I have read many many papers on this and every day I come up with a different answer! My experiments usually consist of multiple transgenic animal lines including WT, treated with either saline or drug. I use stable internal reference genes to calculate dCt (Ct of target gene - Ct of reference gene) for each target gene for each treatment group. Then I calculate ddCt for each target gene by subtracting out the mean dCT of the WT saline group (used as comparator) from the mean dCT of the treatment group. That way everything is normalized to WT saline across all animals. Pretty standard, really. However, I find conflicting reports on how to propagate the error associated with the dCt calculations. Some say to use standard error propagation (square root of the sum of the squares of each error), but I noticed that my t.test values comparing the ddCt of two different drug treated transgenic animals sometimes say a difference is significant when error bars overlap, which I find troubling. Then there are some who say that I do not need to factor in the error of the comparator at all since it becomes arbitrary when applied to all samples - sort of like dividing all numbers by the same factor. This method simply uses the error calculated for the dCT of the treated group. This way does give smaller errors that agree visually with the t.test values, but I am always wary of leaving out the errors associated with calculations.
Should I use error propagation only when comparing a treated animal with saline, but not when comparing two different treated animals that have already been normalized to the same saline group? Is it right to ignore the error in the saline group in this instance?
How do you guys propagate errors when using the ddCt method?
Hi Michael
Mann Whitney and Wilcoxon ranked tests are generally preferred for RT-PCR since the values you use for statistics are actually calculated from complex data - even before you get the Ct the machine makes several assumptions about your data.
You can use the REST package:
Pfaffl MW, Horgan GW, Dempfle L. Relative expression software tool (REST) for
group-wise comparison and statistical analysis of relative expression results in
real-time PCR. Nucleic Acids Res. 2002 May 1;30(9):e36. PubMed PMID: 11972351;
PubMed Central PMCID: PMC113859
which is pretty good at the stats. Be careful to note the conditions needed for Pfaffl calculations - ie your rate of PCR needs to be close for each sample used.
Hope this helps
Paul
Regarding the last answer:
1) There is no reasonable evidence that our knowledge about the deviations of the ct-vcalues is not well represented by the normal probability distribution.
2) no machine makes any assumptions.
Specifically to your problem:
I suppose you actually want to know if the transgene reacts *differently* to the drug than the wildtype. This is called an interaction (of genotype and treatment). You should specifically calculate this interaction (in a linear model like a 2-factorial Anova *with* interaction). Use the delta-Ct values as the response. No need for error-propagation. The model will give the standard error (and confidence interval) for the interaction.
To be honest I think you're overcomplicating things. *Most* people just use the ddCT or a log2(fold change) for statistics and don't factor in all the errors. The given error bars then reflect the test that you have used, which is usually the best way to do things. If your experiment is indeed as Jochen Wilhelm suggested, a 2-way ANOVA is fine.
If you really want to propagate all of your errors you can, but then keep in mind that you allow the data to vary by a whole lot more than the n-2 degrees of freedom that your t-test uses. Your standard error is therefore something else than variance/n, in fact it becomes really hard to determine your degrees of freedom.
I guess you would have to make a hierarchical model, with several random effects (technical replicates as one stratum, and HK-gene variation can be moddeled as a crossed factor). If you're good with R you can try building a model with lme4, or alternatively with PROC MIXED in SAS.
Problem with these models is that it is hard to interpert the p-value you get from them (which is probably what you're interested in). You can approach a p-value with MCMC sampling, but it doesn't have an easy frequentist interpretation.
Read Applied Biosytems Bulletin #2 - it addresses this question. And, yes, dividing by an arbitrary constant eliminates your need to incorporate certain error. This is all still clouded by estimations/assumptions of amplification efficiency, however... so beware.
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