# Bias corrections¶

The sequencing coverage depth obtained at different genomic regions is variable, particularly for targeted capture. Much of this variability is due to known biochemical effects related to library prep, target capture and sequencing. Normalizing the read depth in each on– and off-target bin to the expected read depths derived from a reference of normal samples removes much of the biases attributable to GC content, target density. However, these biases also vary between samples, and must still be corrected even when a normal reference is available.

To correct each of these known effects, CNVkit calculates the relationship between observed bin-level read depths and the values of some known biasing factor, such as GC content. This relationship is fitted using a simple rolling median, then subtracted from the original read depths in a sample to yield corrected estimates.

In the case of many similarly sized target regions, there is the potential for the bias value to be identical for many targets, including some spatially near each other. To ensure that the calculated biases are independent of genomic position, the probes are randomly shuffled before being sorted by bias value.

The GC content and repeat-masked fraction of each bin are calculated during generation of the reference from the user-supplied genome. The bias corrections are then performed in the reference and fix commands.

## GC content¶

Genomic regions with extreme GC content, the fraction of sequence composed of guanine or cytosine bases, are less amenable to hybridization, amplification and sequencing, and will generally appear to have lower coverage than regions of average GC content.

To correct this bias in each sample, CNVkit calculates the association between each bin’s GC content (stored in the reference) and observed read depth, fits a trendline through the bin read depths ordered by GC value, and subtracts this trend from the original read depths.

## Sequence repeats¶

Repetitive elements in the genome can be masked out with RepeatMasker – and the genome sequences provided by the UCSC Genome Bioinformatics Site have this masking applied already. The fraction of each genomic bin masked out for repetitiveness indicates both low mappability and the susceptibility to Cot-1 blocking, both of which can reduce the bin’s observed coverage.

CNVkit removes the association between repeat-masked fraction and bin read depths for each sample similarly to the GC correction.

## Targeting density¶

In hybridization capture, two biases occur near the edge of each baited region:

• Within the baited region, read depth is lower at the “shoulders” where sequence fragments are not completely captured.
• Just outside the baited region, in the “flanks”, read depth is elevated to nearly that of the adjacent baited sites due to the same effect. If two targets are very close together, the sequence fragments captured for one target can increase the read depth in the adjacent target.

CNVkit roughly estimates the potential for these two biases based on the size and position of each baited region and its immediate neighbors. The biases are modeled together as a linear decrease in read depth from inside the target region to the same distance outside. These biases occur within a distance of the interval edges equal to the sequence fragment size (also called the insert size for paired-end sequencing reads). Density biases are calculated from the start and end positions of a bin and its neighbors within a fixed window around the target’s genomic coordinates equal to the sequence fragment size.

Shoulder effect: Letting i be the average insert size and t be the target interval size, the negative bias at interval shoulders is calculated as $$i/4t$$ at each side of the interval, or $$i/2t$$ for the whole interval. When the interval is smaller than the sequence fragment size, the portion of the fragment extending beyond the opposite edge of the interval should not be counted in this calculation. Thus, if $$t < i$$, the negative bias value must be increased (absolute value reduced) by $$\frac{(i-t)^2}{2it}$$.

Flank effect: Additionally letting g be the size of the gap between consecutive intervals, the positive bias that occurs when the gap is smaller than the insert size ($$g<i$$) is $$\frac{(i-g)^2}{4it}$$. If the target interval and gap together are smaller than the insert size, the reads flanking the neighboring interval may extend beyond the target, and this flanking portion beyond the target should not be counted. Thus, if $$t+g < i$$, the positive value must be reduced by $$\frac{(i-g-t)^2}{4it}$$. If a target has no close neighbors ($$g>i$$, the common case), the “flank” bias value is 0.

These values are combined into a single value by subtracting the estimated shoulder biases from the flank biases. The result is a negative number between -1 and 0, or 0 for a target with immediately adjacent targets on both sides. Thus, subdividing a large targeted interval into a consecutive series of smaller targets does not change the net “density” calculation value.

The association between targeting density and bin read depths is then fitted and subtracted, as with GC and RepeatMasker.

CNVkit applies the density bias correction to only the on-target bins; the negative “shoulder” bias is not expected to occur in off-target regions because those regions are not specifically captured by baits, and the positive “flank” bias from neighboring targets is avoided by allocating off-target bins around existing targets with a margin of twice the expected insert size.