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 1 (or equivalently, a change to 2 times), or in common terms, a one-fold increase. Fold change is calculated simply as the ratio of the difference between final value and the initial value over the original value. Thus, if the initial value is A and final value is B, the fold change is (B - A)/A or equivalently B/A - 1. As another example, a change from 80 to 20 would be a fold change of -0.75, while a change from 20 to 80 would be a fold change of 3 (a change of 3 to 4 times the original).

However, confusion and ambiguity can arise from this use. For example, although 1 fold is 100%, or 1x, a 1-fold increase, is, as noted above, understood by some to mean an increase of 200%, or a doubling, as in "60 is 2 times greater than 30." Yet, several dictionaries, including the Oxford English Dictionary[1] and Merriam-Webster Dictionary,[2] as well as Collins's Dictionary of Mathematics, define "-fold" to mean "times," as in "2-fold" = "2 times" = "double." Likely because of this definition, many scientists use not only fold but also fold change to be synonymous with "times," as in "3-fold larger" = "3 times larger."[3][4][5] Yet, among some experts in the field use persists of fold change as in "60 is 1-fold greater than 30." Therefore, one could argue that the use of fold change, as in "A is 2-fold greater than 30" should be avoided altogether, since some will interpret this to mean A is 60 whereas others will understand this to mean that A is 90.

Even more ambiguous is fold decrease, which is more precisely expressed as fractions.

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.[6] A disadvantage to and serious risk of using fold change in this setting is that it is biased [7] 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.

Fold changes in genomics and bioinformatics

In the field of genomics (and more generally in bioinformatics), fold changes are defined directly in terms of ratios.[8][9] If the initial value is A and the final value B, the fold change is defined as B/A. Note that this is different to the definition described above.

In other words, a change from 30 to 60 is defined as a fold-change of 2. This is also referred to as a "2-fold increase". Similarly, a change from 30 to 15 is referred to as a "2-fold decrease".

In genomics, log ratios are often used for analysis and visualization of fold changes. The log2 (log with base 2) is most commonly used.[8][9] For example, on a plot axis showing log2-fold-changes, an 8-fold increase will be displayed at an axis value of 3 (since 2^3 = 8).

See also

Notes

  1. ↑ "Free OED - Oxford English Dictionary".
  2. ↑ "Definition of TWOFOLD".
  3. ↑ Cieńska M, Labus K, Lewańczuk M, Koźlecki T, Liesiene J, Bryjak J. (2016). "Effective L-Tyrosine Hydroxylation by Native and Immobilized Tyrosinase." PLOS One. 11: e0164213. doi:10.1371/journal.pone.0164213. PMID 27711193.
  4. ↑ Cunningham MW Jr, Williams JM, Amaral L, Usry N, Wallukat G, Dechend R, LaMarca B. (2016). "Agonistic Autoantibodies to the Angiotensin II Type 1 Receptor Enhance Angiotensin II–Induced Renal Vascular Sensitivity and Reduce Renal Function During Pregnancy." Hypertension. doi:10.1161/HYPERTENSIONAHA.116.07971. PMID 27698062.
  5. ↑ Li B, Li YY, Wu HM, Zhang FF, Li CJ, Li XX, Lambers H, Li L. (2015) "Root exudates drive interspecific facilitation by enhancing nodulation and N2 fixation." 113(23):6496-501. doi:10.1073/pnas.1523580113. PMID 27217575. PMC 4988560.
  6. ↑ 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. PMC 33173 Freely accessible. PMID 11309499. doi:10.1073/pnas.091062498.
  7. ↑ 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. PMID 12475896. doi:10.1096/fj.02-0351fje.
  8. 1 2 Robinson MD, Smyth GK. (2008). "Small-sample estimation of negative binomial dispersion, with applications to SAGE data." Biostatistics. 9(2): 321-332. doi:10.1093/biostatistics/kxm030. PMID 17728317.
  9. 1 2 Love MI, Huber W, Anders S. (2014). "Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2." Genome Biology. 15: 550. doi:10.1186/s13059-014-0550-8. PMID 25516281.
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