Choosing GWAS Phenotypes and Estimands

Why the Phenotype and Estimand Must Be Chosen Together

A genome-wide association study (GWAS) does not estimate a genetic effect in the abstract. It estimates an association between genetic variation and a specified outcome, on a specified scale, in a specified population. For example, a study of a continuous biomarker asks a different question from one that classifies the same biomarker as above or below a clinical threshold. Neither result is automatically the answer to the other question.

The phenotype definition should represent the scientific outcome of interest: what is measured or classified, on what scale, and, when relevant, over what time window. The estimand states precisely which population quantity is targeted. Choosing both before analysis makes the eventual effect estimate interpretable and helps prevent results from being described more broadly than the analysis supports.

Let \(Y\) denote the phenotype and \(G\) the genotype at a variant, coded as the number of copies of a designated effect allele: \(G=0,1,2\). For imputed data, \(G\) may instead be an allele-dosage value between 0 and 2. The phrase per-allele effect usually refers to the change associated with one additional copy under a model that treats the effect as additive across these dosage values. The allele designated as the effect allele must be stated: changing the allele coding reverses the direction of a signed effect.

Quantitative Phenotypes: Define the Scale and Per-Allele Contrast

For a quantitative phenotype, a common association model is a linear regression of the outcome on allele dosage and prespecified covariates \(C\):

Here, \(\beta_G\) is the conditional mean difference in \(Y\) associated with one additional effect-allele copy, holding the included covariates fixed. Its units are the units of \(Y\) per allele copy. This interpretation relies on the model's additive dosage specification and linear conditional mean relationship. The regression coefficient describes an association; by itself it does not establish that changing the genotype would cause the outcome to change.

The phenotype scale matters. A coefficient for a concentration measured in milligrams per litre is not numerically interchangeable with one for the logarithm of that concentration or a standardized score. A transformed outcome changes the estimand and its interpretation. Likewise, if the scientific question concerns whether a clinical threshold has been crossed, a continuous-trait coefficient does not directly answer that question.

Binary Phenotypes: State the Effect Measure

A binary phenotype takes values such as 0 and 1, with the meaning of each value defined explicitly. For a disease outcome, \(Y=1\) might mean that a participant meets a stated disease definition by a specified time, while \(Y=0\) means they do not. A widely used model is logistic regression:

Under this model, \(\exp(\beta_G)\) is the conditional odds ratio for one additional effect-allele copy, holding \(C\) fixed. It is a ratio of odds, not a ratio of probabilities. The per-allele interpretation also uses the additive dosage assumption on the log-odds scale. It does not imply equal changes in absolute risk for each allele copy.

A binary-trait question can instead target probabilities or their difference. One possible target is a standardized risk: for each genotype value, average the model-predicted risks over a stated covariate distribution in the target population. The difference between two such standardized risks is a population-averaged risk difference. It is a different estimand from the conditional odds ratio, and its value depends on the population over which risks are averaged.

Standardizing Risks Over a Target Population

A standardized contrast makes explicit which covariate distribution the result refers to. For example, a study may want risks averaged over a target population containing both lower- and higher-risk covariate strata. The model provides a predicted risk for each genotype and stratum; averaging those predictions with the target population's stratum weights gives the standardized risk. This does not remove the need to define the binary outcome or target population, and it does not turn an association into a causal effect.

Match the Phenotype Definition to the Scientific Question

A useful phenotype definition answers a concrete question rather than merely naming a data column. For a quantitative trait, specify the measured quantity and units, whether it is analyzed on its original or transformed scale, and which value or summary represents the participant. For a binary trait, define what qualifies as a case, what qualifies as a non-case, and the relevant time horizon. If the question concerns a clinical condition, a threshold or diagnostic definition may be more relevant than the underlying continuous measurement. If the question concerns variation in the measurement itself, dichotomizing it may discard distinctions that matter.

These choices can change the scientific interpretation even when the genotypes and participants are unchanged. A thresholded phenotype asks about the probability of meeting that threshold, not about the average level of the original trait. A different time window or case definition can target a different outcome. The phenotype should therefore be fixed in a way that reflects the intended scientific question, with its coding and units stated so the effect can be read correctly.

Also make the target population explicit. A genetic association estimate is an average or model parameter for the population represented by the analysis and its chosen covariate distribution. If the intended use concerns a different population, the estimated effect need not transfer unchanged. Defining that target is part of defining the estimand, not an optional qualification added after results are known.

Common Mistakes and Why the Distinction Matters

• Treating an odds ratio as a risk ratio. The reasoning “an odds ratio of 1.5 means 50% higher probability” is generally wrong. It means 50% higher odds under the stated contrast and model; the corresponding risk change depends on baseline risk.
• Calling every regression coefficient a causal genetic effect. A coefficient from an association model describes the specified statistical relationship. A causal claim requires additional assumptions and a causal estimand; it does not follow from the coefficient alone.
• Leaving the phenotype definition implicit. “Disease status” is not sufficiently precise if the case definition or time horizon is unclear. State what \(Y=1\) and \(Y=0\) mean.
• Changing the outcome scale without changing the interpretation. A coefficient for a transformed or standardized outcome is not in the original outcome units. Name the scale used and interpret the estimate on that scale.
• Assuming a per-allele model answers every genetic contrast. The additive dosage model summarizes a linear trend in the specified model scale. If the scientific question concerns a particular genotype comparison or a non-additive pattern, that is a different contrast and should be stated explicitly.

These distinctions matter because a result is useful only when its estimand matches the question readers think it answers. Clear definitions also make it possible to compare studies responsibly: two reported effects may differ because their populations, phenotype definitions, or effect scales differ, even if both studies analyzed the same variant.