Copy number and fold change

When configuring the minimum fold change thresholds for calling CNVs, it can be useful to understand the difference between copy number and fold change and the relationship between tumor fold change, sample fold change and sample purity.

The copy number (CN) gives the number of copies of a gene. For a normal diploid sample the copy number, or ploidy, of a gene is 2.

The fold change is a measure of how much the copy number of a case sample differs from that of a normal sample. When the copy number for both the case sample and the normal sample is 2, this corresponds to a fold change of 1 (or -1).

The sample fold change can be calculated from the normal copy number and sample copy number. The formula differs for amplifications and deletions:

Fold change, amplifications (CN(sample) > CN(normal))$\displaystyle = \frac{\text{CN(sample)}}{\text{CN(normal)}}$ (29.17)

Fold change, deletions (CN(sample) < CN(normal))$\displaystyle = -\frac{\text{CN(normal)}}{\text{CN(sample)}}$ (29.18)

Fold change values for amplifications and deletions are asymmetric in that a 50% increase in copy number from 2 to 3 (heterozygote amplification) converts to a fold change of 1.5, whereas a 50% decrease in copy number from 2 to 1 (heterozygous deletion), gives a fold change of -2.0. The difference is even more pronounced if we consider what could be interpreted as a homozygote duplication (copy number 4) and a homozygote deletion (copy number 0). Here, the calculated fold changes land at 2 and $ -\infty$, respectively.

The fact that the same percent-wise change in coverage (copy number) leads to a higher fold change for deletions than for amplifications means that given the same amplification and deletion fold change cutoff there is a higher risk of calling false positive deletions than amplifications - it takes less coverage fluctuation to pass the fold change cutoff for deletions.


Table 29.2: The relationship between copy number and fold change for amplifications and deletions.
  Copy number Fold change
Amplifications
  2 1
  3 1.5
  4 2
  6 3
  8 4
Deletions
  2 -1
  1 -2
  0.5 -4
  0.2 -10
  0.1 -20
  0 $ -\infty$