Relative Genetic Effects and Absolute Risk

Why a Relative Genetic Effect Is Not Yet an Individual Risk

A polygenic score can describe how disease risk changes with genetic score, but a relative change is not itself a probability. Saying that a score is associated with “twice the risk” does not tell a person whether the relevant probability is 2%, 20%, or 80%. To obtain an absolute risk, the relative effect must be paired with a reference risk defined for the same disease, population, predictor profile, and time horizon.

This tutorial uses a risk-ratio model to make that translation precise. It concerns risk over a fixed interval, such as the next ten years, and does not convert odds ratios or hazard ratios into risk. The genetic effect is an association from a fitted or validated model; by itself, it does not show that changing a person’s score would cause their risk to change.

The horizon is part of the definition, not a detail to omit. A 5-year risk and a 20-year risk are different quantities, even when they describe the same person and disease. The reference must also be explicit. Here, the reference profile has score \(s=0\), with the other predictors held at the values used for the individual under consideration. Thus \(r_{H,0}\) denotes that reference risk; it is not automatically the disease prevalence in the population.

A Risk-Ratio Model for a Polygenic Score

Let \(S\) be a polygenic score on a specified scale. A simple model assumes that the log of the risk ratio relative to score zero is linear in the score:

Here, \(r_H(s)\) is the risk by horizon \(H\) for score value \(s\), and \(r_{H,0}\) is the risk for the reference score, with the relevant non-score predictors held fixed. The coefficient \(\beta\) is the change in log relative risk per one score unit. If the score is standardized, one unit may be one standard deviation, but that is true only if the model’s score scale is defined that way.

Solving the model for the risk gives the conversion:

This multiplication is justified only when the supplied effect is a risk ratio for the same disease outcome and time horizon, and when the reference risk corresponds to the same population and other predictor values. The model also assumes the log relative risk changes linearly with the score over the range where it is used. The resulting value must be between 0 and 1. If it is not, the conversion is incompatible with a probability and should not be repaired merely by truncating it at 1.

Deriving the Conversion and Checking Its Meaning

The conversion follows directly from the definition of a risk ratio. For the score value \(s\), the risk ratio relative to score zero is \(r_H(s)/r_{H,0}\). Under the log-linear model, its logarithm is \(\beta s\). Exponentiating both sides gives the ratio, and multiplying by the reference risk gives the risk for score \(s\):

This also clarifies how a reported effect “per score unit” is used. If the relative risk per one unit is \(q\), then \(\beta=\log(q)\), and a person \(s\) units above the reference has relative risk \(q^s\), provided the log-linear assumption holds. A score below the reference has \(s<0\), so its relative risk is below 1 when \(q>1\). The score unit, centering point, and direction must match the effect estimate; otherwise even correct arithmetic gives the wrong interpretation.

The model yields a conditional, model-based probability for the specified profile. It is not a guarantee about an individual outcome, and it should not be described as the probability that the genetic association is causal. A prediction is useful only to the extent that its reference risk and relative effect apply to the intended setting.

Score Position, Reference Risk, and Absolute Difference

A relative effect applies multiplicatively, so its absolute impact depends on the reference risk. The same relative risk can correspond to very different percentage-point differences in settings with different reference risks. This is why a score’s relative association alone cannot communicate an individual’s probability or the size of an absolute risk difference.

Centering the score matters for interpretation. If \(Z=0\) is the mean score in a particular reference group, then the reference risk is the risk at that score and at the specified values of other predictors. It is not necessarily the average risk among people in that group: average risk can differ from risk at the average score when the risk relationship is nonlinear or other predictors vary. A score standardized in one population may also have a different scale in another population, so the effect estimate and the score values must use compatible definitions.

Validity Checks and Common Pitfalls

Before reporting an absolute risk obtained from a score effect, check the inputs and the result. These checks are part of the interpretation, not optional presentation details.

• Match the horizon. A relative effect estimated for one follow-up period cannot automatically be combined with a reference risk for another period.
• Match the effect measure. The multiplication above uses a risk ratio. An odds ratio or hazard ratio is not interchangeable with a risk ratio; using it as though it were one can produce a miscalculated probability.
• Match the reference profile. The reference risk must concern the same disease outcome and relevant population and predictor profile. A general population frequency is not automatically the right conditional reference risk.
• Use compatible score units. A coefficient per standard deviation cannot be applied directly to a raw score difference unless that difference is first expressed in standard-deviation units for the score definition used by the model.
• Check the probability range and model range. A calculated risk must be between 0 and 1, and the score should lie within a range where the model’s relative effect is credible.
• Do not turn association into causation. A genetic score can be predictive or associated with risk without proving that the score itself causes the change in disease probability.

A second mistake is to treat an invalid product as a usable probability. For example, a reference risk of 30% combined with a relative risk of 4 gives \(0.30\times4=1.20\), or 120%. A probability cannot exceed 100%. This signals that the relative effect and reference risk are not jointly valid under this simple model for that profile, perhaps because the model is being extrapolated too far. Replacing 120% with 100% would conceal rather than solve the incompatibility.

Why the Translation Matters

Absolute risk places a genetic effect on a scale that can be understood for an individual and a stated interval. It supports clear communication: “an estimated 4.5% risk over ten years under this model” is more directly interpretable than “2.25 times the reference risk.” Yet the probability is only as credible as its reference risk, effect estimate, score definition, and modeling assumptions. A relative genetic effect is one component of an individual risk estimate, not a complete risk model by itself.