Fold change
Fold change is a measure describing how much a quantity changes going from an initial to a final value. For example, an initial value of 30 and a final value of 60 corresponds to a fold change of 2, or in common terms, a two-fold increase. Fold change is calculated simply as the ratio of the final value to the initial value, i.e. if the initial value is A and final value is B, the fold change is B/A. As another example, a change from 80 to 20 would be a fold change of 0.25, while a change from 20 to 80 would be a fold change of 4. Some practitioners replace a fold-change value that is less than 1 by the negative of its inverse, e.g. a change from 80 to 20 would be a fold change of −4 (or in common terms, a four-fold decrease).
A benefit of expressing a change as the ratio between an initial value and a final value – a fold change – is that the change itself is emphasized rather than the absolute values. For example, an absolute change of 100 is significant for an experiment with only 200 samples but neglibable for an experiment with over a million samples. This property makes the fold change suitable for statistical tests that need to normalize data to eliminate systematic error. The distributional fold change test is based upon this idea.
Fold change is often used in analysis of gene expression data in microarray and RNA-Seq experiments, for measuring change in the expression level of a gene.[1] A common way to express the fold change in a more manageable scaling is by applying logarithm.
A disadvantage to and serious risk of using fold change in this setting is that it is biased [2] and may miss differentially expressed genes with large differences (B-A) but small ratios (A/B), leading to a high miss rate at high intensities. The use of fold-change requires the assumption that the generative process was multiplicative, and thus a boundary bias exists for any study in which additive or mixed (multiplicative + additive) processes are suspected of generating the differences under study. Since the processes are often unknown, the multiplicative-only assumption required by the use of fold change is risky.
Notes
- ↑ Tusher, Virginia Goss; Tibshirani, Robert; Chu, Gilbert (2001). "Significance analysis of microarrays applied to the ionizing radiation response". Proceedings of the National Academy of Sciences of the United States of America 98 (18): 5116–5121. doi:10.1073/pnas.091062498. PMC 33173. PMID 11309499.
- ↑ Mariani, TJ; Budhraja V; Mecham BH; Gu CC; Watson MA; Sadovsky Y. (2003). "A variable fold change threshold determines significance for expression microarrays". FASEB J 17 (2): 321–323. doi:10.1096/fj.02-0351fje. PMID 12475896.