Yes, the described claculation is correct.

The z-score gives you the numer of standard-deviations that a value is away from the mean of all the values in the same group (= same gene).

A z-score of -3 for the gene X in sample A means that this value is 3 standard-deviations lower than the mean of the values for gene X in all the samples (A,B,C...).

When a gene is differentially expressen in two groups (like treated and control or disiesed and healthy), then the z-scores of samples will be (mostly) positive in one group and (mostly) negative in the other group.

The z-score is a signal-to-noise ratio. Large absolute z-scores (=large positive or negative values) is therefore not a direct estimate of the effect (i.e. the strength of the differential expressioin).

The very same (larger absolute) z-score can have different meanings, and this depends on the noise:

- with large noise: a very large effect

- with some noise: a rather large effect

- with only little noise: a rather small effect

- with almost no noise: a tiny effect

The problem for a biological interpretation is that "noise" is not only measurement noise. It is also connected to the "tightness" of the control of gene regulation. Genes that are not tightly controlled (so the expression may vary in a wider range) can be considerably induced or repressed and this would not be recognized by the z-scores. In contrast, genes that are tightly controlled may change the expression only very slighlty, without any biological impact, but they will get large absolute z-scores.

Hi,

Usually the z-score should be calculated on normally distributed data. Raw reads count follow a negative binomial distribution, instead FPKM should follow a normal distribution (since this is a normalization method), but I am not completely sure of this. You should first check the distribution of FPKM in your dataset by plotting a histogram of it. If it follow a normal distribution you should proceed from the step 2 of your pipeline. Otherwise you can log transform the raw read count and then calculate the z-score (see the MM of this paper http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0025260#s4, even though they use a microarray experiment.)

Another suggestion. Different sequencing libraries will have different mean and standard deviation of read counts, so I will calculate the gene z-score for each library and then average it.

Yes, the described claculation is correct.

The z-score gives you the numer of standard-deviations that a value is away from the mean of all the values in the same group (= same gene).

A z-score of -3 for the gene X in sample A means that this value is 3 standard-deviations lower than the mean of the values for gene X in all the samples (A,B,C...).

When a gene is differentially expressen in two groups (like treated and control or disiesed and healthy), then the z-scores of samples will be (mostly) positive in one group and (mostly) negative in the other group.

The z-score is a signal-to-noise ratio. Large absolute z-scores (=large positive or negative values) is therefore not a direct estimate of the effect (i.e. the strength of the differential expressioin).

The very same (larger absolute) z-score can have different meanings, and this depends on the noise:

- with large noise: a very large effect

- with some noise: a rather large effect

- with only little noise: a rather small effect

- with almost no noise: a tiny effect

The problem for a biological interpretation is that "noise" is not only measurement noise. It is also connected to the "tightness" of the control of gene regulation. Genes that are not tightly controlled (so the expression may vary in a wider range) can be considerably induced or repressed and this would not be recognized by the z-scores. In contrast, genes that are tightly controlled may change the expression only very slighlty, without any biological impact, but they will get large absolute z-scores.

Thanks for the information. I think now i better understand z-score.

Now i'll follow the following steps, please correct me if i am wrong.

I have 20 lung tissue samples, for gene i have rpkms values. 

so for gene X, i'll calculate the mean and standard deviation using 20 rpkm values of gene X in these 20 lung tissues.

Now i have the mean and standard deviation value for gene X in lung tissues.

I'll select the gene X from first sample out of 20 samples.

For this gene X, (its rpkm score - mean rpkm score)/ standard deviation.

Using the above approach i'll have the z-score for gene X in first sample. Similarly, i'll calculate the z-score for all the gene X in 20 samples.

First i'll calculate the z-score using rpkm values and then i'll calculate the z-score using the log score of rpkms also. 

Thanks for the information. 

That's correct.

As mentioned above, if the expression data does not follow a normal distribution then you have to log transform it first. You should not simply take the raw RPKM (or FPKM or RSEM) reads and perform a Z-score on the data. At best, that will lead to a misinterpretation of what the Z-score is attempting to convey to your audience.

1. Check if data is already log transformed, if it follows a normal distribution then this is the case (In my experience RNAseq or microarray expression data never does).

2. If it isn't log transformed, perform a log (log2) transform, check for (approximately) normal distribution again.

3. IPerform Z-score calculation.

If your goal is to compare an additional set of data to cosmic data, the first thing that have to be clearly stated is the dimension over which the Z-score transformation has been done in Cosmic. Z-score transformation is something very general which is the simple formula (X_i-mean(X))/std(X). What can change is the data on which the mean and std are calculated.

There is one point that makes me think you are going in the wrong direction by performing the Z-score transformation over the samples: I don't know the cosmic database very well, but let's assume that the data is constantly increasing by submission of new RNA-seq libraries. Now, if the normalization was done in the dimension of the samples, as you suggest to do, when a sample is added, the normalization would have to be performed again, because the average and standard deviation, after adding one sample, would be changed. Therefore, from one database release to the other, the gene expression level of a gene in the same library would change, which, I think is nonsense for a database. Very likely therefore you have to take the normalization for each library, separately. i.e. calculate average and std for all genes in a library, and then transform to Z-scores all the values of the genes in that library. You can check this very easily: calculate mean and standard deviation of one sample from cosmic. If you get 0 and 1, respectively, then you have to take the normalization for each library, separately.

I think Matteo Brilli is right for calculating the z-score. It's accords with the z-score calculation for microarray data in paper "

Analysis of Microarray Data Using Z Score Transformation". By reading the above calculation across samples, I am really confused.