# Assessing Orthogonality in Gene-Environment Interaction Studies Using Polygenic Indices

## TL;DR

This study examines how genetic and environmental factors interact, and proposes a new method to ensure they are not biased by shared influences.

## Contribution

The paper introduces a new test using bivariate GREML to assess genetic correlation in gene-environment interaction studies.

## Key findings

- The proposed test complements correlation-based methods to better assess orthogonality in G×E studies.
- Empirical results show gender failed the correlation-based test but passed the new genetic correlation test.
- Birth district social class and genetic propensity for education appear genetically linked.

## Abstract

Gene-environment interaction (G×E) studies analyze how environmental conditions cushion or exacerbate differences in genetic endowments. A gene-environment correlation (rGE) between the polygenic index (PGI) and the environmental condition employed in these G×E studies could bias the estimation of the interaction effect. In this brief report, we discuss the limitations of the commonplace correlation-based test used to verify the orthogonality of the PGI and the environment, and propose to complement it with an additional assessment of the genetic correlation between the phenotype corresponding to the PGI of interest and the environmental condition in the G×E analysis sample using bivariate GREML. Our proposed test is straightforward to perform with the data typically available to G×E researchers, and bypasses that the PGI reflects the environmental conditions of the training sample used to calibrate it. Using UK Biobank data, we provide empirical illustrations covering three environmental conditions relevant for educational attainment. We confirm the orthogonality of the Raising of School Leave Age 1972 educational reform and of gender, although gender did not pass the correlation-based test. However, birth district social class and the genetic propensity for educational attainment appear to be intrinsically intertwined.

The online version contains supplementary material available at 10.1007/s10519-025-10248-8.