Suppose I have around 20 differentially expressed genes for which RT-qPCR data has been generated, and the samples are a wild-type plant and a knock-out mutant.
Which statistical analysis should be done?
In several papers, people have used one-way ANOVA; in others, they just report the correlation between microarray and RT-qPCR data.
Please suggest the best option.
A correlation would be used to validate the overall result, i.e. to answer the question like "can I trust the array results in principle"? The genes should be selected as a good representation of the whole set of genes on the array. A stratified sample may consider the range of (average) expression intensities and the range of differential expressions. A random selection is often not sensible because the vast majority of the genes will not be differentially expressed and so the random sample will likely lack genes with considerable differential regulation.
If the question is: "I have this set of interesting/selected genes; can I trust the array results for these genes?", then one-sided t-tests are in place (using a pooled estimate for the standard errors and controlling the FWER, like Tukey's HSD test will do).
@David: Your answer is confusing, if not wrong. CT values have a normal distribution, and so have dCT values. Miroarray results are typically provided as log fold changes (LFC), and these LFC values also have a normal distribution. dCT and LFC are both the same thing (i.e. log fold-changes).
The distribution of the fold-changes (2^dCT and 2^LFC) is log-normal, the distribution of the log fold-changes (dCT and LFC) is normal. Since dCT and LFC are known, there is no need to even think about "non-normality". The problems only start when fold-changes are calculated. But the statistics should be done in any case on the log fold-changes.
If you performed the pcr only to validate your array data , i should go for correlation
If you want assess the expression of 20 differential expressed genes then you can go for simple Student's t-test performed between the control and treated groups.
You can perform a simple correlation, yet you are comparing two different techniques. As far as I know, it seems more important for you to get the statistical significance from the qPCR data, as you also have statistical data from microarrays dataset. As you are comparing wild-type plant with a knock-out mutant, i would do a Mann whitney U test (non parametric), since considering that qPCR data generated are under a normal distributions may be somewhat biased.
I generally have done a normal Student's T-test on the normalized delta Ct values on real-time PCR data generated to validate microarray experimental results. You need to have at minimum three biological replicates in the control and treatment groups. Hope you find this information helpful.
Hi
I would suggest that, while analyzing the qPCR data you should first check whether the distributions of the delta CT values (Ct of gene of interest - Ct ref, if you are doing relative quantitation) for the two comparing groups follows a normal distribution (This has to be done for each gene). If it is normally distributed you can use student's t test to confirm that the difference between the two groups are statistically significant. If the distribution is not 'normal' you can use non-parametric test like Mann whitney U test.
Once you establish that the difference that you saw in microarray is reflected in real time data as well, you can do a correlation analysis between microarray and real time data to assert the point.
Hope this was helpful
Ashsa, you are correct Student's T-Test assumes the distribution of the data for the treatment and control groups are normal or approximating a normal distribution. Keep in mind that delta Ct values are logarithmic base 2 and likely have a log-normal distribution. Most microarray data are log2 transformed intensity values and have log-normal distribution. Non-parametric tests such as the Mann Whitney U test unlike the parametric Student's T-test do not make any assumptions as to the distribution of the data but have a drawback of reduced statistical power.
A correlation would be used to validate the overall result, i.e. to answer the question like "can I trust the array results in principle"? The genes should be selected as a good representation of the whole set of genes on the array. A stratified sample may consider the range of (average) expression intensities and the range of differential expressions. A random selection is often not sensible because the vast majority of the genes will not be differentially expressed and so the random sample will likely lack genes with considerable differential regulation.
If the question is: "I have this set of interesting/selected genes; can I trust the array results for these genes?", then one-sided t-tests are in place (using a pooled estimate for the standard errors and controlling the FWER, like Tukey's HSD test will do).
@David: Your answer is confusing, if not wrong. CT values have a normal distribution, and so have dCT values. Miroarray results are typically provided as log fold changes (LFC), and these LFC values also have a normal distribution. dCT and LFC are both the same thing (i.e. log fold-changes).
The distribution of the fold-changes (2^dCT and 2^LFC) is log-normal, the distribution of the log fold-changes (dCT and LFC) is normal. Since dCT and LFC are known, there is no need to even think about "non-normality". The problems only start when fold-changes are calculated. But the statistics should be done in any case on the log fold-changes.
Jochen,
dCT and LFC are not the same thing! The first delta Ct value is calculated by subtracting the Ct value of the gene of interest minus the Ct value of the "housekeep" or reference gene. This is for normalization purposes only. Your statement that microarray results are provided by themselves as log fold change values is true but for a parametric statistical test (ex. t-test, ANOVA and ANCOVA) the individual transcript's microarray log2 intensity values are used and never log fold change (i.e. log2 ratio). The fold change (i.e ratio) is obtain by taking the mean of the intensity values of the experiment group and dividing it by the mean of the intensity values of the control group.
In your last paragraph your state: "The distribution of the fold-changes (2^dCT and 2^LFC) is log-normal, the distribution of the log fold-changes (dCT and LFC) is normal." This is completely backwards do you realize that Ct values are logarithmic values as they are calculated and exported by computer running any real-time PCR machine? Simply subtracting Ct log values to obtain a dCt does not change this. Fluorescent intensity generated by a microarray scanner and recorded by computer are linear intensity values.
David,
"dCT and LFC are not the same thing! The first delta Ct value is calculated by subtracting the Ct value of the gene of interest minus the Ct value of the "housekeep" or reference gene"
Correct. I missed to make it complicated enough ;) - the ddCt is the same measure like the LFC. The dCt refers to the log-ratio of the traget-to-reference gene, and the ddCt is the difference of two such log-ratios, i.e. the log ratio of two normalized concentrations = LFC. [NB: if you would use same amounts of samples with no need to measure this and to normalize agins this, you would calculate the dCt as the difference between Ct[treated] and Ct[control], and then the dCt would directly be the LFC.
"[...] true but for a parametric statistical test (ex. t-test, ANOVA and ANCOVA) the individual transcript's microarray log2 intensity values are used and never log fold change (i.e. log2 ratio). The fold change (i.e ratio) is obtain by taking the mean of the intensity values of the experiment group and dividing it by the mean of the intensity values of the control group."
No, clearly not. This would give biased results. Always the log intensity values are averaged (this corresponds to calculate the geometric mean of the intensity values).
Your last paragraph I do not really understand. I know that Ct values are on the log scale. This is what I said. And therefore their distribution is normal. The distribution of the corresponding (normalized) amplicon concentrations (that is proportional to 2^dCt) is log-normal.
Jochen,
Don't understand nor do you state your reasoning that my approach used often in other publications would yield biased results.
Always the log intensity values are averaged (this corresponds to calculate the geometric mean of the intensity values).
Yes I know what a geometric mean is but this is not what is generally calculated in the analysis of microarray data. It is a log2 of the mean intensity of each sample group and not geometric mean of each sample group from my experience.
The original question like this is a bit too complex to discuss in a internet forum environment in part due to the complexity of experimental design and it effects on correct statistical analysis. I suggest Navjyoti Chakraborty seek knowledgeable and experienced people to discuss this difficult topic in person at sufficient detail.
Can you give me an example of such a publication that averages the intensity values? Any paper I know, any paper I published, any instruction I know clearly sais that the first of all (but possibly after background correction) intensity values are log-ed and that then these log-intensity values are further processed.
Jochen,
Its a bit more complicated than that again due the method of communication I might have over simplified my description. Much of my experience is with Affymetrix platform. Here is a good paper with a really robust analysis algorithm RMA. I mostly use the algorithm as it is implemented in R as a package in Bioconductor.
http://nar.oxfordjournals.org/content/31/4/e15.full.pdf+html
http://nar.oxfordjournals.org/content/31/4/e15.full.pdf+html
David, the paper only subtracts the P and M signals. This is the only occasion where the (un-loged, raw) signal intensities are used. Everything else (and particularily the averaging of signals) is done on the log-scale (once that write that they "suggest a multiplicative model" what is nothing else). This is absolutely in-line with my knowledge that expression data is analyzed on the log-scale.
Jochen,
Then we agree more than we think and all this arguement is likely just a misunderstanding. Sorry if answers seemed confusing.
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