Predictive Validity Is Not Causal Evidence

Why Prediction and Causation Are Different Questions

A polygenic score can forecast a phenotype accurately in a particular population and still fail to identify a causal genetic effect. Prediction asks whether observed information helps estimate an outcome for people drawn from a specified population. Causal inference asks what would happen to the outcome under a defined change in a causal factor, under assumptions that make that comparison interpretable. These questions can have different answers even when they involve the same score and phenotype.

This distinction matters in statistical genetics because a score may track more than the genetic effects researchers hope to summarize. It can also track ancestry, family circumstances, or patterns of study participation. Any of these features may help forecast the phenotype in an evaluation sample. High predictive performance alone does not separate those explanations or establish that changing the score-associated genetic variation would change the outcome.

For example, a score may be useful for forecasting a quantitative trait in the population where it was evaluated, while its association with the trait is partly due to population structure. Earlier material on population structure as predictive signal contamination distinguishes genetic signal from ancestry-related prediction. Here the emphasis is on the broader inference: even a score that predicts well does not tell us which causal process generated that predictive signal.

Prediction From a Score: What the Regression Slope Says

Let \(S\) denote a polygenic score and \(Y\) a quantitative phenotype, measured in a defined population. A simple population linear prediction rule has the form \(a+bS\). Its least-squares slope describes the best linear predictive association between score and phenotype in that population. It is not automatically the causal effect of changing the score, much less the causal effect of any particular allele.

The conditions for the standard slope formula matter. Suppose \(E[Y^2]<\infty\), \(E[S^2]<\infty\), and \(0<\operatorname{Var}(S)<\infty\). These conditions ensure that means, variances, and covariances exist and that the squared prediction error has finite expectation. The slope and intercept minimizing \(E[(Y-a-bS)^2]\) are then:

The slope has units of phenotype per score unit. It summarizes how the best linear prediction changes with observed score. It does not determine whether the score itself has a causal effect: the covariance in the numerator can arise through multiple causal and noncausal pathways.

Why the Least-Squares Formula Holds

A brief derivation clarifies both the interpretation and the needed assumptions. Define the population prediction risk \(R(a,b)=E[(Y-a-bS)^2]\). Under the finite-second-moment conditions above, this risk is finite for finite \(a\) and \(b\). For any fixed \(b\), the risk is minimized over \(a\) when the average residual is zero:

Substitute this intercept into the residual. The prediction error becomes \((Y-E[Y])-b(S-E[S])\). Expanding its expected square gives:

Because \(\operatorname{Var}(S)>0\), this quadratic has positive curvature. Differentiating and setting the derivative to zero gives \(-2\operatorname{Cov}(S,Y)+2b\operatorname{Var}(S)=0\), which yields the stated slope. The finite-moment conditions are not decorative: without them, expectations, covariance, or prediction risk might not exist, and this derivation would not be justified.

Prediction Can Track Family and Environmental Factors

An observed genetic score may be correlated with family-level conditions even when the score has no causal effect on the phenotype under study. Inherited genetic variation and family circumstances can be statistically related through population structure, assortative mating, or other social and familial processes. If family circumstances also predict the phenotype, a score can carry useful predictive information about them.

A predictive association under these conditions is not meaningless: it may genuinely improve forecasts for a target population that shares the same relationships. The limitation is interpretive. That performance does not reveal how much is due to causal genetic effects, how much is due to correlated environments, or whether the same prediction will transfer to a population with different family and social patterns. Within-family benchmarks can provide a different comparison, but a between-person prediction result alone does not substitute for that analysis.

Selection Can Change the Association Being Predicted

Predictive performance is specific not only to a population, but also to how that population was observed. If inclusion in a study depends on variables related to both score and phenotype, conditioning on participation can create or alter an association. A score may then predict within the selected sample even when it has no predictive association in the source population. Conversely, selected-sample prediction may fail to describe the target population.

This possibility is related to cohort participation as a collider and to selective ascertainment. The key point here is not a particular correction method. It is that a predictive association measured after selection does not, by itself, identify the causal process that produced it. A study’s participation mechanism and the intended target population must be considered before interpreting its predictive results.

What Prediction Can and Cannot Establish

A properly evaluated score can establish that it helps predict a specified phenotype in a specified target population, using a stated performance measure and evaluation design. It can also motivate further work on transportability or causal mechanisms. But an association, an \(R^2\), or a reduction in prediction error does not by itself show that the score is a causal exposure, that its variants act through a particular biological mechanism, or that a score effect would persist under a change in population or environment.

A causal claim needs a defined causal contrast and a design or model whose assumptions support identifying it. For genetic questions, relevant concerns include population structure, relatedness and family context, selection, and the interpretation of the genetic variation represented by a score. Evidence that addresses one concern does not automatically resolve the others. In particular, an accurate prediction in an unrelated-person sample is not equivalent to a within-family causal comparison.

This tutorial is not defining gene–environment effect modification. The narrower point is that predictive performance and causal interpretation answer distinct questions, even when prediction varies across populations or settings. Such variation can reflect changes in predictor–outcome relationships without, by itself, specifying a causal interaction.

Common Mistake

Wrong reasoning: “The score predicts the phenotype well in an independent evaluation sample, so the score’s genetic effects must be causal.” Out-of-sample evaluation can show that a predictive relationship generalizes to the evaluation population; it does not rule out ancestry-related signal, correlated family or environmental factors, or selection.

Correction: State the prediction target and the evidence the evaluation provides. Then separately ask what causal contrast is being claimed and whether the study supports it. Treat predictive performance as evidence of forecast utility in its target setting—not as a stand-alone causal estimate.