How to interpret fold-changes when the sample purity is not 100%

If your sample purity is less than 100%, it is necessary to take that into account when interpreting the fold-change values. Given a sample purity of $ X$%, and an observed fold-change of $ F$, following formula gives the actual fold-change that would be seen if the sample were 100% pure:

fold-change in 100% pure sample$\displaystyle = \frac{F - 1}{X / 100\text{\%}} + 1$ (28.21)

For example, if the sample purity is 40%, and you have observed a fold-change of 3, then the fold-change in the 100% pure sample would have been:

fold-change in 100% pure sample$\displaystyle = \frac{3.0 - 1}{40\text{\%} / 100\text{\%}} + 1 = 6.0.$ (28.22)

Figures 28.27 shows the 'true' fold changes for different observed fold-changes at different sample purities. Figure 28.28 zooms in for low-level amplifications and deletions.

Image observed_to_true_conversion_1
Figure 28.27: The true fold-change in the 100% pure sample, for different observed fold-changes, as a function of sample purity.

Image observed_to_true_conversion_2
Figure 28.28: Low-level amplifications and deletions: the true fold-change in the 100% pure sample, for different observed fold-changes, as a function of sample purity.