Log2 Ratio or Log2 Fold Change - terminology confusion and which one should I use?
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6.2 years ago
Genosa ▴ 150

Hi sorry I am totally new to data analysis and I see Log2 FC and Log2 Ratio often being used interchangeably, but they mean the same thing. I see Log2 FC more often used. However, is it more correct to use the term log2 ratio? Because to log2 transform FC data, it is not possible for negative FC values. Please correct me if I am wrong. Thank you for the clarification.

genome • 35k views
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6.2 years ago

FC is a ratio of one value to another. One of the values is used as the reference point. For example, treatment / control where the control value is used as a reference point. IE. fold-change of 2 means treatment is twice the value of control.

This FC ratio is asymmetric around 1, meaning that fold-changes where treatment is larger than control ranges from 1 to a potentially very large number, but fold-changes where the treatment is smaller than control can only range from 0 to 1.

The reason why people log2 transforms FC is to make the ratio easier to interpret. Log2-transforming FC ratio makes it symmetrical around 0. When the treatment is larger than control, the log2-transformed ratio is larger than 0; when the treatment is smaller than control, the log2-transformed ratio is smaller than 0. Both directions are on the same scale (symmetrical), IE fold-change of 2 = log2fc of 1 and fold-change of 0.5 = log2fc of -1.

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I am worried if your choice of word 'symmetric' brings more confusion to the discussion. It can be interpreted as the distribution of FC being symmetric on either side of 0, which is not the case as in differential expression expts, the up/down-regulated genes usually differ in not only numbers, but also in range of FC. Probably something like 'uniform scaling' will be a better choice

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I think Damian's explanation makes sense. The second paragraph reads well and was clear to me. The only thing i'd add is that you don't have to log2() to get a symmetric-around-0 score - any logarithm will do. Actually i have no idea why we use log2 and not log10 or logn.... does anyone know?

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Ah, i see - it seems like it's really only for historical reasons then. The first link gives an example that when the change is 2 fold, then number is '1' which is easy to see when things double.... however that's kind of a cheat because it doesn't really work for any other number. tripling for example gives you the not-so-nice value of 1.584962500721156 :P

To be honest, for my personal use I tend to prefer other calculations anyway. log() is an expensive way to get a ratio that doesn't work with negative values -_-;

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Great explanation Damian, I appreciate it!

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6.2 years ago

You are confused perhaps because traditionally, "Fold Change" is presented as 'log2 Fold Change'. Fold Change has the exact literal meaning, where 'fold' means "how many times".

Fold change (FC) = treatment / control = Number of times the data is chaging w.r.t. control (or reference) = ratio of treatment and control

Note that FC is just a ratio of treatment and control data. It can never be negative and you can always take a log of it.

log2 fold-change = log2(FC) = the above FC in log2 scale = log2 of ratio of treatment and cotrol data = log2 (tretment / control)

The confusion arise because many times the FC and log2(FC) are used interchangeably. Note that FC is a ratio, and thus, it can never be negative. If you are seeing negative numbers in FC, it is 100% sure that it is a log(FC) (most probably log2(FC))

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For what it's worth, there are two different definitions of "fold change". The one commonly used in bioinformatics is the simple ratio you mentioned. The definition used pretty every other field in existence would be "(treatment - control) / control", or the simple ratio minus 1. Thus, a one-fold increase is a doubling of something. This original definition is still what you'll see when talking about economics and what people will find on wikipedia. I'd be interested in finding out who misunderstood a ratio as a "fold change" and popularized that meaning, since it must not have been a recent thing.

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Hmmmm... +1 for bringing this to my notice. Never knew the alternative definition, but the one in Bioinformatics seems more intuitive and logical to me (fold = times, which goes according to the common and dictionary meaning of the term, as noted in wiki also). Let's see if someone can shed more light.

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6.2 years ago
Genosa ▴ 150

I thank you for the explanation. I am now looking at the software which does automated calculation: FC, Log2 ratio and ratio. When I select FC, I see both POSITIVE, and NEGATIVE numbers. Strangely, nothing falls between 0 to 1 and 0 to -1. This looks neither like a ratio, nor a log2 ratio, so what is this actually? Thanks for the clarification

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It would help to specify what software you are using/looking at and how you did the analysis to get to this point.

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This sounds a lot like what I use, where you do essentially A/B, where A is always the larger of the two numbers and you flip the sign depending on whether it's an increase or a decrease from the control. While it's a good metric for humans to look at because it's intuitive, it's not good for computer programs that don't realise -1 and 1 are identical. All negative numbers have to be +1'd and positive numbers -1'd for absolute value differences to be calculated as that gives you how many times more or times less rather than an asymmetric ratio. I use it because the space between -1 to 1 can be used for a different problem - what happens when you go from a negative number to a positive number, or visa-versa.

To double-check, please compute the following fold changes:

  51  100
100   51
-51 -100
-100  -51
-51  100
-100   51
51   51