Why Allele Labels Matter
A GWAS result may report a positive coefficient for one allele and a negative coefficient for the other, even though both results describe the same genotype–trait association. The difference can be entirely due to which allele was counted. To interpret a result correctly, identify the allele labels and the dosage represented by the coefficient before assigning meaning to its sign.
Three terms are central. Reference and alternate describe alleles relative to a specified reference genome. Effect allele identifies the allele whose dosage is counted for the reported association estimate. The effect allele is a coding choice: the name does not imply that the allele is causal, harmful, protective, or biologically active.
These labels answer different questions. REF and ALT describe a variant record; EA describes how an association result is coded. A file can use ALT as its effect allele, but it need not. REF and ALT also depend on the reference genome and variant representation. Therefore, allele labels should be read together with the genome build and the association output's stated dosage convention.
For a diploid individual at a biallelic site, dosage of a specified allele is the number of its copies, from 0 to 2. If dosage counts ALT, a dosage of 2 means two ALT copies. If dosage counts REF instead, the same individual's dosage is complementary: the two dosages sum to 2. This complement relationship is the key to translating coefficient signs.
Worked Example: Reading an Association Output
Suppose a hypothetical variant record has REF = C and ALT = T. The association output labels T as EA and reports a coefficient of \(0.18\) trait units per allele, with standard error \(0.06\) trait units per allele. The estimated frequency of T is \(0.30\). What does the result say?
Because T is the effect allele, the coefficient uses dosage \(D_T\), the number of T copies. Its possible diploid values are 0, 1, and 2. A one-copy increase in T dosage is associated with an estimated increase of \(0.18\) trait units under the reported model. This is an association statement, not a claim that T causes the trait to increase.
The reported frequency \(0.30\) refers to T only if the output's frequency field is defined as effect-allele frequency. Under that convention, the corresponding C allele frequency is \(1-0.30=0.70\). The value \(0.30\) does not make T the reference allele, nor does it determine which allele is the effect allele; those labels come from the variant record and output coding.
Changing the Counted Allele
The sign change can be shown without changing the underlying observations. Consider the same association model written first using dosage \(D\) of an effect allele:
Here \(Y\) is the measured trait, \(\alpha\) is an intercept, \(\beta\) is the coefficient for the counted allele, and \(\varepsilon\) represents the remaining variation. This equation is used here only to track the consequences of changing the dosage coding. Suppose the genotype is diploid and biallelic, the same individuals and trait values are used in both codings, and the fitted model includes an intercept. If \(D\) counts one allele, dosage \(D^*\) of the other allele is \(2-D\). Substituting \(D=2-D^*\) gives:
Thus, after recoding, the intercept becomes \(\alpha+2\beta\) and the coefficient becomes \(-\beta\). The same fitted values and residuals are obtained: the change is a relabelling of the dosage scale, not a change in the data or the association.
The standard error is unchanged because the recoding changes the coefficient's sign but not the amount of uncertainty in that coefficient. A two-sided test compares the magnitude of the estimate with its standard error, so changing the sign leaves the test statistic's magnitude unchanged. A confidence interval also changes sign and order: an interval \([L,U]\) for \(\beta\) becomes \([-U,-L]\) for the recoded coefficient.
Worked Example: Reversing a Coefficient by Recoding Dosage
In a hypothetical study, dosage \(D\) counts allele A in six individuals. Their dosages are \(0,0,1,1,2,2\), and their trait measurements are \(4,6,6,8,8,10\) units. Calculate the slope using A dosage, then recode to dosage of the other allele.
The mean dosage is \(\bar{D}=1\), and the mean trait value is \(\bar{Y}=7\). The slope is the sum of cross-products divided by the sum of squared dosage deviations:
For example, the two individuals with \(D=0\) contribute \((-1)(-3)+(-1)(-1)=4\) to the numerator; those with \(D=1\) contribute 0; and those with \(D=2\) contribute \((1)(1)+(1)(3)=4\). The numerator is therefore 8. The denominator is \((-1)^2+(-1)^2+0^2+0^2+1^2+1^2=4\).
Now let \(D^*=2-D\) count the other allele. The transformed dosages are \(2,2,1,1,0,0\), so \(\bar{D^*}=1\). The cross-product numerator changes from 8 to \(-8\), while the squared-deviation denominator remains 4. Therefore,
The recoded intercept is also different. With A dosage, the fitted line has intercept \(7-2(1)=5\). With the other-allele dosage, it has intercept \(7-(-2)(1)=9\). Both fitted lines give the same fitted trait values for every individual; only the dosage scale and coefficient representation have changed.
What Changes and What Does Not
| Quantity | When dosage is switched to the other allele | Reason |
|---|---|---|
| Effect-allele label | Changes to the other allele | The counted allele has changed |
| Dosage for each individual | Becomes \(2-D\) | Each diploid genotype has two allele copies in total |
| Coefficient | Changes from \(\beta\) to \(-\beta\) | The dosage scale is reversed |
| Standard error | Remains the same | The coefficient's uncertainty is unchanged by this sign reversal |
| Two-sided association p-value | Remains the same | The magnitude of the test statistic is unchanged |
| Allele frequency | Changes to its complement | The two allele frequencies sum to 1 |
For instance, if an output reports \(\hat{\beta}=0.24\) and \(SE=0.08\) for allele G, recoding to the other allele gives \(\hat{\beta}^*=-0.24\) and \(SE^*=0.08\). The absolute ratio is \(0.24/0.08=3\) under either coding. The two-sided p-value is therefore the same when the same test and data are used. A claim such as “the coefficient is positive” is incomplete unless it names the counted allele.
Worked Example: Translating Results Across Allele Codings
Two hypothetical association outputs describe the same biallelic variant: REF = G and ALT = A. Output 1 counts A and reports \(\hat{\beta}_A=0.12\), \(SE=0.04\), and effect-allele frequency \(0.25\). Output 2 counts G. Translate Output 1's coefficient and frequency to G coding, and check the reported Output 2 values of \(-0.12\), \(0.04\), and \(0.75\).
Because the genotypes are diploid and biallelic, \(D_G=2-D_A\). The G-coded coefficient is \(-0.12\) trait units per G copy, and its standard error remains \(0.04\) trait units per copy. The corresponding G frequency is \(1-0.25=0.75\). All three translated values agree with Output 2.
A two-sided statistic based on estimate divided by standard error has magnitude \(0.12/0.04=3\) for either output. If the outputs instead reported different two-sided p-values, allele recoding alone would not explain the discrepancy; one should check whether the samples, model, phenotype, variant representation, or test procedure also differed.
Checking Allele Alignment and Avoiding Misinterpretation
When comparing GWAS results, record at least the variant identifier, genome build, REF, ALT, effect allele, other allele, effect estimate, and the meaning of any reported frequency field. Do not infer effect-allele coding from the column name alone: software conventions differ, and labels such as A1 are not universal. Confirm the documentation or inspect the dosage definition.
Several checks are especially useful:
- Check allele pairs. Confirm that both results refer to the same alleles and variant representation before comparing coefficient signs.
- Check the counted allele. If one result counts ALT and another counts REF, negate the coefficient when translating between them and retain the standard error.
- Check frequency orientation. Under a diploid biallelic convention, effect-allele frequencies for opposite alleles should sum to 1, subject to rounding and matching samples.
- Check strand alignment. Alleles reported on opposite DNA strands may appear as complementary bases (A and T, or C and G). For A/T and C/G pairs, allele labels alone may not reveal orientation; these are often called palindromic allele pairs. Frequency information may help, but can be inconclusive when frequencies are near 0.5.
A common error is to interpret “positive beta” as evidence that the alternate allele increases the trait. That conclusion is not justified unless the alternate allele is the counted effect allele. If the output counts the reference allele, a positive coefficient refers to increasing reference-allele dosage instead. Another error is to assume the minor allele must be the effect allele. Minor-allele status depends on the sample frequency; it does not determine either the reference allele or the output's coding.
The sign-reversal identity also has limits. The simple complement \(D^*=2-D\) assumes diploid genotypes at a biallelic site. It does not directly apply to a multiallelic variant represented with several alternate alleles, or to data with different ploidy unless dosage is defined and transformed using the relevant total copy number. Missingness, different samples, different covariates, or different models can also make two reported results differ for reasons beyond allele coding.
Check Your Understanding
Answer each question, then check the solutions below.
- A variant record has REF = C and ALT = T. An output counts C. Which allele is the effect allele, and which is the alternate allele?
- An estimate is \(0.30\) with standard error \(0.10\) for allele A. What are the estimate and standard error when dosage is recoded to the other allele?
- An effect-allele frequency is \(0.18\) at a diploid biallelic variant. What is the frequency of the other allele under the same sample and frequency convention?
- Why can two outputs report opposite coefficient signs but the same two-sided p-value?
- Does a positive coefficient show that the effect allele causes a trait to increase? Explain.
Solutions. 1. C is the effect allele because the output counts C; T is the alternate allele. 2. The recoded estimate is \(-0.30\), and the standard error remains \(0.10\). 3. The other allele's frequency is \(1-0.18=0.82\). 4. If the outputs count opposite alleles, their dosages satisfy \(D^*=2-D\), so the coefficient changes sign but its magnitude and standard error stay the same; the two-sided test is therefore unchanged. 5. No. A positive coefficient describes an association in the chosen coding and does not by itself establish causation.