Hi., I am trying to compare two samples based on qPCR data collected at ten genes. Rather than doing significance at each gene, I wanted to check the similarity or difference between samples by combining the whole data. So, I am looking for suggestions. My assumption is two samples are same. I really appreciate any suggestions. Thanks in advance.
There is no statistical analysis that would prove anything.
Demonstrating a similarity is notoriousely difficult. I would estimate the confidence intervals for differential expression of the 10 genes and look if any of their boundaries extends to values that I would consider a "relevant". If all boundaries are within the band of non-relevant differences (called the "equivalence band"), I would consider the two samples being similar w.r.t. the expression of these 10 genes.
Example: Say, the equivalence band is (in log-fold changes) from -0.5 to +0.5. Gene A has a CI from -0.2 to +0.4, gene B from +0.1 to +0.5, and gene C from -1.2 to +0.2 (etc). Genes A and B are within the band, but C is outside. Thus, the data does not provide sufficient evidence to claim that the two samples are similar (within the band as defined above).
How wide the equivalence band should be has to be decided on subject knowledge (that's not a statistical decision).
There is no statistical analysis that would prove anything.
Demonstrating a similarity is notoriousely difficult. I would estimate the confidence intervals for differential expression of the 10 genes and look if any of their boundaries extends to values that I would consider a "relevant". If all boundaries are within the band of non-relevant differences (called the "equivalence band"), I would consider the two samples being similar w.r.t. the expression of these 10 genes.
Example: Say, the equivalence band is (in log-fold changes) from -0.5 to +0.5. Gene A has a CI from -0.2 to +0.4, gene B from +0.1 to +0.5, and gene C from -1.2 to +0.2 (etc). Genes A and B are within the band, but C is outside. Thus, the data does not provide sufficient evidence to claim that the two samples are similar (within the band as defined above).
How wide the equivalence band should be has to be decided on subject knowledge (that's not a statistical decision).
Arun, you should calculate confidence interval (CI) by manually observing the data.Or you can design some algorithm by your self.
I'll assume that sample in this case is treatment. The treatment might be applied, or observed. From each treatment, you have many observations (=samples =replicates). The problem is to decide if treatment A is different from treatment B, or not.
qPCR is sometimes used as presence-absence detection, especially when used for tasks like determining if an individual is infected with a disease or not. Other times qPCR is used to quantify the number of copies of the target present.
I would try discriminant analysis. Given the ten variables (genes), how different is treatment A from treatment B? A unitless multidimensional measure of this is the Mahalanobis distance. You can test if the Mahalanobist distance is significantly different from zero.
I would try univariate models. Is gene 1 diagnostic for treatment A versus B? Is gene 2 diagnostic between treatment A versus B? And so forth. If I have ten independent tests of the difference between A and B, and there is no difference between A and B (null-hypothesis is true), and I declare significance if the p-value is 0.05 or less, then I have a 60% chance of having no significant outcomes, a 31.5% chance of having one type I error, a 7.5% chance for two type I error, and a 1.1% chance of three or more type I errors.
One problem in arguing that treatment A=B is that there is a counter paradigm that would say that A is never equal to B, and your failure is simply an issue of having a small sample size. The response to that issue must begin with showing that your sample size would be considered ample by current standards, and then using something like a power analysis to show that "given this outcome a significant difference would be expected only with sample sizes many orders of magnitude larger than current norms." There may be a significant difference, but the effect is too small to be detectable with current experimental methods."
Jochen's statement bears repeating "There is no statistical analysis that would prove anything."
Thank you Jochen Wilhelm for your suggestion. Now, I will try to find the confidence intervals for each gene and look how the samples deviate from CI.
Hi Arun
Are you looking at regulation of genes in two samples and wanted to compare. In that case 2 power delta delta CT can be helpful. For that you should have a control gene to normalise.
I hope this is relevant
Cheers
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