Why Copy-Number Coding Starts With a Baseline
A copy-number call is not yet a dosage code. First, it is necessary to specify what is being counted, which copy count is expected in the absence of the event, and which states qualify as carriers. Without those choices, a value such as 1 or 3 does not by itself say whether a sample has a loss, a baseline state, or a gain.
This tutorial uses total copy number for a defined genomic region. The count is an integer for a sample with a non-mosaic state. Dosage will mean the signed difference between that total and a specified baseline. This makes losses negative, the baseline zero, and gains positive. Other software or analyses may use “dosage” for a count itself, so the coding definition should always be stated.
Both the region and the baseline matter. The region must refer to the same genomic span for the samples being compared, and the baseline must reflect the expected ploidy for that region and sample. For a typical autosomal region in a diploid individual, \(B_i=2\). Sex chromosomes, other ploidies, and sample-specific chromosome complements can require a different baseline. The copy count cannot be negative, so an integer state must satisfy \(C_i\geq 0\), and consequently \(D_i\geq -B_i\).
The coding describes total copies, not which parental chromosome carries them or how copies are arranged. For example, total copy number 2 does not establish that the two copies have the same allelic composition as a reference diploid state. Copy-number coding alone does not resolve that information.
From Integer States to Relative Dosage
Under the diploid autosomal baseline \(B_i=2\), possible total copy counts map directly to signed dosage. A count of 0 is a loss of two copies relative to baseline; a count of 1 is a loss of one; 2 is the baseline; and 3 or 4 are gains of one or two copies, respectively.
| Total copy count \(C_i\) | Baseline \(B_i=2\) | Dosage \(D_i=C_i-B_i\) | Interpretation |
|---|---|---|---|
| 0 | 2 | -2 | Loss of two copies |
| 1 | 2 | -1 | Loss of one copy |
| 2 | 2 | 0 | Baseline state |
| 3 | 2 | 1 | Gain of one copy |
| 4 | 2 | 2 | Gain of two copies |
The conversion is a subtraction, not a recoding based on the most common observed state in a particular sample. If a cohort happens to contain many samples with copy count 3, that does not make 3 the baseline. The baseline is defined by the region and the expected copy state in the absence of the event.
Worked Example: Coding Diploid Autosomal States
Suppose a hypothetical study records total copy counts for the same autosomal region in eight non-mosaic diploid samples. The counts are \(2, 2, 1, 0, 3, 2, 4, 1\). Assume that two copies are the appropriate baseline for every sample. Calculate dosage and identify the samples with any copy-number change relative to baseline.
For each sample, apply \(D_i=C_i-B_i=C_i-2\). The resulting dosages are \(0, 0, -1, -2, 1, 0, 2, -1\), respectively. For example, the third sample has \(D_3=1-2=-1\), a one-copy loss, while the seventh has \(D_7=4-2=2\), a two-copy gain.
Define an any-change carrier indicator as \(I_i^{\mathrm{any}}=1\) when \(C_i\ne B_i\), and 0 otherwise. The samples with counts 1, 0, 3, 4, and 1 differ from the baseline; the other three have count 2. Thus five of eight samples have an altered copy-number state under this definition. This indicator identifies non-baseline states; it does not distinguish losses from gains.
Carrier Indicators Depend on the Event Definition
A carrier indicator converts a copy-number state into a binary value for a specified event or class of states. It is not a single universal code. The rule must say which states count as carrying the event. For a baseline \(B_i\), useful class-specific indicators are:
Here \(\mathbf{1}(\cdot)\) equals 1 when the condition in parentheses is true and 0 otherwise. The any-change indicator is 1 for either a gain or a loss; it equals 0 only at baseline. For a particular event, define a set \(A_i\) of copy states that count as carriers, then use \(I_i^{A}=\mathbf{1}(C_i\in A_i)\). For example, an event defined as having at least one extra copy relative to baseline has \(A_i=\{C_i:C_i>B_i\}\). A study that defines a particular event using a narrower set of states must use that narrower set rather than silently substituting the any-change rule.
These indicators discard information. A gain indicator treats one extra copy and several extra copies alike, while signed dosage preserves the magnitude and direction of the change. An any-change indicator combines gains and losses. Those codes answer different descriptive questions; choosing among them is a matter of defining the target state, not of arithmetic convenience.
Worked Example: Distinguishing Any-Change and Gain Carriers
In a hypothetical diploid autosomal region, six samples have total copy counts \(2, 3, 4, 1, 2, 0\), with baseline \(B_i=2\) for all six. Define one indicator for any copy-number change and another for a gain of at least one copy. Find each sample’s dosage and both indicators.
The dosage calculation is \(D_i=C_i-2\), giving \(0, 1, 2, -1, 0, -2\). The any-change indicator is 0 at count 2 and 1 at every other count, so its values are \(0, 1, 1, 1, 0, 1\). The gain indicator is 1 only when \(C_i>2\), so its values are \(0, 1, 1, 0, 0, 0\).
There are four any-change carriers and two gain carriers. The samples with counts 1 and 0 are included in the first group because they have losses, but not in the gain group. A statement that “four samples carry the variant” would therefore be incomplete unless the indicator definition made clear that gains and losses were both included.
Why Baseline Ploidy Changes the Interpretation
A gain or loss is defined relative to expected copy number, not by an absolute cutoff applied to \(C_i\). A count of 2 is the usual baseline for a diploid autosomal region, but it can be a gain for a region with a haploid baseline. Conversely, a count of 1 can be the baseline state in one sample and a loss in another. For regions whose baseline differs across samples, use each sample’s appropriate \(B_i\) before comparing dosage or carrier indicators.
For example, in a typical non-pseudoautosomal X-chromosome region, a female with two X chromosomes is commonly assigned baseline 2 and a male with one X chromosome baseline 1. That convention assumes the relevant chromosome complement is known and appropriate for the sample; it should not be applied blindly when it is not. On that convention, count 2 is baseline for the female and a one-copy gain relative to baseline for the male. The total count alone cannot determine the interpretation.
Worked Example: The Same Count Under Two Baselines
Consider four hypothetical samples measured at the same non-pseudoautosomal X-chromosome region. Under the stated chromosome-complement convention, assign baseline 2 to the two XX samples and baseline 1 to the two XY samples. Their total copy counts are: XX sample A, 2; XX sample B, 1; XY sample C, 2; XY sample D, 1. Calculate relative dosage and classify each state.
For sample A, \(D_A=2-2=0\), so the state is baseline. For sample B, \(D_B=1-2=-1\), so it is a one-copy loss relative to the assigned baseline. For sample C, \(D_C=2-1=1\), so it is a one-copy gain relative to baseline. For sample D, \(D_D=1-1=0\), so the state is baseline.
Using \(I_i^{\mathrm{any}}=\mathbf{1}(C_i\ne B_i)\), samples B and C have indicator 1, while A and D have indicator 0. In particular, count 2 is not automatically “normal,” and count 1 is not automatically a deletion. The comparison with \(B_i\) determines the coding.
A Short Justification for the Coding Rules
The subtraction \(D_i=C_i-B_i\) translates a count into its signed distance from baseline. The sign therefore gives the direction of the difference: if \(C_i<B_i\), subtracting \(B_i\) yields a negative value; if \(C_i=B_i\), the result is zero; and if \(C_i>B_i\), the result is positive. Conversely, once the baseline is fixed, \(C_i=D_i+B_i\), so the dosage and baseline together recover the total count.
This equivalence justifies defining loss, baseline, and gain indicators using either the copy count or the signed dosage. It also shows why dosage without its baseline is not enough to reconstruct the absolute copy count: the same \(D_i\) can correspond to different \(C_i\) values when \(B_i\) differs.
Practical Checks Before Comparing Samples
Before coding a set of copy-number states, specify the region, the counting convention, the expected baseline for each relevant sample, and the carrier rule. For the integer-state coding described here, assume the calls represent non-mosaic states. An estimated average copy number in a mosaic sample may be non-integer; rounding it to an integer can change the assigned state and is not justified by these definitions alone.
Keep the total copy count, signed dosage, and carrier indicator distinct in data tables and descriptions. A column called “dosage” should be accompanied by its definition, such as \(C_i-B_i\), so that readers can tell whether the value is a signed change or an absolute count. If a carrier indicator is used, name the included states—for example, “gain carrier if \(C_i>B_i\)”—rather than relying on an ambiguous label such as “carrier.”
- Check that all samples refer to the same genomic interval or a harmonized region.
- Set the baseline using the expected ploidy for that region and sample, not the cohort’s most frequent observed count.
- Verify that every reported count is a nonnegative integer under the assumed non-mosaic state representation.
- State whether carriers include gains, losses, both, or only a specified subset of copy states.
Common Mistake
A frequent error is to classify every sample with \(C_i=1\) as a deletion carrier and every sample with \(C_i=2\) as baseline. That reasoning silently assumes a diploid baseline for every sample and region. The correction is to calculate \(D_i=C_i-B_i\) using an explicitly assigned baseline: count 1 is a loss when \(B_i=2\), but it is baseline when \(B_i=1\); count 2 is baseline when \(B_i=2\), but a gain when \(B_i=1\). A second related error is to call every non-baseline state a carrier of a particular deletion, even when the state is a gain. An any-change indicator and an event-specific carrier indicator must not be treated as interchangeable.
Check Your Understanding
Use the stated baseline in each question and distinguish total copy count, dosage, and carrier status.
- For an autosomal region with baseline 2, what are the dosages corresponding to total copy counts 0, 1, 2, and 4?
- For a sample with baseline 1 and total copy count 2, is the relative dosage positive, negative, or zero? What does it indicate?
- In a diploid region, explain why an indicator for any copy-number change can differ from an indicator for gain carriers.
- Two samples have the same total count of 2, but their baselines are 2 and 1. Calculate both dosages and interpret the difference.
- What information is lost when signed dosage is converted to an any-change carrier indicator?