Two-Stage Screening For Genome-Wide Interaction Searches

Why Screen a Genome-Wide Interaction Search?

With \(p\) variants, an exhaustive search of distinct pairs involves \(p(p-1)/2\) tests. Even a modest number of variants can therefore create a very large computational burden. Two-stage strategies reduce the number of expensive interaction models that must be fitted, or separate candidate discovery from confirmatory testing. Their advantage comes with a trade-off: if the screening step discards a true interaction pair, later testing cannot recover it.

The key distinction is what gets screened. Marginal-effect screening first selects individual variants using their single-variant associations. Marginal-pair screening ranks or filters pairs using a relatively inexpensive pair-level interaction statistic, before fitting more complete models to a shortlist. Independent validation tests a discovery-selected shortlist in data that played no part in selecting it. These approaches can be combined, but they address different parts of the search problem.

What Is Being Tested?

For a quantitative trait, a common model for a specified pair \(A,B\) is

Here \(X_A\) and \(X_B\) are the chosen genotype codings, \(\mathbf{C}\) contains prespecified covariates, and \(\beta_{AB}\) is the product-term effect under this coding and model. An interaction test asks whether the pair contributes an interaction beyond the included main effects and covariates; for this one-degree-of-freedom example, the null hypothesis is \(H_0:\beta_{AB}=0\). Other genotype codings can require several interaction terms and a joint test. For a binary trait, the same idea can be expressed in a model with an appropriate link function.

The model and its coding define the interaction being tested. A cheap screen need not be identical to the final model, but differences in coding, covariate adjustment, trait scale, or sample can change what it detects. A screen is therefore a way to prioritize candidates, not a substitute for specifying the final estimand and test.

Marginal-Effect Screening: Cheap, but Not Interaction-Neutral

In marginal-effect screening, each variant is assessed separately for association with the trait, without first testing its interactions with all other variants. Investigators might retain variants passing a chosen single-variant threshold, or retain a fixed number of top-ranked variants, and then test all pairs among those retained. The final pair models should still include both locus main effects, whether or not either locus passed the marginal screen.

This strategy can greatly reduce the pair count when interaction partners also have detectable single-variant effects. But an interaction does not require a marginal effect. A variant can have no average association across the other locus’s genotypes even when the joint genotype means differ strongly. Marginal screening can therefore discard one or both members of a true interaction pair before the pair is ever formed.

Marginal-Pair Screening: Screen the Pair, Not Just Its Members

A pair-level screen calculates a low-cost statistic for candidate pairs and uses it to prioritize pairs for fuller analysis. For example, a screen might use an unadjusted product-term score or a two-locus genotype-table contrast. A pair can rank highly even if neither variant ranks highly in a single-variant screen. This makes pair-level screening better aligned with the target signal than variant-level screening when the signal is primarily interactive.

The word “marginal” matters: the screening calculation may omit covariate adjustment or use a simplified model, whereas the final interaction test may adjust for covariates and use the prespecified genotype model. If there are \(p(p-1)/2\) pairs, calculating even a cheap statistic for all pairs still requires visiting that many pairs. Pair screening can reduce the number of expensive model fits, but it may not remove the cost of generating and scoring all pairs. In practice, its value depends on whether the screen is substantially cheaper than the final analysis and whether its ranking is useful.

Pair-level screens can still miss interactions. Sparse genotype cells make cell means or contrasts unstable; a screen based on one coding may fail to capture an effect represented by another coding; and covariate adjustment or linkage disequilibrium may alter the evidence seen in a simplified analysis. A threshold also creates a direct sensitivity–burden trade-off: a stringent screen advances fewer pairs but risks discarding weaker true signals. A permissive screen retains more signals but leaves more full tests to perform.

Independent Validation: Separate Selection From Confirmation

A shortlist selected using one data set can be tested in a separate validation sample. Because the validation outcomes and genotypes did not determine which pairs were selected, the validation tests are not made significant merely by selecting pairs with promising discovery results. This separation is especially useful when a screening statistic and the final test use the same discovery data: the discovery results prioritize candidates, while the validation data provide the confirmatory evidence.

Validation does not mean testing one selected pair without accounting for the number of pairs on the shortlist. If \(K\) pairs are tested and family-wise error control at level \(\alpha\) is desired, a simple Bonferroni rule compares each validation \(p\)-value with \(\alpha/K\). Provided the validation \(p\)-values are valid under their null hypotheses, this controls the probability of one or more false rejections among the \(K\) tested pairs at no more than \(\alpha\). The validation analysis should prespecify the pair coding, model, outcome, and testing rule; changing these after examining validation results weakens the confirmatory interpretation.

Choosing and Combining the Strategies

A practical design should match the screening step to the kind of signal the study aims to detect. Marginal-effect screening is attractive when it is important to shrink the variant set quickly and there is reason to expect interaction partners also to have detectable marginal associations. It is a poor sole filter when interactions with little or no marginal association are plausible. A pair-level screen targets joint evidence more directly, but its computational cost, coding, covariate omissions, and ranking performance need consideration. Independent validation provides a stronger basis for confirmation, at the cost of requiring a separate sample with adequate information for the selected pairs.

The methods can also be staged: a permissive variant screen can form a manageable set; a cheap pair screen can prioritize pairs within it; and a separate validation cohort can test a prespecified shortlist. Each filter creates an opportunity to lose true signals. The final validation family must include the pairs actually tested, and error control should reflect that family. For discovery-only scans that do not have independent validation, screening and testing on the same data require an analysis that accounts for selection or otherwise provides valid multiple-testing control; a nominal final-stage threshold is not automatically valid just because fewer pairs remain.

Common Mistake and Key Takeaway

Wrong reasoning: “Neither variant was associated with the trait on its own, so their interaction cannot matter.” This assumes that a joint effect must produce an average single-variant effect. The balanced example above shows that this is false: effects across the partner’s genotypes can cancel in the marginal comparison while the joint pattern remains pronounced.

Correction: A marginal screen is a prioritization rule, not a test of whether interactions exist. State what signals it may exclude, and do not interpret a screened-out pair as evidence of no interaction. Pair-level screens may align better with interaction signals, while independent validation helps separate candidate selection from confirmation; neither removes the need for a suitable model and multiplicity control.