What statistic test I can use to prove that a gene is expressed in RNA-seq? For example, after RNA-seq, one gene has a RPM of 100, how can I determine this gene is expressed?
Another way to think about it, say one gene has a RPM of 100, another gene has a RPM of 2000, we can say the second gene is significantly expressed than the first gene. What I want to do is do firstly prove that the first gene and the second gene is expressed and then testify the second one is significantly expressed comparing to the first one.
If you are committed to using RPKM as your normalization technique, and assuming you have a bare minimum of 2 biological replicates for each condition (3+ would be vastly superior, IMO), you can use simple T-tests or an ANOVA to test for statistically significant differential expression between two populations. The actual determination of "significant" differential expression need be no more complicated than that.
The more important issues are - do you actually have biological replicates, as any statistical significance will only be possible with replication. Without biological replication, all you can compare is the observed magnitude of the expression signal, but you cannot make any rigorous assessment of significance of the difference between any pair of samples.
Also, are you satisfied with using RPKM as a normalization technique? There are numerous other approaches to normalizing RNA-seq count data, and they all may have a potentially profound affect on your interpretation of what is or is not significantly differentially expressed. At this stage in the development of RNA-Seq analyses, you really should explore some of the many alternative normalization techniques available, many of which are tightly coupled with specific methods of statistical inference testing.
Personally, I apply my lower limit cutoff based on raw mapped read counts, prior to normalization. In my own work, we've decided to discount all summarized gene counts other than those with raw counts > 10.
Keep in mind that RNA-seq has a much greater variance on estimated expression for features with low counts than on features with high counts. In other words, your estimates of low count features will be much more variable (and thus the mean across replicates for those features will have a much greater standard error) than that for high count features. The lower your threshold for inclusion of features, the more problematic your determination of significance for those low expression features (and the greater the probability of including false positives in any tests).
There's a literature on presence/absence calls. Just to name one paper, Hebenstreit D et al. Molecular Systems Biology, 2011. To compare expression of a feature under two or more conditions, the science of statistics doesn't make an exception for sequencing: multiple biological replicates are needed.
I think the gene can be seen as at active status if RPKM > 0. It was due to the transcript of the gene was detected by RNA-seq.
For second question, you can set a value (for example, 2.0 ) to fillter the diferential expressed genes. If the ratio of rpkm value for the genes between different samples were less or more than 2.0, the genes were down/up-regulated. Of course, two or more biological replicates are necessary.
I do not agree with Chao that RPKM>0 means expression. I suspect, for a long time, that there is "background expression level", which is independent of transcription regulation. I don't know if its measurement noise or biological noise, but I suspect that every place in the genome occasionally can be found as RNA, and that this RNA is not functional.
Saying one gene is significantly expressed compared to the other is poor phrasing. What you can say is that one is highly expressed and the other is lower.
I agree with Eitan that a >0 cutoff for expression is too relaxed. I'm not sure however that you can recover the background level of expression. Let me put it this way: If you were to do a histogram of the RKPM's, you would expect the background level to show up as a hump on the lower side of the spectrum. I don't remember seeing such a hump too often. What you usually get is a pretty decent Poisson. Then, you can use something like the 10'th quantile as a cutoff for "expressed".
Following this, one gene having higher RPKM means there is more of it around. So you should be able to safely say that the gene with RPKM 2000 is more expressed than the RPKM 100.
Paul: I agree that 2000 vs. 100 is probably indicative of higher expression; I am not sure the same is true for 2000 vs. 1800, even if the difference is statistically significant: you have to account for efficiency of detection in RNA-seq. You are starting with many steps that could be GC-content dependent, and even sequence dependent.
ER
If you are committed to using RPKM as your normalization technique, and assuming you have a bare minimum of 2 biological replicates for each condition (3+ would be vastly superior, IMO), you can use simple T-tests or an ANOVA to test for statistically significant differential expression between two populations. The actual determination of "significant" differential expression need be no more complicated than that.
The more important issues are - do you actually have biological replicates, as any statistical significance will only be possible with replication. Without biological replication, all you can compare is the observed magnitude of the expression signal, but you cannot make any rigorous assessment of significance of the difference between any pair of samples.
Also, are you satisfied with using RPKM as a normalization technique? There are numerous other approaches to normalizing RNA-seq count data, and they all may have a potentially profound affect on your interpretation of what is or is not significantly differentially expressed. At this stage in the development of RNA-Seq analyses, you really should explore some of the many alternative normalization techniques available, many of which are tightly coupled with specific methods of statistical inference testing.
Personally, I apply my lower limit cutoff based on raw mapped read counts, prior to normalization. In my own work, we've decided to discount all summarized gene counts other than those with raw counts > 10.
Keep in mind that RNA-seq has a much greater variance on estimated expression for features with low counts than on features with high counts. In other words, your estimates of low count features will be much more variable (and thus the mean across replicates for those features will have a much greater standard error) than that for high count features. The lower your threshold for inclusion of features, the more problematic your determination of significance for those low expression features (and the greater the probability of including false positives in any tests).
Have you considered comparing the RPKM values to some "known negatives" for your tissue of interest? For example, we work with lymphocytes and look for things like CD19 levels in T-cells and CD3 levels in B-cells. This gives you an idea background that may be due to contaminating cells of another type or from ectopic expression, and should allow you to establish a threshold for a "true positive".
I agreed May's comments and thanks for Rubin, but I do not think backgroud was brought by sequencing errors such as measurement noise or biological noise. Any detection of fragments from chromsome indicated that it was transcripted, Although it did not make affects on entirely biological processes.
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