I intend to study the gene expression in a group of humans. Is it a viable idea to pool all the RNA samples of baseline and compare it to post samples like how it is followed in various animal models? Please suggest the reasons for this methodology not being commonly used in Microarrays.
Thanks in advance!
Hallo Frank :) Grüße aus Giessen!
There are research questions where one is interested only in some "average effect" (for instance the mean difference of something between two groups) and where one does not care about inter-individual differences (to my experience, such questions are quite common, at least outside of epidemiology). The inter-individual differences are recognized as "biological variance". The existence of this source of variability only makes it neccesary to measure several (many) individuals in order to get a sufficiently precise estimate of the average effect. The larger the biological variance, the larger sample sizes are required to get a desierd precision of the estimate.
Now, given it is the aim just to estimate an average effect, then it does not matter if the average is calculated from individually measured values or if an average value is measured directly (using a pooled sample). Let the inter-individual variance be given by V (whatever value; you may also see this as the sum of biological and technical variance) and consider a sample size of n to determine the "mean" (of something):
In the first case (individual measurements), the estimate is Sum(xi)/n and the variance of this estimate is V/n.
In the second case (pooled measurements: m pools of size k, so mk=n), the estimate is Sum(xi/k)/m = Sum(xi)/(km) = Sum(xi)/n and the variance is again V/n.
This is both identical, independent of V and n! The practical issue is, that V is not known and has to be estimated, too. It can only be estimated when there are at least two (better more) independent measurements. The first case makes optimal use of the samples and allows the best possible estimation of V. At the other extreme, having a single measurement after pooloing all n samples does not allow to estimate V at all.
Therefore, for purely statistical reasons, the first case is the better, because it allows to estimate V with the best possible precision. But in reality, costs sometimes matter, and this means that you have to literally pay for this precision. Pooling means lower costs menans lower precision to estimate V. The more you pool, the less you pay, and the less you get. The aim is to find a reasonable trade-off between the precision to estimate V and the costs. Noteably, the actual estimate and the precision of the average effect is not affected by pooling (given there are no technical hinderances!). Pooling only makes it "more difficult" to provide a reliable value for the precision of the estimate. Pooling everything in a single measurement gives the same result, but we gain no knowledge about the precision of this result.
If you are interested only in the average profiles, then yes. You can save some money for the arrays at the cost of a less precise estimation of the biological variance. From a pure scientific point-of-view, pooling is always suboptimal, but given economical limits may make pooling a worthwile option. If you can afford 20 arrays, it may be better to analyze 20 pools of 10 individuals (so the total n=200) rather than only 20 individuals each on a separate array. Certainly, this design will not allow you to identify possibly interesting inter-individual differences (but that might anyway not be the research question).
If you pool, then you should not pool more than about 5-10 individuals (to make sure that each individual can significantly contribute to the average profile) and you must take care that the amount of pooled RNA is similar for each individual in a pool.
Another disadvantage of pooling is that if you have a bad sample ("outlier"), you are either unable to see this or you will have rendered a whole pool unusable for analysis.
If you need it only as a control, then you can pool the RNA. For all other issues the inter individual differences are to high.
Hallo Frank :) Grüße aus Giessen!
There are research questions where one is interested only in some "average effect" (for instance the mean difference of something between two groups) and where one does not care about inter-individual differences (to my experience, such questions are quite common, at least outside of epidemiology). The inter-individual differences are recognized as "biological variance". The existence of this source of variability only makes it neccesary to measure several (many) individuals in order to get a sufficiently precise estimate of the average effect. The larger the biological variance, the larger sample sizes are required to get a desierd precision of the estimate.
Now, given it is the aim just to estimate an average effect, then it does not matter if the average is calculated from individually measured values or if an average value is measured directly (using a pooled sample). Let the inter-individual variance be given by V (whatever value; you may also see this as the sum of biological and technical variance) and consider a sample size of n to determine the "mean" (of something):
In the first case (individual measurements), the estimate is Sum(xi)/n and the variance of this estimate is V/n.
In the second case (pooled measurements: m pools of size k, so mk=n), the estimate is Sum(xi/k)/m = Sum(xi)/(km) = Sum(xi)/n and the variance is again V/n.
This is both identical, independent of V and n! The practical issue is, that V is not known and has to be estimated, too. It can only be estimated when there are at least two (better more) independent measurements. The first case makes optimal use of the samples and allows the best possible estimation of V. At the other extreme, having a single measurement after pooloing all n samples does not allow to estimate V at all.
Therefore, for purely statistical reasons, the first case is the better, because it allows to estimate V with the best possible precision. But in reality, costs sometimes matter, and this means that you have to literally pay for this precision. Pooling means lower costs menans lower precision to estimate V. The more you pool, the less you pay, and the less you get. The aim is to find a reasonable trade-off between the precision to estimate V and the costs. Noteably, the actual estimate and the precision of the average effect is not affected by pooling (given there are no technical hinderances!). Pooling only makes it "more difficult" to provide a reliable value for the precision of the estimate. Pooling everything in a single measurement gives the same result, but we gain no knowledge about the precision of this result.
Thanks very much for the detailed explanation. As you had rightly pointed out, my concern was the funds to meet the analysis of all samples. As individual differences will also be an interesting factor, i will not pool the samples.
Thanks again for taking time and helping me understand.
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