Phenotype Definitions and the Meaning of GWAS Weights

Why Phenotype Definition Matters for a Score

A GWAS weight is not a universal measure of how much a variant “matters.” It is an estimated association with a particular phenotype, defined and measured in a particular way, under a particular model. A weight for height measured in centimetres, a weight for log-transformed biomarker concentration, and a weight for disease odds each have different meanings and scales. Using a weight in a polygenic score carries that meaning into the score.

This matters even when the same variants and allele coding are used. Changing the phenotype’s units rescales a quantitative coefficient; transforming the phenotype changes the scale being modeled; defining cases more narrowly can change which individuals count as affected. For a constructed score to be interpretable, its weights must be understood in relation to the phenotype that produced them.

Quantitative Phenotypes: Coefficients Have Units

For a quantitative phenotype \(Y\), a basic association model is a linear regression of the phenotype on allele dosage and relevant covariates \(C\):

Here, \(\beta\) is the difference in the modelled mean \(Y\) associated with one additional allele copy, conditional on the included covariates. Its units are the units of \(Y\) per allele copy. This interpretation relies on an appropriate linear conditional-mean model, suitable handling of covariates, and a sampling and analysis procedure that supports the intended inference. The coefficient describes an association; it does not by itself establish a causal effect.

A change of measurement units changes the numerical coefficient without changing the underlying physical association. If height is recorded in metres rather than centimetres, a coefficient of 0.4 cm per allele becomes 0.004 m per allele. Standardizing a phenotype also changes its scale: if \(Z=(Y-\bar{x})/s\), where \(s\) is the standard deviation used for scaling, then the corresponding coefficient is expressed in standard-deviation units rather than the original measurement units.

Transformed Phenotypes Change the Effect Scale

A phenotype may be transformed because its distribution is skewed, because proportional rather than additive differences are scientifically useful, or because a particular analysis uses a transformed outcome. The resulting coefficient refers to the transformed outcome. It should not be presented as though it were a coefficient in the original measurement units.

For example, suppose the natural logarithm of a positive phenotype is modeled linearly:

A one-copy increase in \(G\) is associated with a difference of \(\beta\) in the conditional mean of \(\log(Y)\). Exponentiating that difference gives a multiplicative factor of \(\exp(\beta)\) for the conditional geometric mean of \(Y\). The corresponding percentage difference on that geometric-mean scale is \(100\{\exp(\beta)-1\}\%\). This statement concerns geometric means under the model, not a fixed percentage change in every individual’s value or necessarily the arithmetic mean.

Other transformations require their own interpretations. For example, an inverse-normal rank transformation maps observations to a normal-score scale; a coefficient on that scale is not directly a change in the original trait’s units. Such a coefficient can be useful for association analysis, but the transformation and its reference data-processing choices should be reported when the weight is interpreted or reused.

Binary Phenotypes and Case-Control Sampling

A common model for a binary phenotype \(Y\), coded 1 for cases and 0 for controls, is logistic regression:

In this model, \(\beta\) is a change in log odds per allele copy, conditional on the covariates. Exponentiating it gives the odds ratio \(\exp(\beta)\) per allele copy. An odds ratio is not a risk difference or a risk ratio. In particular, a case-control sample generally has a case fraction set by the study’s sampling design, so its observed case fraction should not be read as the disease prevalence in the source population.

Under standard conditions, outcome-based case-control sampling changes the logistic intercept but not the genotype slope. The essential conditions are that cases and controls are sampled at rates that depend on case status, not additionally on genotype within outcome groups, and that the logistic model is appropriate. The implication for the slope can be seen directly. Let \(s_1\) and \(s_0\) be the sampling probabilities for cases and controls. Then, at a given genotype and covariate value, the odds among sampled participants are the population odds multiplied by \(s_1/s_0\):

Taking logarithms adds the constant \(\log(s_1/s_0)\) to the population log odds. It shifts the intercept, while leaving the coefficient of \(G\) unchanged. This result does not mean that the sample intercept estimates population disease risk, nor does it automatically convert an odds ratio to an effect on a liability or absolute-risk scale.

Trait Definitions Are Part of the Weight

“Disease status” is not always a single, self-evident phenotype. A GWAS might define a case using a diagnostic code, a clinical measurement threshold, self-report, or a combination of criteria. The eligible age range, follow-up period, control definition, and handling of uncertain diagnoses can also differ. These choices determine which outcomes are analyzed and therefore which association the estimated weight describes.

Changing a threshold for a quantitative measurement to create a binary case definition changes the phenotype from a continuous value to a particular classification. A weight for that binary outcome describes the association with the odds of crossing that threshold, not the original measurement in its units. Differences between two GWAS estimates can therefore reflect different trait definitions, sampling, covariate adjustment, or analysis scales, rather than a simple disagreement about one invariant genetic effect.

Reading and Reporting Weights Carefully

Before interpreting a weight or a score built from weights, identify the phenotype, its coding, its units or transformation, and the association model. Also establish which allele is counted and whether the coefficient is per allele copy. These details are needed to distinguish a positive association with higher quantitative values from a positive association with case status, and to understand whether the coefficient is in original units, standard deviations, log units, or log odds.

• For a quantitative trait: report the coefficient per allele copy in the phenotype’s units, or state clearly that it is standardized or transformed.
• For a log-transformed trait: distinguish the log-scale coefficient from the exponentiated multiplicative interpretation.
• For a binary trait: state the case and control definitions and interpret \(\exp(\beta)\) as an odds ratio, not as an absolute risk change.
• For a score: describe the phenotype and weight scale from which the weights were obtained. The sum \(\sum_j\beta_jG_{ij}\) inherits that context; it is not automatically a clinical unit or an individual’s probability of disease.

A frequent mistake is to treat a GWAS weight as an intrinsic, scale-free effect of a variant and compare its numerical size directly across studies. The correction is to first align the allele coding and then compare the phenotype definitions, transformations, units, models, and sampling conditions. A coefficient of \(0.2\) in centimetres, \(0.2\) in standard deviations, and \(0.2\) in log odds are not interchangeable quantities.