficult. Read counts accumulated across a gene cannot be used directly to estimate fold change because the transcripts making up the gene may have different lengths. For this reason, methods such as Cufflinks, RSEM or eXpress (and most recently Sailfish recently reviewed on this blog) use the EM algorithm to “deconvolute” ambiguously mapped reads. The following thought experiment (Figure 1 in our paper describing Cufflinks/Cuffdiff 2) illustrates the issue:
Changes in fragment counts for a gene do not necessarily equal a change in expression. The “exon-union” method counts reads falling on any of a gene’s exons, whereas the “exon-intersection” method counts only reads
on constitutive exons. Both of the exon-union and exon-intersection counting schemes may incorrectly estimate a change in expression in genes with multiple isoforms as shown in the table. It is important to note that the problem of fragment assignment described here in the context of RNA-Seq is crucial for accurate estimation of parameters in many other *Seq assays.
“Count-based” methods for differential expression, such as DESeq, work directly with accumulated gene counts and are based on the premise that even if estimated fold-change is wrong, statistical significance can be assessed based on differences between replicates. In our recent paper describing Cuffdiff 2 (with a new method for differential abundance analysis) we examine DESeq (as a proxy for count-based methods) carefully and show using both simulation and real data that fold-change is not estimated accurately. In fact, even when DESeq and Cufflinks both deem a gene to be differentially expressed, and even when the effect is in the same direction (e.g. up-regulation), DESeq can (and many times does) estimate fold-change incorrectly. This problem is not specific to DESeq. All “count based” methods that employ naive heuristics for computing fold change will produce inaccurate estimates:
Comparison of fold-change estimated by Cufflinks (tail of arrows) vs. “intersection-count” (head of arrows) reproduced from Figure 5 of the supplementary material of the Cuffdiff 2 paper. “Intersection-count” consists of the accumulated read counts in the regions shared among transcripts in a gene. The x-axis shows array fold change vs. the estimated fold-change on the y-axis. For more details on the experiment see the Cuffdiff 2 paper.
In other words,
it is essential to perform fragment assignment in a biological context where absolute expression differences are relevant to the system.
What might that biological context be? This is a subjective question but in my experience users of microarrays or RNA-Seq (including myself) always examine fold-change in addition to p-values obtained from (modified) t-statistics or other model based statistics because the raw fold-change is more directly connected to the data from the experiment.
In many settings though, statistical significance remains the gold standard for discovery. In the recent epic “On the immortality of television sets: ‘function’ in the human genome according to the evolution-free gospel of ENCODE“, Dan Graur criticizes the ENCODE project for reaching an “absurd conclusion” through various means, among them the emphasis of “statistical significance rather than magnitude of effect”. Or, to paraphrase Samuel Johnson,
statistical significance is the last refuge from a poor analysis of data.